THE YOUNG MAN'S NEST COMPANION, OR MATHEMATICAL COMPENDUIM, Containing a great variety of very useful RULES AND EXAMPLES IN MATHEMATICS FOR THE Merchant, Clerk, Accountant and the Mechanic, Worked out so as to be QUICKLY UNDERSTOOD BY ANY ONE WHO UNDERSTANDS THE FOUR FUNDAMENTAL RULES OF ARITHMETIC BY AMOS W. WA;RREN. RUTLAND: TUTTLE & CO., PRINTERS, 1872. PREFACE. It has been said by one wiser than we, "' ispise not the day of small things." The want of a book like the Young Man's Best Companion, in which the principles of mathematics are clearly demonstrated, has long been felt. Others of a larger size for schools and academies have been multiplied. The young man will herein find a great variety of very useful rules and examples worked out so as to be easily understood; suited to ordinary business so that but-little time is required to refresh the mind with the desired information, for an author says "if they do not daily practice the majority of people forget." Let the young man, the clerk, merchant, accountant, mechanic, or the proprietor of the warehouse, have this readily at hand, aund he is proof against any mistake incident to forgetfulness or any other cause. This is the great secret of its peculiar adaptation to the business man. And the author hereby hopes that the public will realize in this little book what has so long been sought elsewhere in vain. CONTENTS. V; CONTENTS. Percentage,. 1 Insurance,...... 10 Stocks,... 13 Loss and Gain,... 17 To Find the First Cost,. 26 Partnership,.... 27 Commission and Brokerage, 35 Commission Deducted in Advance,. 40 Simple Interest,. 42 Discount by Compound Interest.. 50 To Find the Principal from the Interest and Rate Per Cent,..... 51 Compound Interest Table,.... 53 Semi-Compound Interest Table,.... 54 Partial Payments,.. 55 Banking,........ 57 Equation of Payments, 2. Average,........ 66 Domestic Exchange,... 68 Exchange with England, 74 Exchange with France,.... 78 Discount on Bills and Invoices,. 79 Wood -per Cord, ~..... 83 Custom House Business,.... 85 iv. CONTENTS. Federal Money,. 90 Assessment of Taxes,... 91 Assessment of Taxes to Raise a Given Net Amount, 97 Simple Proportion,..... 97 Compound Proportion,.. 100 Boards,..... 102 Plank,..... 104 Joists,..... 105 Scantlings,. 105 Timber,..... 106 Carpeting Rooms,..... 109 Plastering Rooms,...... 110 Painting Rooms,..... 111 Papering Rooms,..... 112 Flooring Rooms,..... 113 Lathing Rooms,. 114 Glaziers' Work,...... 115 To Measure Round Timber, 116 Slating Roofs,....... 117 Shingles for a Square,... 119 Perches in Cellar Wall,.... 119 Cubic Yards in Cellar Wall, 120 Boards to Cover a Frame,.. 121 Bricks for Walls of a House,.... 122 Bricks for Flooring Room,.. 123 Bushels in Bin,. 123 Gallons in Barrel,.... 123 Vulgar Fractions,.... 124 Addition of Fractions, 125 To Find the Greatest Common Divisor,.. 128 Subtraction of Fractions.... 129 Multiplication of Fractions,... 130 dONTENTS. sit. Division- of Fractions,... 132 Addition of Decimal Fracrons,... 134 Subtraction of Decimal Fractions,. 136 Multiplication of Decimal Fractions, 137 Division of Decimal Fractions, 137 To Read a Decimal Fraction,. 139 Duodecimals,. 148 Triangles to Find the Third Side,... 146 Circles,... 147 Square Root,..... 148 Cube Root,.... 151 Measurement of Surfaces,. 154 Denominate Numbers,.... 156 Miscellaneous Table,. - 160 Weights of Bushel Produce,.... 161 Numeration Table,......161 Bankruptcy,...... 162 Goods Bought and Sold by the Ton,... 163 Goods Bought and Sold by the Hundred, 165 Goods Bought and Sold by the Thousand,.. 167 Miscellaneous Examples,... 167 PERCENTAGE. The term percentage and per cent. signifies a certain part of a hundred; thus, 4 out of a hundred, is 4 per cent.; 6 out of a hundred, is 6 per cent.; and so on for other rates per cent. When we say 5 per cent of the population of the State of New York, we mean five persons out of every hundred. RULE.-Find the amount by substraction, multiply the gain or loss by 100, and divide the product by the purchase price. Ex. 1. The amount of my capital invested in business is $7,500, and I have sold goods to the amount of $8,400; what per cent is it? 900 100 8400 7500 7500) 90000 900 gain. 12 per cent. Ans. Ex. 2. A hotel cost $350,000; was rented for $24,500 a year. What per cent did it rent for on the cost? 24500 100 Purchase price, 350000) 2450000 7 per cent. Ans. 2 PERCENTAGE. Ex. 3. A merchant received $862.50 dividend on $17,250 stock; what was the rate per cent.? 862.150 100 17250.00) 86250.00 5 per cent. Ans. The $862.50 are hundredths; the dividend and diviser must be of the same denomination; we annex 2 ciphers to 17250 and it becomes 17250 00 hundredths. Ex. 4. A merchant bought calico at 12 cts. per yard, and sold it at 12 1-2 cents per yard; what per cent did he gain? Ans. 4 1-6 per cent. 12.5 —-12 1-2 cts. 100 12. =12 " 5 5 mills 120 mills) 500 mills. 4 1-6 12 cents per yard. 10 " a mill. 120 mills. Ex. 5. A man paid $24.54 insurance on $6544; 375 what was the rate per cent.? Ans. 305 24.54 100 6544.00) 2454.000 (0.375 1963200 4908000 4580800 3272000 3272000 -- signifies equality. PERCENTGE 3 Annex ciphers to the diviser as Ex. 3, to make it of the same denomination as the dividend. We now see that the decimal places in the dividend exceed those in the diviser by 3, counting the ciphers 375 annexed making -- per cent. the ans. See rule in Decimal Fractions. Ex. 6. A bought goods amounting to $550; what per cent profit must he make to gain $66. 66 gain.. 100 Purchase price, 550) 6600 12 per cent. Ans Ex. 7. The Rutland Marble Co. sold Lyman Strong of Cleveland, O., a lot of marble for $300; being a wholesale dealer, 1-6 is discounted from his bill; what per cent. would S. make to sell it at its prime cost, exelusive of freight? 5000 100 25000) 500000 6) 30000 5000 20 per ct. Ans..250.00 purchase 800.00 price. 250.00 50.00 gain. Ex 8. What is 8 per cent of $1567825.46? 1567825.46 8 per cent is written thus,.08 Ans. $125426.03.5 $125426.03,68 There are four decimal places in both factors; we point in the product 4 decimal places; the figures at 4 PERCENTAGE. the left of the point will be dollars, and those at the right will be cents and mills, making one hundred and twenty-five thousand, four hundred and twenty-six dollars, three cents and six mills. Ex. 9. What is 71 per cent of 8875794 bushels of wheat? Ans. 630181374 bus. 1us) 8875794 71 per cent is written thus,.71 8875794 62130558 6301813.74 There are two decimal places in one factor; we point off two decimal places in the product; those at the left will be the whole number of bushels, and those at the right will be fractions of the same. Ex. 10. What is 50 per cent of $875590? Ans. $437795. 1St method. 875590.00 2d method..50 2) 875590 $437795.0000 437795 There are 4 decimals in both factors; we point off 4 decimals in the product; those at the left are dollars. Ex. 11. What is 2 per cent of $350. Ans. $7. 350.00 2 per cent is written thus,.02 $7,00.00 Point off in the product the same as in example No. 1Q. Ex. 12. What is 3 per cent of $145.25. Ans. $4.35. 145.25 3 per cent is written thus,.03 4.35.75 PERCENTAGE. 5 Point off in the product the same as example 8. Ex. 8. What is 1-2 per cent of $180.42? Ans. 90c' 1st method. 2d method. 180.42 2)180.42 1-2 per cent is written thus,.005 ____- _.90.21 In 1st method,.90.210 There are 5 decimal places in both factors; we point off 5 decimal places in the product; those at the right of the point will be cents and mills. Ex. 14. A has a brick block of stores, which cost $16000, consisting of three stores, 4 offices and 3 tenements; what had it ought to rent for to make 10 per cent. Ans. $1600. 16000.00 10 per cent is written thus..10 $1600.0000 Point off in the product the same as Ex. 10. Ex. 15. What is 3-4 per cent of $128.63? Ans..96.4 1st method. $128.63 3-4 per cent is written thus,.0075 64315 90041.96.4.725 There are 6 decimal places in both ftactors; point off 6 decimal places in the product; all at the right of the point will be cents and mills. 2d method. 4.2) 128.63 6431= —1-2 3215=3-4.96.'46 8 PERCENTAGE. Ex. 16. A stockholder owned 10 shares of $100 each of the Hudson Railroad stock; received a dividend of $50 every 6 months; what per cent is it on the money invested? $100 each share. 10 shares, $1000. Recd. $100 a year. 100 1000) 1000( 10 per cent. Ans. Ex. 17. The population of New York in 1850 was 515,647, and in 1860 was 814,277; what per cent was the increase? 814,277 515,647 298,630 100 515,547) 298,630.00 58 per cent., nearly. Ans. Ex. 18. A has 840 bbls. of flour and sold 20 per cent of it; how many bibls. did he sell. Ans. 16$ bbls. 840 20 per cent is written thus,.20 168.00 Point off in the product the same as Ex. 9. Ex. 19. If a fleece of unwashed wool weighs 17 lbs&, PERCENTAGE. 7 8 ozs., the same fleece weighs 7 lbs., 8 1-2 ozs., washed; what per cent of shrink in cleaning? 17-8 16 ozs. lb. 280 120.5 159.5 159.5 100 280)15950.0(56.9 1400 7-8 12 2 16 ozs. lb. 1950 1680 112 8 1-2 2700 2520 120.5 The decimal places in the dividend exceed those in the divisor by one, hence we point off one decimal place in the quotient, making 56 9-10 per cent., the answer. Ex. 20. The following report is the condition of the finances of the liabilities of the town of Rutland, Vermont: Liabilities, - - - - $12,266 53 Resources, - - - - 2,13 13 Balance of liabilities, - - $10,253 40 They estimate the current expenses of the ensuing year as follows: Building the Moulthrop road, - $1,000 Support of the Poor, - 1,300 Other expenses, - 1,700 4,000 Amount to be paid for, - - $14,253 40 g PERCENTAGE. The Grand List of the town is $24,456 28, and the amount to be provided for is $14,253 40; what per cent is required on the Grand List to meet the above tax. 14253.40 100 24456.28)1425340.00(58.28 Ans. 12228140 20252600 19565024 6875760 4891256 198455040 19565024 The decimal places in the dividend exceed those in the divisor by 2, counting the ciphers annexed, hence we point off in the quotient 2 places for hundreths, and those at the left hand will be the whole number of percentage, making 58i-O per cent. PERCENTAGE TABLE. I per cent is written thus, - - -.01 2 i " " - -.02 3 "i " " - - -.03 6 L" " " - -.06 7 " " " - - -.07 10 i" " " -.10 12 "' it - -..12 50 " " L - -.50 100 " " " - - - 1.00 103 " " " - 1.03 125'L " " - - 1.25 PERCENTAGE IN INTEREST. 9 1-2 per ct., that is, 1-2 1 per ct., written thus,.005 1.4 " " 1-4 "," ".0025 3-4 " " 34 " " ".0075 100 100 per cent is 1.00 100 or the whole. 120 per cent is 1.20'20 more than the whole. PERCENTAGE IN INTEREST. To find the rate, per cent., when the principal and the interest and time is given. RULE.-Divide the given interest by the interest of the principal at 1 per cent. for the given time, and the quotient will be the required per cent. Ex. 1. A merchant borrowed $90 for 5 years, and paid $36 for the use of it; what is the rate per cent.? No. 1. Ans. 8 per cent. 90.00 90.01 per cent. 5 years..90.00=90 cts. per 1 year. 4.50 int. of the principal. 4,50)36.00 8 per cent. There are 4 decimals in both factors of No. 1, hence we point off 4 decimals from the product; those at the right of the point will be cents. Ex. 2. A merchant is worth $25,000, at what per cent. must he loan his capital that his income may be just $1,000. 25000.00.01 250)1000 $250.00.00 4 per cent. ans. Point off the same as Ex. 10 in percentage. 10 INSUSANCE. INSURANCE. Insurance is a contract by which one party engages, for a stipulated premium, to make a loss which another may sustain. RULE.-Multiply the sum insured by the given rate per cent., expressed in decimals, and the product will be the premium. The same as interest and discount' Policy is the contract-premium is the tax on the property insured. Ex. 1. A machine shop is insured for 5 years for $6,000; premium note 22 per cent., of which 4 1-2 per cent. was paid down, and 2 1-2 per cent. assessments; what did it cost per year? Ans. $18.48. No. 1. No. 2. 2)1320.00 6000.00.021-2 22 264000 2)1320.0000 66000.04 1.2 33.00.00 52800000 59.4000 6600000 5)92.40.00 59.40.0000 18.48 Point off in Nos. 1 & 2 first products the same as Ex. 10 in percentage, and in 2d product of No. 2, 6 decimals; all at the left are dollars, and those at the right are cents. INSURANCEr 11 Ex. 2. What is the premium on my house valued at $4365, at 1-2 percent.? Ans. $21.82.5. 4365.00 1-2 per cent. is written thus,.005 21.82.500 We point off 5 decimals in the product; all at the left of the point are dollars, those at the right are cents and mills. What is the insurance on $15550 at 1 1-2 per cent.? Ans. 233.25. 15550.00 11-2 per cent. is written thus,.015 233.25 000 Point off in the product the same as Ex. 2. Ex. 4. If a policy be taken out of $6400 at 4 per cent., what net amount is it after paying the insurance? 6400 6400.00 256.04 —-4 per ct. $6144 Ans. $256 00.00 There are four decimals in the two factors; point off in the product the same as Ex. 2, Percentage in Interest. Ex. 5. If the premium is 5 per cent., for what amount must a policy be taken out to cover $8835, together with the premium paid for insurance? 100 per ct. is written thus, 1.00 Ans. $9300. 5 " " ".05 95.' " ".95)8835.00(9300 ~c; c; C 855 X ~a go 285 Q28 00 12 rNS1RANCE. When the decimal places in the divisor exceed those in the dividend, make them equal by annexing ciphers to the right of the dividend, and the quotient will be a whole number. Ex. 6. A woolen factory and contents valued at $64800, and insured at 24-5 per cent., if destroyed by fire, what would be the actual loss of the company? 64800 64800 00 1814.40.028=2 4-5 $62985.60 Ans. 51840000 12960000 $1814.40.000 There are 5 decimals in both factors; point off the same as Ex. 2. Ex. 7. What is the premium on my household furniture valued at $500, premium note 8 percent.; paid 3 per cent. on. premium note, $2.10 for policy and application. Ans. $3.30. 500.00.08 40.0000.03 1.20.0000 2.10 $3.30 There are four decimals in the first two factors, hence we point off in the product the same as Ex. 10 in Percentage. There are 6 decimals in the next two factors; we point off the same as Ex. 1 in No. 2, 2d product. STOCKS. 13 STOCKS. By the term stocks is meant the capital of monied institutions, incorporated banks, manufactories, railroads, insurance companies and State bonds. The original cost of a share is called its nominal or par* value. In most companies $100 is called a share, though in some companies more and in some less, but the market value varies according to circumstances. RULE.-Multiply the par value of the stock by the rate per cent., decimally. Ex. 1. A buys 20 shares of Boston & Worcester R. R. stock at 7 per cent. advance; how much did his stock cost, original shares $100. Ans. $2140. 100 per cent. is written thus, 1.00 7 " " " ".07 107 " " " " 1.07 2000.00;,, 1.07 14000.00 200000 2140.0000 Point off in the product the same as Ex. 10 in Percentage. Ex. 2. What will 20 shares of the same stock amount to at 7 per cent. discount? Ans. $1860. *By par value is meant the original cost or E stimate value of stock. When it is worth more than the original c st it is said to be above par. When it is worth less than the original cost it is said to be below par. 14 STOCKS. 100 per cent. is written thus, 1.00 7 " " " ".07 93' " ".93 2000.00 a.. 93 600000 1800000 1860.0000 Point off in the product the same as Ex. 10. Ex. 3. A merchant employed a broker to buy 55 shares of bank stock, which is 20 per cent. below par, and pays him 3-4 percent. brokerage; how much will his stock cost? 100 per cent. is written thus, 1.00 20' " ",~.20 80 " " " " 80 aW $100.00 a share ~rix 55 shares 5500.00 4.2)5500.80 C3 Q) 2750=1-2 > 4400.0000 1375=3-4 ~c 41.25 4441.25- $an $41.25 and brokerage. 4441.25 ans. Ex. 4. A stock jobber bought 45 shares of the Vt. Central R. R. stock at 3 per cent. discount, which he sold at 7 per cent. advance; how much did he make, the original shares $100. 100 per cent. is written thus, 1.00 3 " " L ".03.97 " " "it.97 cz~ c;" Q 100.00 a~ ~~45 I cot 2 4500.00.97 4365.0000 STOCKS. 15 100 per cent. is written thus, 1.00 7 " " " ".07 1'07 " " " " 1.07 4-a 4500.00 eC a_ X1.07 4815.0000 4365.0000 $450 ans. Point off in the product the same as above. Ex. 5. A cotton factory valued at $12000, is divided into 100 shares; if the profits amount to 15 per cent. yearly, what will be the profits accruing to 25 shares? 100 shares)12000 Ans. $450 $120 a share 120.00 a share 25 sharss 3000.00 15 per cent. is written thus,.15 $450.00.00 There are 2 decimals in one of the factors; we point off 2 decimals in the product; all at the left are dollars. In the 2d product the same as Ex. 10 in Percentage. In the above factory, repairs are to be made which cost $340, what will be the tax on 10 shares? 100 shares)340 $3.40 a share 10 shares $34.00 ans. Ex. 6. A farmer bought 52 shares of the Missisquoi 16 STOCKS. Bank and sold it at 13 per cent. premium; how much did the stock come to? Ans. $5876. 5200.00 am't of shares 113 per cent is written thus, 1.13 $5876.0000 Point off in the product the same as above. Ex. 7. Cornelius Vanderbilt owns 17000 shares of the Hudson River Railroad; what amount has he invested? 17000 shares 100 —-$100 a share $1,700,000 It reads one million, seven hundred thousand dollars, the answer. Ex. 8. If the Rutland & Burlington Railroad declare an annual dividend of 12 per cent., what will a stockholder receive who owns 250 shares? 250 Ans. $3000 100.00 25000.00 12 per cent. is written thus,.12 $300.00.000 Point off in the product in the same manner as above. Ex. 9. If the capital stock of a bank be $600,000, what amount is necessary to declare a dividend of 8 per cent. Ans. $48000 600000.00 8 per cent is written thus,.08 48000.0000 Point off in the product the same as Ex. 10. LOSS AND GAIN. 17 Ex. 10. What is the value of 10 shares in the Rutland Gas Light Co. at 85 per cent.? Ans. $850 100.00 amt. of share 10 1000 00 85 per cent. is written thus,.85 per cent. 850,0000 Point off in the same manner as above. Ex. 11. A bank went into operation with a capital of $100,000, it is divided into 1000 shares of $100 each; at the end of 6 months the profit amounted to $5000; what per cent is it on the capital? what will be the profit on one share? Ans. to the first, 5 per cent. " " last, $5 on a share. 5000 100 100.00 a share 100000)500000.05.05 per cent. $5.00.00 LOSS AND GAIN. Loss and gain is an excellent rule by which merchants discover their profit or loss per cent. It also instructs them to raise or fall the price of their goods so as to gain or lose so much per cent., &c. RULE.-Find the gain or loss, as the case may be, by substraction, then annex two ciphers, or multiply it by 100, and divide it by the first cost, the quotient will be the per cent. 2 18 LOSS AND GAIN. Ex. 1. A bought broadcloth at $4.50 per yard, and sold the same for $5.50 per yard; what was the gain per cent? 5.50 price sold for. 100 4.50 first cost. 100 1.00 450)10000 22 2-9 per cent., ans Ex. 2. Bought broadcloth at $4.00 per yard and sold the same at $3.50 per yard; what was the per cent. lost? 400 350 400)5000 2 ciphers annexed. 50 12 1-2 per cent., ans. Ex. 3. Bought 63 gallons of molasses at 42 cents per gallon, but by accident, 8 gallons leaked out; how shall the remainder be sold, per gallon, to gain upon cost, at the rate of 10 per cent? Ans., 52 cents, 9 mills. 100 per cent. is written thus, 1.00 63 gals. 110 it ".10 42 cts. 110 I'.. 1.1( 63 gals. bought. 26.46 8 " leaked out. 1.10 o 55'" remaining. 55)29.1060(0.52.9.2 275 160 110 506 495 110 110 LOSS AND GAIN. 19 We point off in the first product 2 decimals; those at the left will be dollars; those at the right will be cents, and in the 2d product, the same as Ex. 8 page 3. We now see that the decimal places in the dividend exceed those in the divisor by 4, which we point off in the quotient; those at the right hand will be cents and mills. Ex. 4. Bought 16500 gals. of oil for $8000, allowing 11-2 per cent. leakage; how much must it be sold for to gain 15 per cent.? 100 per cent. is writ ten thus, 1.00 15 " " " ".15 115 " and " " 115 165 0.015=1 1-2 per cent. 247.500 There are 3 decimals in one factor; we point off from the product 3 decimal places; the figures at the left are the whole number of gallons, and those at the right are fractions of the same. 8000 1.15 16500 247 16253)9200.00 -- 16253 gals. remaining. 056.6 Point off from the product or dividend the same as Ex. 3, 1st product, page 18. The decimal places in the dividend exceed those in -the divisor by 3, counting the cipher annexed, hence we point off in the quotient 3 decimals, making 56 cts. 6 mills. Ex. 5. Bought 480 yds. linen at 82 cts. per yard, which shrank in bleaching 1 1-2 per cent.; after keep 20 LOSS AND GAIN, ing it 6 mos. it was sold on 4 mos. credit at 20 per cent. advance on a yard; what was made, allowing 6 per cent. on the money invested? Ans., 98 cts. 4 mills per yard, and made $51.48.2. 100 per cent. is written thus, 1.00 20 " " "i ".20 120 " and "' 1.20 Q) No. 1. No.2. X141 480 yards. 472.32'X ~.82 cents per yard..984 e 393.60 464.76.288 1.20 No. 3. 413.28 PA -- 393.60 ~ 480)472.3200 50 —1-2 the mos. 51.48.2 0.98.40 19.68.8000 393.60 413.28 Point off from the 1st product of No. 1 the same as Ex. 3, 1st product, page 18, and in 2d product or dividend, 4 decimals; those at the left will be dollars, and those at the right will be cents. The decimal places in the product or dividend exceed those in the divisor by 4; hence we point off 4 decimals from the quotient. In the product of No. 2, the same number decimals as Ex. 2, page 11, and in the product of No. 3, according to the rule in Simple Interest. Ex. 6. Bought a house for $4280; at what price must it be sold so as to gain 30 per cent.? 4280.00 130 per cent is written thus, 1.30 5564.0000 LOSS AND GAIN. 21 Point off in the product the same as Ex. 10, in percentage, page 5. Ex. 7. Bought goods for $7500 and retailed them at 15 per cent. profit; how much was the gain? 7500.00 15 per cent. is written thus,.15 1125.0000 Ex. 8. Bought land for $25000 and sold it at 25 per cent. advance; how much was made by the operation? 100 per cent. is written thus, 1.00 25 " " ".25 100 " and " " 1.00 25000.00 1.25 ~ ur~ fi31250.0000 25000 $6250 ans. Ex. 9. Bought land amounting to $110,000, and keeping it 11 years, and sold it at fifty per cent. advance; allowing money to be worth 6 per cent., how much was made? 100 per cent. is written thus, 1.00 50 " I I "i.50 150 " and " " 1.50 on~ ~ 110000.00 1.50 165000.0000 11 years. C> 72600.0000 X,0 ~ 110000 182600 1650000 $17600 ans. 22 LOSS AND GAIN. Point off the last 3 examples the same as Ex. 10 in Percentage, page 4. Ex. 10. A drover bought 46 horses at $85 a piece; 70 cows at $25 a piece; 72 oxen at $28 a piece; what must he sell the whole at, a piece, in order to make $200? 46X85-=3910 70X25=1750 72X28 —2016 188 )7676(40.829 7.2 1560 1504 1s8)20000 560 376 1.06.3 40.82.9 1840 1692 $41.89.2 We now see that the decimal places in the dividen d exceed those in the divisor by 3, counting the ciphers annexed, and none in the divisor; hence we point off 3 decimal places in the quotient; all the figures at the left hand of the point are dollars, and all at the right will be cents and mills. Ex. 11. Bought 110,000 yards sheeting for 8 cents per yard, and sold the same at 40 cents per yard; what profit was made on the purchase? 110000 110000.08 cts. per yd..40 cts. per yd. 8800.00 4400000 8800 $35200 ans. LOSS AND GAIN. 23 There are 2 decimals in one factor; we point off 2 decimals in the product; those at the left hand will be dollars. Ex. 12. A bought 1250 bbls. beef at $10.50 per bbl., and sold it at a loss of 10 per cent.; how much did he lose, and what did he get a bbl.? Ans. 9.45 per bbl. Lost $1312.50. 100 per cent. is written thus, 1.00 1250 10 " " " ".10 10.50 90 " and " ".90 o), 13125 13125.00 _Ic 11812.50.90 1312.50 11812.50.00 1250)11812.50 9.45 There are two decimals in one of the factors, and 4 in the next two. Point off in the first product the same as Ex. 5, first product, No. 1, page 20, and in the second product the same as Ex. 8, page 3. We now see that the decimal places in the dividend exceed those in the divisor by 2; hence we point off from the quotient 2 decimals; the figures at the left hand will be dollars, and those at the right hand will be cents and mills. Ex. 13. Bought candles at 16 cts, 7 mills per lb., and sold them at 20 cts. per lb.; what profit will be made by laying out $100? 20 sold for 3.3 16.7 cost. 100 3.3 16.7)330.0 $19.760 ans. 24 LOSS AND GAIN. The decimal places in the dividend exceed those in the divisor by 3, counting the ciphers annexed; hence we point off 3 decimals from the quotient; the the figures at the left of the point will be dollars; those at the right will be cents and mills. Ex. 13. Bought goods for $5025 and sold them on 6 months credit at 22 1-2 per cent. above cost; what was the profit, allowing 7 per cent. interest? Ans. $954.75. 100 per cent. is written thus, 1.00 22 1-2 " " ".22 5 122 1-2 " and'" Li 1.22.5 No. 1. No. 1. No. 2. 5025.00 5025.00 f1.225 30 6155.62500 6)150.75000 int. at 6 per ct. a cJ 5200.875 25.12500 $954.750 1 75.875 " 7 " 50.25 $5200.875 Point off the product of No. I the same as Ex. 2, page 11, and in No. 2 according to the rule in Simple Interest. To ascertain at what price merchandise must be sold to gain or lose a stipulated price. RULE.-lst, Multiply the cost by the rate per cent., and in the product point off two decimal places. The result will be the whole gain or loss. 2d. If a gain, add it to the cost, and if a loss, deduct it therefrom, and you will obtain the selling price. Ex. 14. A merchant bought cloth for 50 cents per LOSS AND GAIN. 25 yard, wishes to mark it so as to gain 12 per cent.; what price must he put on them? 50 cts. purchase price. 50.12 per cent. profit. 6 6.00 56 cts. selling price. Must sell them for the purchase price, together with per cent. of that price. Ex. 15. Bought broadcloth at $4.50 per yard; how much must it be sold at, per yard, so as to lose 15 per cent.? 450 purchase price. 450 67.5.15 per ct. loss. $3.82.5 ans. 67.50 amt. loss. Ex. 16. If I buy 1650 yards flannel for $379.50, how must I retail it, per yard, to gain 25 per cent.? 23 cents per yard..25 per cent. profit. 5.75 23 cts cost. 1650)379.50(0.23 5.7 3300 Ans. 28.7 49.50 49.50 The decimal places in the dividend exceed those in the divisor by 2, hence we point off 2 decimals in the quotient for cents. To make 10 per cent, on goods that cost $5.00, the merchant should ask $5.50 for them, no matter whether the price of the goods falls or raises on his hands, or remains the same as it was when he bought them. 26 LOSS AND GAIN. TO FIND THE FIRST COST. RULE.-Divide the selling price by the increased rate per cent. and the qnotient will be the purchase price. Ex. 1. A merchant sold broadcloth at $5.40 per yard, and gained 20 per cent.; how much did the cloth cost? Ans. $4.50. 100 per cent is written thus, 1.00 20 " " " ".20 120 " and " " 1.20 1.20)5.40(4.50 O.. 2> 480 ~;2~ 6000 600 The decimal places in the dividend exceed those in the divisor by 2, counting the ciphers annexed; we point off 2 decimal places in the quotient; the figures at the left hand will be dollars, and those at the right will be cents. Ex. 2. Sold cloth for $2.10 per yard, by which was lost 30 per cent. on the primex cost; what was the prime cost? Ans. 3.10. 100 per cent. is written thus, 1.00 30 " " i ".30 70 " and " ".70 ~a; X 70)2.17 -c O S3.10 Point off the quotient the same as Ex. 1. *Prime cost means the first cost. PARTNERSHIP. 27 Ex. 3. In order to sell coffee at $6.50 per hundred pounds and make 10 per cent., what must be my purchase price? 100 per cent, is written thus, 1.00 10 "' " ".10 110 " and " 1.10 1.10)6.50 5.90.9 ans. The decimal places in the dividend exceed those in the divisor by 3, counting the ciphers annexed; hence we point off 3 decimal places in the quotient; those at the left will be dollars and at the right will be cents and mills. PARTNERSHIP. Partnership is the association of two or more persons in business. The money employed is called the capital or stock, and the profit or loss to be shared among the partners is called the dividend. To find the gain or loss when the stock of each is employed for the same timeRULE.-As the whole stock is to each partner's stock, so is the whole gain or loss to each partner's stock. 28 PARTNERSHIP. Ex. 1. A, B and C enter into trade; A put in $500, B put in $700, and C put in $800. They gained $400; what is each ones part of the gain? 500 A put in 700 B " 800 C " In trade, $2000 amount of stock. As 2000: 500:: 400 As 2000: 800:: 400 400 400 2000)200,000 2000)320,000 100 160 Dolls. As 2000: 700:: 400 100 A's gain. 400 140 B's " 160 C's " 2,000)280,000 $400 140 Ex. 2. Five persons, A, B, C, D and E, are to share between them $2400; A is to have 1-6, B is to have 1-4, C is to have 3-8, D and E are to divide the remainder in proportion to the numbers 5 & 7; how much does each one receive? A receives 1-6 of 2400=$400 B " 1-4 " - 600 C " 3-8 " = 900 1900 5 represents D's part. 7 " B's " 12 " the sum. Hence D receives 5-12 of 500=208.33 1-3 E " 7-12 " -291.66 2-3 $500.00 PARTNERSHIP. 29 Ex. 3. A and B venture equal stock in trade and clear $164; by agreement A was to have 5 per cent. of the profits, because he managed the business. B was to have 2 per cent.; how much was each one's gain, and how much did A receive for his trouble? Ans. A's gain $117,143 164 B's " 46,857.05 164 820.02 per cent. 328 328 1148 Operation by Proportion. 1148: 820:: 164 1148: 328:: 164 164 164 1148)134480(117,143 nearly. 1148)53792(46,857 1148 4592 1968 7872 1148 6888 8200 117,143 9840 8036 46,857 9184 1640 $70,286 A received) 6560 1148 (tor his trouble. 5740 4920 8200 4592 8036 3280 Point off the same as Ex. 10, in Loss and Gain, page 22. Ex. 4. A and B. bought and sold wool; A purchased to the amount of $7840, and paid $250 expenses; B purchased to the amount of $4900, and paid 30 PARTNERSHIP. $288 expenses; A disposed of the wool for $12,475; how must A and B settle the loss to be shared equally? 7840 A purchased. 4900 B purchased. 250 " expenses. 288 " expenses. 8090 13278 5188 5188 12475 313.749 13278 $803 loss. $4874.251 amt. A pays B. Operation by Proportion. 13278: 5188:: 803. 803 13278)4165964 318.749 B's loss substracted from his stock will be what A is to pay B. Ex. 5. A and B enter into partnership for one year; A furnishing $1500, B $1000, and receiving $150 for overseeing; how much did B receive? They gained $2256; what was each one's share of the gain? 2256 Deduct 150 2106 hal. of gain to be divided. Operation by Piroportion. 2500: 1000::2106 1500 1000 1000 2500)2106000 2500 amt. whole stock. 842.40 1263.60 A's sh are. 2500: 1500::2106 842.40 B's share. 1500 842.40 $2106.00 150 2500)3159000 $992.40 amt. B receives. 1263.60 Point off in the quotients, Nos. 4 and 5, as Ex. 3. PARTNERSHIP. 31Ex. 6. Divide $360 into 4 equal parts which shall be to each other as 3, 4, 5 and 6. 3-3 18-1-6 of 360= 60 ] 4=4-18=2-9 " 83 Ans. 5=5-18=5-18 " =100 6=6-18=1-3 " =120 J 18 $360 To find the gain or loss when their capital is employed for different timesRULE.-Multiply each partcner's stock by the time it is in trade; then say as the sum of all the products is to each particular product, so is the whole gain or loss to each man's share of the gain or loss. Ex. 7. A and B enter into partnership; A furnishing $500 for 4 months, and B $700 for 5 months; they gained $275; what is each one's share of the gain? 500 4 months in trade. 2000 700 3500 5 months in trade. 5500 3500 As 5500: 2000::275 As 5500: 3500:: 275 2000 3500 $100 A's gain. 5500)5500 00 $175 B's " 5500)962500 100 $275 175 Ex. 8. A B. and C. enter into partnership; A put in $85 for 8 months, B put in $60 for 10 months, and C put in $120 for 3 months, by misfortune they lost $51; what must each man sustain of the loss; 680 85 60 120 600 8 mos. 10 mos. 3 mos. 360 680 600 360 1640 sum of products. 32 PARTNERSHIP. 1640: 680::41 1640: 600::41 1640: 360:: 41 41 41 41 1640)27880 1640)24600;640)14760 17 15 9 $17 A's loss. ) $15 B's " SAns. $9C's " 41 Ex. 9. A and B trade in company for one year only; on the first of January A put in $1200, but B could not put in any money into the stock until the 1st of April; what did he then put in to have an equal share with A? B 9 mos. in trade: A 12 mos. in trade:: 1200 12 9)1]4400 $1600 Ans. The answer to the question is given in money; place the dollars for the 3d term. The answer is to be more, place the next greater number (12) for the 2d term, and the less number (9) for the 1st term. See rule in Simple Proportion. Ex. 10. Two men engaged in partnership for four years; A put into the firm $12.500; B put in $2500. B is to superintend the business and is paid $10,000, the difference between his and A's capital. At the end of the year A increased his capital to $25,000. They gained by trade $10,655; what is each one's share of the gain? PARtTNERSHIP. 33 12500 2500 2500 10000 10000 difference between A & 12500 B's capital. 4 yrs. in trade. 50000 12500X4 yrs.-=50000 12500X3 " =37500 $25000 87500 A's product. 50000 B's " 137500 137500: 87500:: 10655 87500 137500: 50000:: 10655 50000 137500)932312500 137500)532750000 6780.455 nearly. 3874.545 3874.545 10655.000 Point off in the quotients the same as Ex. 10, p. 22. Ex. 11. Three men engaged in partnership for 18 months; A put into the firm $3200, and at the end of 4 months he put in $500 more, but at the end of 14 months he took out $800. B at first put in $2200, but at the end of 9 months he took out $1100, and at the end of 12 months he put in $2000. C put in $1500; at the end of 6 months he put in $1500 more,- and at the end of 12 months he put in $1500 more, but at the end of 14 months he took out $1000. They gained $3260; what is each man's share of the gain? Ans. A's share, 1307.40.7 B's " 887.92.9 C's " 1064.66.4 3 34 PARTNERSHIP. A put in A put in 3200 500 18 mos. in trade. 14 mos. in trade. 57600 7000 7000 A ad'd at the end 4 mos. A took out. 64600 (14 mos. 800 (trade. 3200 A took out at end of) 4 mos. out of) 61400 A's product. 3200 41700 B's " 50000 C's " B put in 2200 153100 sum of products. 18 mos. in trade. B put in 39600 2000 9900 6 mos. in trade. 29700 12000 12000 41700 C put in 1100 B took out. 1590 9 mos out of trade 18 mos. in trade. 9900 27000 9000 C put in 18000 1500 12 mos. in trade. 54000 - 4000 C took out. 18000 50000 C put in 1500 6 mos. in trade. 9000 C took out 1000 4 mos. out of trade. 4000 COMMISSION AND BROKERAGE. 35 Operation by Proportion. 153100: 50000:: 3260 50000 153100)163000000 1064.66.4 nearly. 153100: 61400:: 3260 3260 153100)200164000 1307.407 nearly. 153100: 41700:: 3260 3260 153100)135942000 887,929 Point off in the quotients the same as Ex. 10, p. 31. 1307407 A's gain. 1064664 B's " 887929 C's " $3260,000 COMMISSION AND BROKERAGE. Commission and Brokerage is the per cent. or sum charged by agents for their services in buying and selling goods, or transacting other business. To compute commission brokerage, discount or stocksRULE.-Multiply the given sum by the decimal which expresses the rate per cent. Ex. 1. A sold goods amounting to $1432.36; how much is the commission at 4 per cent.? Ans, $57.29. 1432.36.04 $57.29.44 36 COMMISSION AND BROKERAGE. Point off in the same as Ex. 8, in Percentage, p. 3. Ex. 2. What is the brokerage on $6200 at 3-4 per cent.? Ans. $46.50. 1st method. 2d method. 6200.00 6200.00.0075=3-4.01-1 per ct. 46.50.0000 4-2)62.0000 at 1 per ct. 31.0000=1-2 15.5000 —=3-4 $46.50.00 ans. In the first method there are 6 decimals in both factors, and in the 2d method 4 decimals in both factors. In the 1st method we point off from the product 6 decimal places; the figures at the left will be dollars, those at the right will be cents. In the 2d method the same as Ex. 2, p. 9. The decimal places in the dividend exceed those in the divisor by 4; hence we point off 4 decimal places in the quotients; those at the left hand will be dollars, and those at the right will be cents. Ex. 3. Engaged a broker to purchase 12 shares of Boston & Maine Railroad at $112.50 per share; what is the commission at 1-4 per cent.? -1st method. 2d method. 112.50 112.50 12 shares. 12 shares. 1350.00 1350.00.0025 —-1-4.01 3.37.5000 4)13.50.00 at 1 per ct. 3.37.50 COMMISSION A-ND BROKERAGE. 37 In the 1st method there are 2 decimals in one of the factors and 6 in the next two. We point off in the 1st product 2 decimals; all at the left hand will be dollars. In the 2d product 6 decimals; those at the left will be dollars, and those at the right will be cents and mills. In the 2d method we point off in the 1st product the same as we did in the 1st product in the 1st method, and in the 2d product the same as Ex. 8, p. 3. The decimal places in the dividend exceed those in the divisor by 4; hence we point off four decimal places in the quotient-those at the left will be dollars, and those at the right will be cents and mills. Ex. 4. What must be paid to a New York broker for $5000 of City Bank bills on Eastern Banks at 1-4 of 1 per cent.? 5000.00 5000.01 12.50 4)50.00.00 —1 per ct. $5012.50 ans. 1:.50 Ex. 5. A drover exchanges $2240 of country money for city bills, paying 1-8 per cent. on his country money; what does he receive? 2240.00.01 2240 2.80 8)22.40.00 at 1 per cent. $2237.20 ans. 2.80 Ex. 6. A sells for an individual 90 shares of Boston & Worcester Railroad stock for $125 a share, receiving 88 COMMISSION AND BROKERAGIE. 1 per cent. on what money he gets; what does he receive? 125.00 a share. 90 shares. 11250.00.01-1 per cent. $112.50.00 Point off in the 1st product the same as in 1st method Ex. 3, 1st product, and in 2d product 4 decimals; the figures at the left will be dollars, and those at the right will be cents. Ex. 7. A sold 12 pieces of cloth for B containing 28 yards, at $3.75 per yard, and charged 2 1-2 per cent. commission and 3 per cent. guaranteeing the payment; how much will A receive? No. 1. 28 12 No. 2. 1260.00 336.055=5 1-2 3.75 - 69.30.000 1260.00 69.30 1190.70 Ans. In No. 1 we point off in the product the same as Ex. 3, 1st method, 1st product; in No. 2 the same as Ex. 6, Insurance, p. 12. Ex. 8. A merchant in Chicago consigned 450 bbls. of beef at.$11.25 per bbl., and charged 2 1-2 per cent. commission; the merchant sold a draft on his agent COMMISSION AND BROKERAGE. 39 for the sum due him at 1 per cent. premium; how much did he receive for his beef? 100 per cent. is written thus, 1.00 1 " " " ".01 101 " and " " 1.01.' ~ No. 1. No. 2. e 11.25 5032.50 P4 2 450 126.56 5062.50 4935.94.025=2 1-2 1.01 $126.56.250 4985.29.94 Ans. In No. 1 we point off in the 1st product the sameas Ex. 3, p. 36, 1st method, 1st product, and in the 2d product the same as Ex. 6, p. 16, and in No. 2 the same as Ex. 8, p 3. Ex. 9. A manufacturer in Albany sent 256 pieces of cloth, containing 28 yards in a piece, to Wm. F. Smith of Boston, and agreed to pay him 2 per cent. commission and 3 per cent. for guaranteeing. S. sold the cloth at $4.65 per yard, paid $28.35 freight and $15.17 insurance; how much did A receive for his cloth? Ans. $31621.12. 256 33331.20 1666.56 28 1710.08 28 35 - 15.17 7168 yds 31621.12 ans. 4.65 per yd. $1710.08 33331.20 (teeing..05=5 per cent. for commission and guaran-) 1666.56.00 Point off in the 2d and 3d products the same as Ex. 3, 2d method, p. 36. 40 COMMISSION DEDUCTED RN ADVANCE. COMMISSION DEDUCTED IN ADVANCE. If the commission is to be deducted from the given sum, it is evident that we ought not to pay an agent commission on his own money, which, however, is often unjustly practiced. RuLE.-Divide the given sum by the increased rate per cent., the quotient will be the amount to be invested; substract the amount from the given sum and you have the required commission. Ex. 1. A sent his agent $1200 to purchase wool, how much had he ought to pay out, after deducting his commission of 5 per cent.; what was his commission? 100 per cent. is written thus, 1.00 5 " " " ".05 105 " " " " 1.05 1st method ~U~ ~;~ e1.05)1200.00(1142,857 - A ~ 105 2d method. 105:5::1200 150 5 105 105)6000(57,142 450 525 420 750 300 735 210 150 900 105 840 450 600 420 525 -1200 300 1142.85.7 750 210 - 735 $57,143 Ans. See rule in Division of Decimal Fractions. COMMISSION DEDUCTED IN ADVANCE. 41 Where the decimal places in the dividend exceed those in the divisor, make them equal by annexing ciphers to the right of the dividend, and the quotient will be a whole number. We now see that the decimal places in the dividend exceed those in the divisor by 3, counting the ciphers annexed; hence we point off 3 decimal places in the quotient. The figures at the left of the point will be dollars, and those at the right will be cents and mills. Ex. 2. H. Kinsman sold for Benj. Billings of Rutland, 3600 lbs. butter at 20 cents per pound; 2670 lbs. cheese at 8 cents per lb., at a commission of 5 per cent. He invested the balance in books, after deducting his commission of 2 1-2 per cent., for purchasing; what amount of goods ought he to receive? 100 per cent. is written thus, 1.00 21-2 " " 2".5 1021-2" and " " 1.02.5 1.02.5)886,920,. 3600 $865.287 ans. nz.20 933.60;1 720.00 46.68 C> 213.60 c - $886.92 933.60.05 2670 8 46.68.00 commission. 213.60 We annex one cipher to the right of the dividend and point off in the quotient in the same manner as Ex. 1, p. 41. 42 SIMPLE INTEREST. Ex. 3. Winm. F. Grooms sent a broker $15000 to invest in goods; after deducting his commission of 13-4 per cent.; what amount of goods ought he to receive? 100 per cent. is written thus, 1.00 13-4 " " ".0175 1013-4 " and': " 1.01.75, a C; (D1.0175)15000.0000 14742.014 Ans. Ex. 4. A man sent a broker $10478.13 to lay out in stocks after deducting his brokerage at 1-2 per cent.; what was the brokerage, and how much stock did he receive? 100 per cent. is written thus 1.00 1-2 " " " " 0.5 1001-2" " " " 1.00.5 u, X 1.005)10478.130 c 10478.13 $10426 his stock. r_1 10426. $52.13 brokerage. The last two examples are worked in the same manner as Ex. 1. SIMPLE INTEREST. There are three things to be mentioned in Interest; 1st. The principal, or money lent. 2d. The rate or sum per cent. agreed on. 3d. The amount, or principal and interest added together. SIMPLE INTEREST. 43 Interest is of two kinds, Simple and Compound. Simple Interest is that which is allowed for the principal. Compound Interest is that which arises from the interest being added to the principal and continuing in the hands of the lender and becomes a part of the principal at the end of each stated time of payment. RULE.-Write down half the greatest even number of months for a multiplier —there being an odd month it must be reckoned 30 days-add the given days, if any; seek how many times you can have 6 in the sum of them; place the figure for a decimal at the right hand of half the even number of months already found, by which multiply the principal, observing in pointing off the product to remove the decimal point two figures from its natural place towards the left hand; that is, point off two more places for decimals in the product than there are decimal places in the multiplicand and multiplier counted together. Then all the figures at the left of the point will be dollars, and those at the right will be cents and mills. Should there be a remainder in taking 1-6 of the days, reduce it to a regular fraction, for which take aliquot parts of the multiplicand. ThusIf the remainder be 1= divide the multiplicand by 6 " " 8-X " ii (" "' 2 " 4=-4 " " " " 3 twice " " 5-X&Y:6" " " 2 & 3 The quotients which in this way occur, must be added to the product of the principal, multiplied by half' the months, &c. When there are days less number than 6, so that 6 cannot be contained in them, put 44 SIMPLE INTEREST. a cipher in place of the decimals at the right hand of the months, then proceed in all as above directed. To compute interest when the rate is greater or less than 6 per cent. RULE.-First find the interest on the given sum at 6 per cent.; then add to this interest or substract from it such fractional part of itself as the given rate exceeds or falls short of 6 per cent. When the required rate is 61-2 per cent., we first find interest at 6 per cent. and add 1-12 of it to itself. When the required rate is 7 per cent., we first find the interest at 6 per cent. and add 1-6 of it to itself. If 7 1-2 per cent., we add 1-4 of it to itself. When the required rate is 8 per cent., we first find the interest at 6 per cent. and add 1-3 of it to itself. When the required rate is 8 1-2 per cent., we first find the interest at 6 per cent. and add 5-12 of it to itself. When the required rate is 9 per cent., first find the interest at 6 per cent. and add 1-2 of it to itself. If 9 1-2 per cent., find the interest at 6 per cent. and add 7-12 of it to itself. If 10 per cent., find the interest at 6 per cent. and add 2-3 of it to itself. If 10 1-2 per cent., find the interest at 6 per cent. and add 3-4 of it to itself. If 11 per cent., find the interest at 6 per cent. and add 5 6 of it to itself. If 111-2 per cent., find the interest at 6 per cent. and add 11-12 of it to itself. If 12 per cent., find the interest at 6 per cent. and multiply it by 2. If 1 per cent., we find the interest at 6per cent; and slbstract 5-6 of it from itself. SIMPLE INTEREST. 45 If 1 1-2 per eent., we find the interest at 6 per cent. and substract 3-4 of it from itself: If 2 per cent., we find the interest at 6 per cent. and substract 2-3 of it from itself. If 21-2 per cent., we find the interest at 6 per cent. and substract 7-12 from itself: If 3 per cent., we find the interest at 6 per cent. and substract 1-2 from itself. If 3 1-2 per cent., we find the interest at 6 per cent. and substract 5-12 from itself. If 4 per cent., we find the interest at 6 per cent. and substract 1-3 from itself. If 4 1-2 per cent., we find the interest at 6 per cent. and substract 1-4 from itself: If 5 per cent., we find the interest at 6 per cent. and substract 1-6 from itself. If 51-2 per cent., we find the interest at 6 per cent. and substract 1-12 from itself. Ex. 1. What is the interest of $76.54 for 1 year, 7 months and 11 days at 6 per cent.? Ans. $7.41.1. 3.2)76.54 9.6 45924 68886 3827=1-2 2557=1-3 7.41.168 Note. —The number of months being 19 the greatest even number is;8, 1-2 of which is 9, which write down, then seeking how often 6 is contained in 41, (the sum of the days in the odd month and given days), we find it will be 6 times, which also set down at the 46 SIMPLE INTEREST. right hand of 1-2 of the even number of months for a decimal, by which, together, we multiply the principal. In taking 1-6 of the days (41) there will be a remainder of 5=1-2 and 1-3, for which we take first 1-2 the multiplicand or principal; that is, divide the multiplicand by 2, then by 3, and these quotients added, with the products of 1-2 the number of months, &c., the sum of these will show the interest required; observing to count off 2 more figures for decimals in the product than there are decimal figures in both the multiplier and multiplicand counted together. Ex. 2. What is the interest of $375.58 for 6 months at 6 per cent.? Ans. $11.26.7. 375.58 3.0 $11.26.7.40 Put a cipher in the place of the decimals at the right hand of half the even number of months. See rule, page 43. Ex. 3. What is the interest due on a note of $523 from March 5th, 1869, to Aug. 20, 1870, at'7 per cent. Ans. $53.38.9 yrs. mos. dys. 2)523.00 1870 8 20 8.7 1869 3 5 - - - - 366100 1 5 15 418400 12 30 26150 2)17 mos. 6)45 - - 6)45.76.250 int. at 6 per cent. 8 7 7.62.708 $53.38.958 int. at 7 per cent. See rule for pointing off in the products, p. 44. SIMPLE INTEREST. 47 Ex. 4. What is the interest of $800 for 4 months and 3 days at 5 per cent.? Ans. $21.86.. 2)800.00 2.0 1600000 40000 3) 16.40000 int. at 6 per cent. 5.46666 $'21.83.666 Ex. 5. What is the interest of $240.38 for 7 months and 10 days at 5 per cent.? Ans. $7.34.4 30 3.3)240.38 2)7 10 3.6 3- 6)40 144'228 - 72114 6-4 8012 8012 6)8.819!)2 int. at 6 per cent. 1.46898 7.34.494 int. at 5 per cent. Ex. 6. What is the interest of $462 for 3 years at 6 per cent.? 462 00 Ans. $83.16..06 27.72 00 int. for 1 year. 3 years. 83.16.00 int. for 3 years. Ex. 7. What is the interest of $550 for 1 year at 7 3-10 per cent.? 550.00 7.3=7 3-10 165000 385000 $40.15.000 Ans. 48 SIMPLE INTEREST. Ex. 8. What is the interest of $746.28 for 1 year, 4 months at 10 per cent.? 746.28 8 0=half the mos. 2 of 5970-11940 3 3 59.70.240 39.80 3)11940 $99.50 int at 10 per cent. 39.8() Ex. 9. What is the interest of ~587 16s. 3d. for 3 years at 6 per cent.? Ans. ~105 16s. ld. RuLE.-Reduce the shillings and pence to a decimal of a pound, then compute the interest as though the sum were dollars and cents, and finally reduce the decimal figures in the answer to shillirgs and pence. 16.3 240)19500 587.8125 12 -.06 -- 8125 195 35.268750 for 1 year. __ —~~~ 3 240 105.806,250 for 3 years..806 decimal of a pound. 20 shillings a pound. 16,120 12 pence a shilling. 1,440 Ex. 10. What is the interest of $700 for 5 years at 1 per cent. per month? Ans. $35. 700o.oo00.01=1 per cent. 7.00.00 interest 1 month 5 months. 35.00.00 *Reduced to a decimal.of a pound. SIMPLE INTEREST. 49 Ex. 11. What is the interest of $1000 for 1 year, 9 months at 2 per cent. a month? Ans. $420 1000.00.02 20.00.00 21 months. $420.0000 Ex. 12. What is the interest of $100,000 for 3 years at 3 per cent. a month? Ans. $108,000. 100000.00 1.08 80000000 10000000 108000.0000 Three per cent. a month is 36 per cent. a year, and for 3 years is 108 per cent. Point off in the products in the same manner as Ex. 11, in Percentage, p. 4. RULE.-For casting interest by multiplying the principal by the number of days. Reckon 30 days to a month, 360 days a year. If there are no cents in the principal, annex two ciphers in place of them. Divide the product by the following numbers, because it takes so many days for $1 to gain $1. If 3 per cent. divide the product by 12000 " 4 " " " " " 9000 "5 " " " " " 7200 " 6 " " " " " 6000 4" 7 " " " " " 5143 "8 " " " " " 4500 " 9 " " " " " 4000 "10 " " " " " 3600 Point off in the quotient two figures; the figures at the left hand will be dollars —those at the right hand will be cents and mills. 4 50 DISCOUNT BY COMPOUND INTEREST. Ex. 1. What is the interest of $268 for one year, 2 months and 7 days at 6 per cent.? 360 days a year. 26800 60 days in 2 months. 427 7 days. 6,000)11443,600 427 $19.07 ans. Ex. 2. What is the interest of $58.28 for 1 month and 3 days at 5 per cent.? 5828 33 7200)192324 26 cents, ans. Ex. 3. What is the interest of $800 for 12 days at 7 per cent.? 80000 12 5143)960000 1.86 DISCOUNT BY COMPOUND INTEREST, Is the present worth of a debt payable at some future time without interest, is the sum which, being put at legal interest, will amount to the debt at the time it becomes due. RULE.-Divide the debt by the amount of $1, for the given time, and the present worth, which, if substracted from the given sum will leave the discount. Ex. 1. What is the present worth of $600, due 3 years hence, at 6 per cent., compound interest; what is the discount? INTEREST. 51 The amount of $1 for 3 years at Compound interest is 1,191016)600,000000 600,000 given sum. 503,771 present worth. See table, p. 53. $503.771 96.229 discount. Ex. 2. WVat is the present worth of $500, due 4 years hence, at 7 per cent., Compound Interest? Ans. $381,447. The amount of $1 for 4 years, Compound Interest, at 7 per cent. is 1,310796)500,000000 $381.447 Annex ciphers to the right of the dividend and point off in the quotient in same manner as Ex. 1., Comra mission Deducted in Advance, p. 40. TO FIND THE PRINCIPAL FROM THE INTEREST AND THE RATE PER CENT. RULE.-Divide the given interest by the interest of $1 for the given time and rate per cent. Ex. 1. What principal will, in 1 year, 7 months and 15 days, at 6 per cent.., give $9.75 interest? 2)1.00 9.75 9.7 100 9700 975)97500 50 $100 ans..09.750-=' cts. 7 1-2 mills int. Ex. 2. Mexico pays England, France and Spain $3,000,000 interest a year; what principal will, in one year, at 6 per cent., give that interest. 52 INTEREST. 1.00 3000000.06 100.06.00=6 cents interest. 6)300000000 $50,000,000 Ans., Fifty millions of dollars. TO FIND THE TIME FROM THE PRINCIPAL AND THE RATE PER CENT. RULE.-DIivide the given interest by the interest of the given principal for 1 year at the given rate per cent. Ex. 1. In what time will $700, at 7 per cent., give $85.75? Ans., I year, 9 mos. 700.00 8575.07 100 49.00.00 )857500(1 490000 367500 12 mos. a year. 4410000(9 4410000 Ex. 2. In what time will $50, at 6 per cent., give $2.05? Ans., 8 mos., 6 days. 50.00 205.06 100 3.00.00 30000)20500 12 mos. a year. 246000(8 240000 6000 30 days a month. 180000(6 180000 COMPOUND INTEREST. 53 COMPOUND INTEREST TABLE, Showing the amount of $1 it 5, 6, 7 and 8 per cent. fromn 1 to 12 years. Yrs 5 per cent. 6 per cent. 6 per cent. 8 per cent. 8 p ent. 1 1,050,000 1,060,000 1,070,000 1,080,000 2 1,102,500 1,123,600 1,144,900 1,166,400 3 1,157,625 1,L91,016 1,225,043 1,259,712 4 1,215,506 1,262,476 1,310,796 1,360,489 5 1,276,281 1,338,225 1,402,552 1,469,828 - 1,340,095 1,418,519 1,500,730 1,586,874 7 1,407,100 1,5038630 1,605,781 1,713,824 8 1,477,455' 1,593,848 1,718,186 1,850,930 9 1,551,328 1,689,479 1,838,459 1,999,005 10 1,628,894 1,790,847 1,967,151j 2,158,92,5 11 1,710,339 1,898,298 2, t104,8.52 2,331,639 12 1,795,856 2,012,196 2.252,191 2,518,170 Ex. 1. What is the compound interest of $425 for 9 years, 2 months and 8 days at 6 per cent,? Ain't of $1 by the table is 1,689,479 425 principal. 3) 718,028575 principal and int. 1.1 8.13,756 718.02 726.15 425 -301.15 aas. 54 COMPOUND INTEREST. COMPOUND SEMI-ANNUAL INTEREST TABLE, Sowing the amount of $1 at 5, 6, 7 and 8 per cent., from 1 to 12 years. Yrs 5 per cent. 6 per cent. 7 per cent. 8 per cent. 1 1,050,625 1,060,900 1,071,225 1,081,600 2 1,103,812 1,125,508 1,147,522 1,169,858 3 1,159,692 1,194,051 1,229,254 1,265,318 4 1,218,401 1,266,768 1,316,807 1,368,567 5 1,280,082 1,1343,914 1,410,596 1,480,241 6 1,344,886 1,425,759 1,511,065 1,601,028 7 1,412,970 1,512,587 1,618,690 1,731,671 8 1,484,501 1,604,703 1,733,981 1,872,974 9 1,559,653 1,702,429 1,857,483 2,025 807 10 1,638,610 1,8,6,106 1,989,781 2,191,112 11 1,721,564 1,916,098 2,131,503 2,369,906 12 1,808,718 2,032,187 2,283,319 2,563,290 Ex. 1. What is the compound seini-aunnal interest of $300 for 3 years and 10 days at 7 per cent.? The am't of $1 for three years by the table is 1.229254 300 3,3)368,77.6200 0.1=1-6 of the days. 33,8.77=36 cents, 8 mills. 12,2.92 12,2.92 6)61,4.61 int. at 6 per cent. 10.243 71,7.04 int. at 7 per cent. 36877 369.48 300 deduct the principal. $69.48 ans. PARTIAL PAYMENTS. 55 PARTIAL PAYMENTS. RULE.-If the payment exceeds the interest, the surplus goes toward discharging the principal, and the subsequent interest is to be computed on the balance of the principal. If the payment be less than the interest, it must not be taken out of the prinucipal, but interest continued on the former principal until the period when the payments taken together exceed the interest due them, surplus is applied toward discharging the principal. Ex. 1. What is due on a note of $750, dated Jan. Ist, 1868, with interest at 6 per cent. after deducting the following endorsements: August 10 1868, paid $110. April 13 1869, "' 115. What was due on taking up the note Nov. 20, 1869. Years. Mos. Days. 1868 8 10 1868 1 1 7 9 time to 1st paym't, Aug. 10,'68. Years. Mos. Days. 1869 4 13 1868 8 10 8 3 time on bal. after Lst paym't, Aug.) Years. Mos. Days. (10,'68. 1869 11 20 1869 4 13 (paym't Apr. 13,'69 7 7 time on bal. after deducting the last) Principal, - - 750.00 Int. to Ist paym't, Aug. 10'68, - 27,375 777,375 st paym't to be deducted friom amount, - 110 jBaL due after 1st paym't, - - - B67,375 56 PARTIAL PAYMENTS. Int. on bal. to Apr. 13,'69, - - - 27,028 694,403 2d paym't to be deducted from amount, 115 579,403 Int. due on taking up the note, - 20,955 Answer, $600,358 Ex. 2. What is due on a note of $875, dated March 8, 1867, with interest at 7 per cent, after deducting the following endorsements: Sept. 8, 1867, paid $75. June 18, 1868, " 15. Mar. 24, 1869, " 90. What was due on taking up the note Jan. 9, 1870. Principal, - $875.00 Interest to 1st paym't, Sept. 8, 6 mos., 30.625 905.625 1st paym't deducted from amount, - 75 Bal. due after 1st paym't, Sept. 8,'67, $830.62.5 Int. on bal. 2d paym't, June 18,'68, 9 mos., 10 days, - - 45.222 2d paym't being less than int. due, 15 Surplus int. unpaid June 18,'68, 30.222 Int continued on bal. from June 18, to Mar. 24,'69, 9 mos., 6 days, 44.576 74.798 905.423 3d paym't being greater than the int. due is to be deducted from the ain't. - - 90 815.423 Int. on bal. to Jan. 9,'70, 9 mos., 15 days, 45.187 $860.61.0 BANKINaG. 57 BANKING. A bank is a corporation chartered by law for the purpose of receiving money and furnishing a paper currency. It is customary for a bank in discounting a note or draft, to deduct in advance the legal interest on the given sum fiom the time it is discounted to the time when it becomes due. Bank Discount is the same as Simple Interest paid in advance; thus, the bank discount on a note of $106, payable in one year at 6 per cent., is $6.36, while the true discount is but $6. A Teller is a clerk in a bank who receives and pays the money on checks and drafts. A check is an order for money. A draft is an order from one man to another, directing the payment of money-a bill of exchange. RULE.- Compute the interest on the face of the note for 3 days more than the specified time, (these are called days of grace), then calculate the interest at the given rate; the result is the bank discount and the face of the note, diminished by the discount, is the present worth. Ex. 1. What is the discount, and what is the present worth of a note for $460 at 60 days, discounted at a bank at 6 per cent., and grace. Ans. $455.17 is the present worth. and 4.83 " discount. 460.00 2)460.00 4.83 1.0=1-2 the mos. 455.17 460.000 23.000 $4.83.000 58 B ANKING. See rule in Simple Interest for pointing off the decimals in the product, p. 43. Ex. 2. What is the bank discount on a note at 7 per cent. for $850.64, payable in 90 days and grace? 2)850.64 Ans. 15.38. 1.5=1-2 the mos. 425320 85064 42532 6)13.18 492 interest at 6 per cent. 2.19.748 15.38.240 bank discount, or int. at 7 per ct. Ex. 3. What is the present worth of a note at 8 per cent. for $1500, payable in 12 days, and grace discounted, at a bank? 2)1500.00 6)12 days 0.2=1-6 of days. 2 30.0000 7.5000 1500 5.00 3)3.75000 int. at 6 per cent. 1.25 $1495.00 ans. 5.00 int. at 8 per cent. Ex. 4. What is the bank discount on a note at 7 3-10 per cent., for $125 for 6 mos. and 10 days? RULE.-Multiply the principal by 2, that will give the interest for 1 day-because it is 2 cents a day on $100-that product by the number of days. 182 1-2 days in 6 months. 10 " added 192 1-2 days BANKING. 59 125.00.02 2).02.5000=2 1-2 cents per day. 192 1-2 4.81.2500 We point off in the 1st product according to the rule in Simple Interest, p. 43. We prefix one cipher in the!st product because cents occupy 2 places. In the 2d product point off 6 decimals, because there are 6 decimals in the multiplicand. All at the left will be dollars, and those at the right will be cents and mills. Ex 5. A bought 20400 lbs Rice at 10 cts. per pound, cash, and sold it immediately for 15 cts. per pound on 6 months credit. If he should get this discounted at a bank, what will he gain on the Rice? 1 2 20400 20100'.10 cts. a pound..15 20.40.00 30.6000 91.80 3.0=1-2 the mos. 2131 80 91.80.000 3060 2131.80 $928.20 ans. Point off in two products of Nos. 1 and 2 the same as Ex. 11, in Loss and Gain, p. 17; and the last product of No. 2 according to the rule ill Simple Interest, p. 43. THE PROCEEDS OF A NOTE FIND THE FACE. It is often required to make a note of which the present value shall be a given number, 60 BANKING. RULE.-Divide the proceeds of a note by the proceeds of $1 for the given time and rate mentioned, and the quotient will be the face of the note. Ex. 1. A merchant wishes to borrow $400 at a bank, for what sum must he draw his note, payable in 60 days, so that when discounted at 6 per cent., he will receive the desired amount? 2)100 1.0 100.0105 1000 50.9895 (from $1. 01.0.50 int. on $1 is 1 cent., 5-10 of a mill; deduct this).9895)400,0000(404,244 39580 42(00 39580 24200 19790 44100 39580 45200 39580 Annex ciphers to the right of the dividend and point off in the quotient in the same manner as Ex. 1, in Commission Deducted in Advance, p. 40. Ex. 2. What is the face of a note at 60 days at 7 per cent. which yields $670, when discounted at a bank? 2)100 Ans. $67.318. 1.0 100.01225 1000 50.98775 BANKING. 61 6)1.0.5C=1 cent and 5-10 of a mill, int at 6 per cent. 175 01.2.25=-1 cent, 2 mills, 25-100 of a mill int. at 7 per ct..98775)670,00000 $678.31 nearly. Ex. 3. What is the face of a note at 90 days at 5 per cent. of which the proceeds are $1000, when discounted at a bank? 2)100 100 1.5=1-2 the mos. 1292 1500.98708)1000.00000 50 Ans. 1013.089 6)1.5.50 258 01.2.92 int. at 5 per ct. is 1 et., 2 mills, 92-100 of a mill Ex. 4. What is the ftace of a note at 30 days at 8 per cent., of which the proceeds are $1500, when discounted at a bank? 2)100 5 500 50 3)5.50 int. at 6 per ct. is 5 mills and 5-10 of a mill. 183 7.3.3 int. 7 mills, 33-100 of a mill at 8 per cent. 100 00.733.99267) 1500,00000 Ans. $1511.076 Nos. 2, 3 and 4 examples are worked in the same manner as Ex. 1, p. 60. ,62 EQUATION OF PAYMENTS. EQUATION OF PAYMENTS. Equation of payments is the equalized or average time when two or more payments, due at different times, may be made at once without loss to either party. RULE.-Multiply each payment by the time at which it is due, then divide the sum of the products by the sum of all the payments, the quotient will be the answer. Ex. 1. A owes B. $600 to be paid in 4 mos., $700 to be paid in 6 mos., and 1200 to be paid in 7 mos.; what is the average time for the payment of the whole? Aus. 6 mos. Operation. $600X4 mos.-2400 700X6 =" 4200 1200X7 " -8400 Sum of pay'ts, 2500 2500)15000 sum of products. Ans. 6 mos. Ex. 2. A bought a store for $17380 on 2 years credit; in 8 months he paid $1238; in 4 months more he paid $2217; 3 months later he paid $3369, and 2 months after he paid $1865; how long ought the payment of the balance to be deferred? RULE.-Multiply each payment by the time it was made before it becomes due, and divide the sum of the products thus obtained by the balance remaining unpaid, the quotient will be the time required. When EQUATION OF PAYMENTS. 63 there are months and days, the months must be reduced to days. Ans. 19 months, 9 days. 1238X16=-19808 2217 X 12=26604 3369X 9=30321 1865X 7=-13055i 8689 )89788(10 8689 2898 30 days a month. 86940(9 78201 Ex. 3. A merchant bought the following bill of goods on 6 months credit: Jan. 1, $60; Jan. 19, $80; Jan. 25, 30; Feb. 19, $225, and March 10, $100). At what time must'a note for the whole amount be dated so that the buyer shall have 6 mos. credit? RULE.-Multiply each charge by the number of days from the date of the first charge to its own date; divide the sum of the products by the sum of the charges, and the quotient will be the average time from the first charge. days. Jan. 1st, $60X00-00000 " 19, 80X18 — 1440 "' 25, 30X24= 720 Feb. 19, 225 X49=11025 Mar. 10, 100X68= 6800 Sum of products, 495 )19985 40 days. Therefore the note must be dated Feb. 9, counting from Jan. 1, the $60 will have no time of credit. 64:EQUATION OF PAYMENTS. Ex. 4. A bought a bill of goods March 11, 1869, to the amount of $1980, on a credit of 4 months, and made the following payments: April 7, $500; May 15, $250, and June 20, 300; when should he pay the balance'? Ans. Sept. 22d. RULE.-Multiply each sum by its time of payment and divide the sum of products by the balance remaining unpaid. days. 1980 500X95 —47500 1050 250X57= —14250 - 300X21= 6300 930bal. unpaid. 1050 930)68050 73 days. The equated time for the payment of the above bill is 73 days from July 11th, which will be Sept. 22d, averaging accounts bearing interest at 6 and 7 per cent. RULE.-Multiply each item of debt and credit by the number of days from its entry to the time of settlement. Divide the sum of the products on each side by 6000 if 6 per cent., and 5143- if 7 per cent., and the quotients will be the interest due on the respective side. Finally, substract the amount of the small side from that of the greater and the remainder will be the true balance. Henry A. Warren in account with Geo. W. Warren. 1869 Feb. 1, To mdse 35')s0 1869 Feb. 2q, By cash, 13600 " Mar 15, "n I 255.10 " May 1,, " 16500 "' Apr. 24, " I 660 0? 5, " " 217(0 What is the amount due Aug. 1st, 1869, at 6 and 7 per cent.? *See page 49. EQUATION 01 P&YMEN'Is. 65 To find the amount due at 6 per cent. days. Drs. j days. Crs. 850.00 X 1S1635000 136.00 X 162'-22032 255.OOX [39 —3.544500 165.00X 92=1518000 660.00X 996534000 215.00X 88=1892000 27.35 int. 9.35 int. 6,000)16413,500 6,000)5613,200 #127.35 1 525.35 $9.35 1292.35 525.35 $767.00 ans. at 6 per cent. To find the amount due at 7 per cent. 350.00 136.00 255.00 16X5.00 660.00 215.00 31.91 int. 10.91 int. $1296.91 $526.91 526.91 $770 00 ans. at 7 per centL Sum of products, Sum of products, Dr. side. Cr. side. 5143) 16413500 5143)5613200 $31.91 $10.91 Ex. 5. A bought a bill of goods, amounting to $560, April 3d, on 30 days time, and made the following payments; when in equity should he pay the balance? April 7, $75 12, 30 " 17, 65 75X26-1950 30X21= 630 65 X 161040 170 390)3620(9 days. 560 3510 170 110 390 bal. unpaid. 5 66 AVERAGE. The equated time for the payment of the above bill is 9 days from May 3d, which will be May 12th. The fraction of a day is never regarded in business operations. AVERAGE. RULE.-If the sum of the quantities of different values be divided by the number of those quantities, the quotient is called the average of the given quantities, or their mean value. If there are but two quantities, their mean value is the half sum of the values of those quantities. Ex. 1 At one of the public schools (of Rutland, Vt.) the number of pupils in attendance on Monday was 694; on Tuesday 675; on Wednesday 681; on Thursday 653; and on Friday 622. What was the average attendance for that week? Ans. 665. 694 675 681 653 622 [5 is the )3325 number quantities. - 665 Ex. 2. If No. 1 marble cost 80 cents per superficial foot, and No. 2 cost 45 cents per superficial foot; what is the average cost? 80 45 2 is the )125 number of quantities. -- 62 1-2 ans. AVERAGE OF STORAGE. 67 AVERAGE OF STORAGE. RULE. —Multiply the number of barrels or boxes, as the case may be, by the number of days they are in store, and divide the sum of the products by 30, or any other sum agreed upon. The quotient will be the number of articles on which storage is charged for the term. If the fraction is less than one-half, reject it; but if contains more than one-half, regard it as an entire article. Ex. 1. What will )be the cost for the storage of flour at 6 cents per barrel, which was received and delivered as follows? Received May 1, 1869, 2000 bbls. " "s 26, " 4000 " Delivered M ty 16, 1869, 1000 bbls. " June 1, " 2000 " " " 12 " 2200 " " July 2, " 800 " bbls. dys. prod. 1869. May 1, Received 2000 X 15= 30000,' " 16, Deliv'd 1000 Bal. 1000 X 1C= 10000 " 26, Received 4000 Bal. 5903 X 5= 25000 " June 1, Deliv'd 2000 Bal. 3000 X 11 — 33000 " 12, Deliv'd 2200 Bal. 800 X 2C= 16000 July 2, Deliv'd 800 3,0)11400,0 3800 Chargeable for 1 mo. 3800 bbls. a e C —i28, the ans. 68 DOMESTIC EXCHANBE. DOMESTIC EXCHANGE. Domestic Exchange is the act of remitting bills to places in the same country, and when the drawer and drawee both live in different countries it is called a foriegn bill of exchange. By this means debts are discharged more conveniently than by cash remittances payable at sight or after sight. At Sigbt, means at time of its presentation to the person ordered to pay. After Sight, is requiring payment to be made at the time specified in the draft or bill. Drawer, one who draws a bill. Drawee, one on whom a bill is drawn. Payee, one to whom a note is payable. RULE.-For Sight Drafts, if at premium, multiply the face of draft by the increased rate per cent., and if at a discount, multiply the face of the draft by the decreased rate per cent. For Draft payable after sight, find the interest of $1 where the draft is purchased; then add the rate of exchange if at a premium, or substract when at a discount; and multiply the face of the draft by this result. Ex. 1. A merchant in New York wishes to remit DOMESTIC EXCHANGO. 69 to New Orleans $5742.50, exchange 1 1-2 per cent. below par; what must he pay for a bill? Ans. $5656.36. 100 per cent. is written thus, 1.00 1 1-2 " " " ".01.5 98 1-2 " and.9'.6 5742. 50.985 5656.36.250 Point off the same decimals in the product as Er. 2 in Insurance, page 11. Ex. 2. A merchant at Chicago wishes to pay a bill at sight in New York amounting to $4582, and finds that exchange is 1 1-4 per cent. premium; what must he pay for a bill? 100 per cent. is written thus, 1.00 1 1-4 " " ".01.25 101 1-4 " and " " 1.01.25 e;d g~ 4582.00 1.01.25 4639.27.5.! 00 Point off in the product the same number of decimals as in Ex. 4 in Banking, page 58. Ex. 3. What will be the cost in Syracuse, N. Y., of a draft on Albany for $800, payable at sight, exchange being 3-4 per cent premium? Ans. $806. 70 DOMESTIC EXCHANGE. 100 per cent is written thus, 1.00 00 3-4 " " " " 00.75 100 3-4 " and " " 1.00.75 Xor X 1st method. 2d method.'., 1.00.75 4.2)800 800 400 $8U6,0000 Ans. 200 600 800 $806.00 What costs for a bill on Buffalo for $550, at 5-8 of 1 per cent. discount? 550.01 8)5.50 at 1 per cent. 550. 0.6875 3.4375 5 $546.5.255 $3.43.75 Ex. 4. At sight pay to the order of Wm. F. Smith fifty-five hundred eighty-eight dollars, value received, and charge the same to GEO. R. CHAPMAN. SUGGESTION.-Since Exchange is 2 per cent. premium, the draft is worth the amount stated in it and 2 per cent besides We therefore find 2 per cent. of $5588. 5588.00.02 111.76.00 5588. $5599.76 ans. DOMESTIC EXCHANGE. 71 Point off in the product the same as as Ex. 8 in Percentage, page 3. Ex. 5. A merchant in St. Paul orders goods from New York amouliting to $659, which amount he remits by draft, exchange being at a premium of 2 3-4 per cent; if he pays $27.64 freight, what will the goods cost him in St. Paul? Ans.$ 695.51.5. 100 per cent is written thus, L00 2 3-4 "s " " ".02.75 102 3-4 i" and " " 1.02.75 orC Z: Ct 1.0275 650.00 51375000 61650 667.87.5000 We add freight, 27.64 $695.51.5 Point off in the product the same decimals as Ex. 3, 1st method, 2d product, page 36. Ex. 6. What will be the cost in Kalamazoo, Mich., of a draft on Hartford, Conn., for $600, payable in 60 days after sight, including grace, exchange at a premium of 2 per cent.? Ans. 604.65. 2)100 100 1.0 01.225 1000 98775 50 Add 2 per et. prem. 6)1.050 int. at 6 per cent. 1.00775 175 600 01.225 is 1 cent, 2 mills $604.55.000 ans. and 25 hundredths of a mill. 72 DOMESTIC EXCHANGE. Interest is 7 per cent in Michigan. Point off in the product the same number decimals as in Ex. 4, 1st method, Commission and Brokerage, page 36. Ex. 7. What will be the cost in Boston of a draft on Cincinnati for $560, payable in 30 days after sight, allowing grace? what is the cost of the above draft, exchange at a premium of 3 per cent.? Ans. 573.72. 2)100 5 500 50 5.5.0 int. is 5 miIIs and 5 tenths of a mill at 6 per cent. 100.0055.9945 Add 3 per cent. rate of exchange. 1.0245 560.00 61470000 51225 573.720000 Point off in the product the same as Ex. 5, p. 71. Ex. 8. A flour dealer in Worcester receiving from his agent in Milwaukee 350 bbls. flour at $5.25'per bbl., in payment for which he remits a draft on Milwakee at 2 3-4 per cent. discount. The freight on his flour cost $70; what must he sell it per barrel to gain $100? DOMESTIC EXCHANGE. 73 100 per cent is written thus, 1.00 2 3-4 " " " ".02.75 97 1-4 " and " ".9725 3850 a X y5.25 1837.50.9725 1786.96.8750 70.00 freight. 100.00 gain. 350)1956.96 $5.59 Ans. Point off in the 1st product the same as Ex. 3, 1st product, 1st method, page 54, and in the 2d product the same as Ex. 5, page 17, and in the quotient the same as Ex. 1, page 38. Ex. 9. A merchant in Boston purchased a draft on St. Louis for $400, payable in 30 days after sight; what did it cost him, allowing grace, exchange 1 1-2 per cent discount? Ans. $391.80 2)100 100 5 00.55 500.9945 50 Deduct 15 =1 1-2 rate of ex. 5.5.0 int., the same.9795 as Ex. 7, page 72. 400 $391.83.00 Point off in the product the same as in Ex. 5, p. 71. To find the Face of a Draft a given sum will purchase: 74 EXCHANGE WITH ENGLAND. RULE.-The same as in The Proceeds of a note to Find the Face, page 60. Ex. 10. What draft may be purchased for $487.20, exchange at 1 1-2 per cent. premium? 100 per cent is written thus, 1 00 1 1-2 " "'' 0 10.5 101 1-2 " andl " " 1.01.5, ~ m1.015)487.200 cJ sl $480 ans. Annex a cipher to the right of the dividend to make the same number decimals equal to those in the divisor. See rule and example, page 40. Ex. 12. What draft may be purchased for $$158.40, exchange at 1 per cent. discount? 100 99)158.40 -- $160 ans. 99 EXCHANGE WITH ENGLAND. A Foreign Bill of Exchange may be defined a written order; the drawer and drawee live in different countries. Enrgland and France are the principal countries with which United States have exchanges. In Great lBritain accounts are kept in Pounds, Shillings, Pence and Farthings. The Pound Sterling, or Sovereign, is received at the custom house in payment of duties at $4.84 The exchange is 4.44 4-9 To which we add 9 per cent. premium, 40 $4.84 4-9 EXCHANGE WITH ENGLAND. 75 To change English Sterling money to U. S. money, divide by 9-40 and the quotient will be dollars. To change dollars into English Steiling money, multiply the dollars by 9-40 and the product will be Pounds Sterling. To find the decimal of a Pound Sterling, multiply the decimal by as many of the next lower d(enomination as makes one of the given denomination. Point off from the product as many decimal places as are in the given decimal. Proceed thus to the lowest denomination; the figures on the left of the points are the value of the decimal. Ex. 1. What must a merchant in Boston pay in dollars and cents for a bill of ~3765 15s. 61. on Liverpool, the premium 9 per cent.? 15.6 1 penny is 1-240 of a pound. 12 pence a shilling. 186 (age, p. 1. 240)18600 two ciphers annexed. See rule in Percent-) 775 reduced to a decimal. 100 per cent. is written thus, 1.00 9 " " " ".09 109 " and " " 1.09 o, 8765,775 40 9)350631,030 38959 1.09 $42465.31 ans. Ex. 2. Henry Kinsman of New York, has eonsigned a cargo of coal, valued at ~18000, to Geo. W. 76 EXCHANGE WITH ENGLAND; Warren, of Liverpool. Wm. F. Smith, of New York, is about importing flour; has purchased of H. Kinsman a bill of exchange at 7 per cent. premium for the value of the above coal; what should be paid for the above bill? 80000 18000.07 40 5600.00 9)720000 80000 5600 $856.00 Ex: 3. J. M. Jones of Boston, has the net proceeds of a consignment amounting to $7000, which he is desirous of remitting to his principal in London. For what amount in Sterling money must he purchase a bill-exchange, 9 per cent.? Ans. ~1444 19s. 100 per cent. is written thus, 1.00 9 " " " ".09 109 " and " " 1.09 1.09)1575.00(1444 109 o 7000 9 per cent. 485 436 4.0)6300.0 490 1575 436 540 436 104 20 shillings pound. 109)2080 19s. EXCHANGE WITH ENGLAND. 77 Ex. 4. What is the par value in Federal money of Z248 16s. 6d.? Ans. $1105.88.8 240)19800 248,825 166 -- 40 12 825 - -- 9)9953,000 198 1105.888 Ex. 5. Geo. R. Chapman, of Vermont, wishes to turchase a bill of ~18761 10s. on Liverpool-premium 1-2 per cent.; what will be the cost of the bill? Ans. ~20356 4s. 6 1-4d. 100 per cent. is written thus, 1.00 18761.50 8 1-2... ".08.5 1.085 1081-2 and' " 1.085 20356.22750. 240 j12000(50 227 decimal of a pound. 1200 20 shillings a pound. i? 20110 12 0 4,540 -- 12 pence a shilling. 24i0 6,480 4 fairthings a penny. 1,920 Ex. 6. How many dollars, cents and mills in ~29 4s.? 4.84 pound sterling. 24 1-5 is 1 shilling. 29 4 shillings. 140,36 96 96.8 0.8 $141.32.8 ans. 96.8 78 EXCH.iNGE WITH FRANCE. EXCHANGE WITH FRANCE. Accounts in France are kept in francs and centimes. The mercantile value of some of the principal coins of France in United States currency is as follows: The Double Napoleon or Louis, 40 francs, - 7.40 The franc, 100 centimes, is - - - - 18.6 Ex. 1. If Chas. Chapman, of Boston, should remit to Paris 18400 francs, exchange 1 1-2 per cent. premium, what will be the cost of his bill in U. S. currency? Ans. $34737.36. 100 per cent. is written thus, 1.0 11-2 " " ".01.5 1011-2 " " " " 1.015 184000,A3 k;f.186=-1 franc. 34224,000 1.015 34737.36.0000 Ex. 2. What must a merchant in New York pay for a bill on Havre for 7000 francs-exchange 5 francs, 8 centimes for a dollar? 5 8-100 7000 100 100 508 )700000 $18779.52 Ex. 3. What is the value of a bill on Paris for 44000 francs-exchange 2 per cent. below par? DISCOUNT ON BILLS AND INVOICES. 79 100 per cent. is written thus, 1.00 2 4 " " " ".02; 98 " and " ".98 44000 5d p, c.186=18 cents, 6 mills. 8181,0t~0.98 $8020.32.000 Ex. 4. Henry A. Warren remits to Paris $12350the exchange 5 francs, 10 centimes for a dollar-required the amount in francs? 5 10-100 100 510 510X12350-=1.00)2985.00 100 100 1 62985 francs, ans. DISCOUNT ON BILLS AND INVOICES. Merchants and traders deduct a percentage from Invoices and Bills of goods sold for ready pay. RULE.-Reckoned the same as Interest. Ex. 1. A bought a bill of goods amounting to $962, on 6 mos. credit, but B offers to deduct 15 per cent. for ready pay; what is the amount to be deducted? 96200 Ans. $144.30.15 144.30.00 Ex. 2. A sells B an invoice of goods for $1500, and 80 DISCOUNT ON BILLS AND INVOICES. allows him 3 per cent. for ready pay; what amount must A receive? 1500.00 1509 00.03 ~L5.00 45.00.00 $1455.00 Ex. 3. A sells B 100 bbls. flour at $6 per bbl., and allows him 2 per cent. off for cash; what amount must A receive? 100 per cent. is written thus, 1.00 2 "'& " ".02 98 " and " ".98 a M~ 1st method. 2d method. P, 100 100 6.00 6.00 600.~0 600.03 600.00.02.98 1200 12.0003 $588.0000 $588.00 Point off from the first product the same as Ex. 11, in Loss and Gain, p 22, and in the 2d product the same as Ex. 10 in Percentage, p. 4. Ex. 4. If the gross price of one pair of shoes cost 1.75, what is the net cash, less 17 and 6 per cent.? No. 1. No. 2. 1.75 1.75.17 per cent. 2975 145 087.29.7.5 1.45.25.06 $1.36.3 ans..08.7.150 No. 1 we point off the same number decimals as in Ex. 8, in Percentage, p. 3. The product of 2 the same as Ex. 4, pages 58-9. We prefix one cipher to the DISCOUNT ON BILLS AND INVOICES. 81 product of No. 2 to make the number of decimal places equal to those in the factors. Ex. 5. A sold goods, $312), to be paid one-half in 3 months, and the other half in 6 months; what must be discounted for present payment? 100 1.5 2)3120.01.500 interest 1 1-2 cents. 1560 100 on $1, 3 months. 1,015)1560,000 1536,945 100 3.0 -- 3120.03.0.00 —-3 cts. int. on $1, 6 mos. 1536,945 100 1583,055 1.03)1560.00 1514,563 1514,563 $68,492 ans. Ex. 6. A sells B an invoice of marble to the amount of $4059.63; what will be the amount of his bill, less 1-6 and 3 per cent? 6)4059.63 4059.63 3383.03 676.60 101.49 676.60=1-6 the amt. 3383.03 $3281.54 ans..03 101.49.09 Point off in the product the same as Ex. 8, in Percentage, p. 3. Ex. 7. A receives $10.50 for his work; what will he receive, discounting 15 per cent? Ans. 8.92.5. 6 t82 DISCOUNT ON BILLS ANDI INVOICES. 100 per cent. is written thus, 1.00 15 " " " "'.15 85 " and " ".85 a ~ 10.50 I;:.85 v-4 8.92.50 See p. 3, Ex. 8, for pointing off the decimals from the product. Ex. 8. A merchant bought an invoice of goods amounting to $43.60, on 30 days credit; what will he pay on his bill if paid within 30 days at 1 per cent. discount? 43.60 43.60 1 per cent. is written thus,.01 43.43.60 $43.17 ans. Ex. 9. What will 29 feet of belting come to at 82 cents per foot, less 25 and 8 per cent.? No. 1. 29.82 No. 2. 4)23.78 17,83.5 5.945 —1-4.08 per cent. 17.835 1.42.680 1.426 $16.40.9 ans. See Ex. 11, p. 17 for pointing off the decimals from 1st product No. 1, and in No. 2 see Ex. 2, p. 11. WOOD PER CORD. 83 WOOD PER CORD. Multiply the length by the height and divide the product by 32* (if the wood is 4 feet long) the quotient will be the number of cords. If there are inches, reduce them to a decimal by the following RuLE.-Divide the numerator by the denominator; annex as many ciphers to the numerator as may be necessary. Point off as many places in the quotient as there were ciphers annexed to the numerator. Ex. 1. How many cords of 4 foot wood are there in a pile of wood 32 feet long and 4 feet 2 inches, or 2-12 high? Ans. 4 cords, 17 hundredths. 12)200 4.17=4 ft. 2 in. high, nearly. 32 feet long..17 re-) duced to a 832)133.44 decimal. ) 4.17 Ex. 2. How many cords are there in a pile of wood 4 feet wide, 12 feet long and 4 feet high? 12 4 32)48 1 1-2 cords the ans. Ex. 3. What is the cost and how many cords are there in 6 piles of wood measuring as follows: Ans. $565.16. 66 9- cords. *Divide by 82, because it takes so many superficial feet to make a cord. 84 WOOD PER CORD. 1 pile wood 144 1-2' feet long, 10 feet 2 inches (or 2-12) high —45.923 cords at $9= 413.30 1 pile 61 ft. long, 6 ft. high=11.43 cords at $7.25= 82.86 1 do 39 ft. long, 4 1-2 ft. high-.=5-48 cords at $8.00- 43.84 I do 4 ft. long, 4 ft. high==0.50 cords at $7.0 — 3.75 1 do 8 ft. long, 4 ft. hight —=1.00 cord at $7- 7.00 1 do 14 ft. long, 6 ft. high=2.62 cords at $5.50 14.41 12)200 _-~~~~ t$565.16.17 reduced to a decimal. 144.,5=1441-2 ft long. 39 ft. long. 10.17 4.5 —=4 1-2 ft. high. 32) 1469.565 32)175.5 45.923 5.48 9.00 per cord. 8.00 per cord. 413.30700 $43.84.00 61 ft. long. 8 ft. long 6 ft high. 4 ft. high. 32)366 32)32 11.43 1 7.25 per cord. 7.00 per cord. $82.86.75 $7.00 4 ft. long. 14 ft. long. 45.92 4 ft. high. 6 ft. high. 11.443 -- - 5.48 32)16.00 32)84 0.50 1.00 0.50 2.62 2.62 7.50 per cord. 5.50 per cord. - 66.95==66) $3.75.00 $14.41.00 (cords, 95-100 CUSTOM HOUSE BUNESS. 85 CUSTOM HOUSE BUSINESS. Duties are sums of money assessed by government upon imported goods. A Specific Duty is a certain sum per ton, hundred weight, pound, hogshead, gallon, square yard, etc. An Advalorem duty is a certain per cent. on the cost of the goods in the country from which they are imported. A Port of Entry is a port designated by law where goods from a foreign country may be landed. In the custom house weight and guage of goods, certain deductions are made for the hogshead, box, cask, etc., containing the goods, also for leakage, breakage, etc. These deductions must be made before the Specific Duties are imposed. Gross Weight is the whole weight of the goods, together with that of the casks, bags and boxes which contain them. Draft or Tret is allowance made for waste which is to be deducted from the gross weight, and is as follows: On 112 lbs. it is I lb. From 112 " to 336 " 20 " " 336 " to 1120 " 4 " " 1120 " to 2016 " 7 " Above 2026 " anywt. " 9" Consequently 9 lbs. is the greatest draft allowed. 86 CUSTOM HOUSE BuSINESS. Tare is allowance made for waste for the weight of the hogshead, box, bag, cask, etc. It is to be deducted from the remainder of any weight or measure after the Draft or Tret has been allowed. Net Weight is the weight of the goods after deducting the weight of the box, bale, etc., making aII other allowances, customary Tare or liquors in casks is sometimes allowed on the supposition that the cask is not full, or what is called its actual wants and then an allowance of 5 per cent. for leakage, (a tare of 10 per cent. is allowed on porter, ale or beer in bottles, for breakage,) and 5 per cent. on all other liquors in bottles. SPECIFIC DUTIES. RULE.-First, deduct from the given quantity of goods the legal allowance for draft, tare, breakage or leaxkage. Second, Multiply the remainder by the duty on a unit of the weight or measure of the goods, and the product will be the duty required. Ex. 1. What is the speeififc duty on 120 barrels of figs, each weighing 84 lbs., gross tare, on the whole 680 lbs., at 4 cts per pound? Ans. $376. 120 84 10080 680 lbs. tare. 9400.04 cts. per pound. 37600 CUSTOM HOUSE BUSINESS. 87 Ex. 2. What is the duty on 396 bottles of Porter at 6 cents per bottle, allowing 10 per cent. for breakage? No. 1. Ans. $256.62. 396 12 No. 2. 4752 4752 10 per ct. for breakage. 475 47520 4277.06 cents per bottle. 256.62 In the last product of No. 1 we point off from the product the same as Ex. 11, p. 17, and in the product of Ex. 2, same as No. 9 p. 4. Ex. 3. What is the duty on 6 bbls. of Spanish tobacco, the first weighing 174 lbs. gross, the second 154 lbS. gross, the third 122 lbs. gross, the fourth 140 lbs. gross, the fifth 50 lbs. gross, the sixth 112 lbs. gross, at 6 cts. per pound, the customary allowance being made for draft and 16 lbs. per barrel Ans. $29.12. 16 lbs. per bbl. for tare. 174 6 bbls. 154 122 96 Ibs. tare. 140 50 112 752 4 lbs. draft. 748 96 lbs. tare. 652 net weight..06 cts. per pound. $39.12 Point off from the product the same as Ex. 2, last product of No. 1. 88 CUSTOM HOUSE BUSINESS. Ex. 4. What is the duty on 6 pipes of Port Wine, gross guage as follows: No. 1,162 gals., No. 2, 142 gals., No. 3, 118 gals., No. 4, 144 gals., No. 5, 158 gals., go. 6, 110 gals.; wants of each pipe 4 gals., duty 15 cts. per gallon, allowing 2 per celit. waste. 834 6 pipes. 162.02 4 gals. each pipe. 142 - - 118 16.68 24 gals. 144 158 110 834 24 810 16.68'793.32 15 cts. per gal. 118.99.80 Ex. 5. What is net* weight of 6 boxes sugar weighing as follows, tare 15 per cent.: 2480 ~o lbs. No. 1. No. 2. 29.6 456.15 480 520 441.90 480 470 540 2946 gross wei _ht. 6X4_ 24 draft. 2922 441.90 2480.00 net weiglht *See p,. 86 explaining net weight. CUSTOM HOUSE BUSINESS. 89 See Ex. 9. p. 4, for pointing off from the product of No. 1. Ex. 6. What is the net weight of a hogshead of sugar weighing, gross, 1250 lbs., tare 12 per cent.? 1243 1250.12 7 lbs. draft. 149.16 1243 149 1094 lbs., ans. Point off from the product the same as Ex. 5, No. 1. ADVALOREM DUTIES. Advalorem duties are estimated upon the actual cost of the goods. It is plain that they are found by simply multiplying the cost of the goods by the given per cent. Note.-In advalorem duties no deductions of any kind are to be made. Ex. 1. What is the advalorem duty at 28 per cent. on 30 yards of English broadcloth which cost $4.75 per yard? Ans. $39.90. 4.75 30 142.50.28 per cent. duty. 39.90.00 Ex. 2. What is the advalorem duty at 20 per cent. on a piece of Turkey carpeting, containing 145 yards, and cost $1.88 per yard; what is the duty on one yard? For how much must it be sold, per yard, to gain 25 per cent. on the cost and duty? Ans. $2.82. 90 FEDERAL MONEY. 100 per cent. is written thus, 1.00 25 " " " ".25 125' and " " 1.25 ", ~ ~ 188 145 yds. d 37.6 1.88 2.25.6 272.60 1.25.20 2.82.000 $54.52.00 duty advalorem. cost 1.88 per yard. 20 per cent. duty. Duty on 1 yd. is 37.60=-37 cts. 6 mills. Ex. 3. What is the duty on an invoice of goods which cost in London ~964 sterling at 44 per cent. advalorem? The pound sterling being $4.84. Ans. $2052.93. 964 4.84 4665.76 1st product..44 per cent. duty. $2052.93.44 2d product. FEDERAL MONEY. Federal currency of the United States was established by Congress in 1786. Its denominations are eagles, dollars, dimes, cents and mills. To read Federal money, call all the figures -on the left of the decimal point dollars, the first two figures on the right of the point cents, the third figure mills, the other places on the right decimals of a mill. Thus, $4.26.2.32 is read 4 dollars, 26 cents, 2 mills and 32 hundredths of a mill. ASSESSMENT OF TAXES. 91 ASSESSMENT OF TAXES. Assessment of taxes is a sum imposed on an individual for a public purpose. A pole tax is a specific sum assessed on male citizens above'1 years of age; each person assessed is called a poll. Taxes are usually assessed either on the person or property of the citizens, and sometimes on both. Property is of two kinds, personal property and real estate. Personal is movable property, such as money, notes, cattle, furniture, etc. Real estate is unmovable property, such as land, houses, stores, etc. An Inventory is a list of articles. RULE.-First find the amount of tax on all the polls, if any, at the given rate, and substract this sum from the whole tax to be assessed. Then divide the remainder by the whole amount of taxable property in the State, county or town, etc.; the quotient will be the per cent., or tax on one dollar. Second, multiply the amount of each man's property by the tax on one dollar, and the product will be the tax on his property. Third, add each man's poll tax to the tax he pays on his property, and the amount will be the whole tax. Proof.-Where a tax bill is made out, add together the taxes of all individuals in the town, district, etc., and if the amount is equal to the whole tax assessed, the work is right. 92 ASSESSMENT OF TAXES. TAB LE. $1 pays.03 $ 20 pays.60 $ 300 pays $9.00 2 ".06 30 ".90 400 " 12.00 3 ".09 40 " 1.20 500 " 15.00 4 ".12 50 " 1.50 600 " 18.00 5 ".15 60 " 1.80 700 " 21.00 6 ".18 70 " 2.10 800 " 24.00 7 ".21 80 " 2.40 900 " 27.00 8 ".24 90 " 2.70 1000 " 30.00 9 ".27 100 " 3.00 2000 " 60.00 10 ".30 200 " 6.00 4000 " 120.00 In making out a tax list by the preceeding table containing the taxes on 1, 2, 3, etc., to 10 dollars, then 20, 30, to 200 dollars, then 300, 400, to 4000 dollars; then knowing the inventory of any individual it is easy to find the tax on his property. Ex. 1. In the above assessment, what is a man's tax who is rated at $2256, and pays for 3 polls at 50 cents each. Operation. $2000 pays 60.00 $200 " 6.00 $50 " 1.50 $6 i.18 3 polls 1.50 $69.18 ans. Now if we add together the tax paid on each of these sums as found by the preceeding table the amount will be the tax on $2256. Ex. 2. A township composed of 16 citizens, levies a tax of $5700. The town contains 30 polls which are assessed 50 cts. each, and its taxable property is inventoried at $199,500; what amount of tax must ASSESSMENT OF TAXES. 93 be raised to pay the debt and 5 per cent. commission for collection, and what is the tax on a dollar. Ans., the sum to be raised is $6,000, and the, tax is 3c. on the dollar. 100 per cent. is written thus, 1.00 5 " " " ".05 95 " and " ".95)5700.00 50 6000 6000 C t 30 15 15.00 5985 (p. 1. Multiply by 100 see rule in Percentage,) 199500)5985.00 0.03 Point of from the quotient the same as Ex. 2, p. 26, No. 3. A tax of $29505 is levied on a certain county whose property is valued at $1,125,750, and which has a list of 11,650 polls, which is assessed at 60 cents apiece; what per cent is the tax and what is the amount of A's tax who pays for 6 polls and has property valued at $5625? 11,650 polls. 60 cts each. 29,505.00 6990.00 $6990.00 Whole sum of taxable prop'ty, 1,125,750)22515.00 0.02 cts. on the dol. 5625.02.60 6 polls. 112.50 3.60 3.60 $116.10 Amount of A's tax. 94 ASSESSMENT OF TAXES. Ex. 4. If a tax of $750 is assessed on a district to build a new school house, the property of the district is valued at $15,000; what is the tax on the dollar, and what is a man's tax whose property is valued at at $1150? 1150 15000)750.00.05 0.05 cts. on the dol. $57.50 Ex. 5. If my town tax is 25 per cent. on my grand list, and I pay 50 cts. tax, what is the amount of my grand list. 50 100 25)5000 Ans. $2.00 Ex. 6. If my grand list is $185.72, what is the amount of the following taxes made upon the grand list of 1870? Town tax of 76 per cent. is -. - 141.14 Union tax of 15 " - - - - 27.85 Dis. No. 19, 30 " " - - - 55.71 Village corporation 18 per cent. is - - 33.42 Amount of tax is - - - - $258.12 185.72 185.72 185.72 185.72.76 15..30.18 141.14.72 27.85.80 55.71.60 33.42.96 Point off from the prodncts the same as Ex. 8. p. 3. Ex. 7. What is the amount of my tax on $5675 at 7-l0ths of 1 per cent? Ans. $39.72.5. 5675.00.01 —-1 per cent. 56.75.00 at I per cent..7= 7-10 " 39.72.500 at 7-10 per cent. ASSESSMENT OF TAXES. 95 Point off in the 1st product the same as Ex. 6, 2d product, page 38; and in the 2d product the same as Ex. 2, page 11. Ex. 8. [ he city of Chicago levied a tax of 1-8th of 1 mill on all real and personal property; what is the amount of tax on $7500? Ans. 93 cts., 7 mills. 7500.00.001-=1 mill. 8)7.50.000 0.98.750 The decimal places in the dividend exceed those in the divisor by 5, hence we point off 5 decimals from the quotient; all the figures at the right of the point will be cents and mills. Ex. 9. A tax of $3900 is to be assessed on the town of Rutland. The real estate is valued at $840,000, and the personal property at $210,000; and there are 500 polls, each of which is taxed $1.50;-what assessment on $1? 840000 1.50 210000 500 1050000 $750.00 3900 750 3150 100 1050000)3150.000 0.003 mills ans. Ex. 10. What is A's tax, whose real estate is valued at $74.36, and his personal property at $3215, and who pays for 6 polls? 96 ASSESSMENT OF TAXES. 1.50 7436 6 3215 9.00.0 10651.003 31.953 9.00 $40.95.3 Ex. 11. A certain district paid $130 for teacher's salary, $34 ior board, $19.42 for fuel and $2.58 for repairs; the district drew $30 public money, and the whole number of days' attendance was 2400; what was the rate per day? and how much was A's tax, who sent 115 days? 130. teacher's salary. 34. " board. 19.42 for fuel. 2.58 " repairs. 186.00 30 156.00 11.5 days. 100.065 2400)1560.000 $7.475 A's tax..06.5 ans. To find the percentage see Rule, page 1. The decimal places in the dividend exceed those in the divosor by. three, counting the cipher annexed; hence we point off three decimal places in the quotient; all the figures at the right of the.point will be cents and mills. ASSESSMENT OF TAXES. 97 ASSESSMENT OF TAXES TO RAISE A GIVEN NET AMOUNT. RULE.-Subtract the given per cent. from $1, and the remainder will be the net* value of $1 assessment. Divide the net amount to be raised by the net value of $1 assessment, and. the quotient will be the sum assessed. Ex. 1. Allowing 5 per cent. for collection, what sum must be had to raise $12425, net? 100.95)12425.00 5 -- $13078.947 ans..9.5 net value of $1. SIMPLE PROPORTION. Simple Proportion is called the Golden Rule from its excellent performance in arithmetic or in other points of mathematical learning. And it is called the Rule of Three, because from three numbers given proposed, or known, we find out a fourth number required, or unknown, which leaves such proportion to the third as the second does to the first number. To find out a fourth proportional to three given numbers placed thus, 4:8::6 6 4)48 12 *Clear of all charges. And multiply the second and third numbers together and divide by the first; the quotient is 12, which leaves the same proportion to 6 that 8 does to 4. Ex. 1. If 24 lbs. butter cost $5.29, what is the plice Of albs? 24: 3:: 5Q9 24)1587 66 1-8 cents the ans. RULE wPrH EXAMPLE.-In this question there are two things mentioned, butter and money, is the answert-o the question to be given in butter or money. You see at once it is to be given in money. Put down the money, $5.29, for the third term. Having done this, you have now to consider where you are to place the 21 lbs. and 3 lbs. Read over the question and you will see that the anewer must be less than the third term; for 3 lbs. will not cost as much as 24 lbs. If, then, the answer is to be less, put the less number for the second term, and the greater for the first. In all questions let the third term be the same as the answer, and it the answer is to be greater than the third term, put the greater second; if it is to be less, put the less second. Ex. 2. If 11 yards makes 2 rods, how many rods are there in 1617 yards? 11:1617::2 2 11)3231 294 rods. 8IIPLZ PgOPOT'Ol. g' The answer to the question is to be given in rods; place rods for the third term. The answer 2 is to be more than the third term, therefore place the greater number for the second term, and the less number for the first. Ex. 3. If 21 barrels of flour cost $180, what wiUl 112 barrels cost at the same rate. 21: 112:: 180 112 21)20160 $9.60 ans. Ex. 4. What will 136 feet of wood come to at $4 per cord? 128: 136:: 4.30 4.00 128).544.00 $1.25 ans. 128 cubic feet in a cord (of wood. Ex. 5. What will 22 inches of beaver cloth come to at $2.50 per yard? 36: 22:: 2.50 22 36)55.00 $1.52 7-9 ans. 1 yd. is 36 inces long. 100 COMPOUND PROPORTION. COMPOUND PROPORTION. When, in order to find a fourth proportional, several circumstances require to be considered, it is called Compound Proportion. Ex. 1. If 14 horses eat 56 bushels of oats in 16 days, how many bushels will be required for 20 horses 24 days? 14:20:: 56 16 24 224 480 56 224)26880 120 bushels ans. RULE WITH EXAMPLE.-Write down for the third term that number which is of the same kind with the answer required -56 bushels. Then take two numbers of the same kind, 14horses and 20 horses, and consider, as in Simple Proportion, whether from the nature of the question, the greater or less is to be put in the first or second term. Here it is obvious that the greater must be in the second term, as 20 horses will eat more than 14 horses. Take the other two terms and proceed in the same manner. After all the terms have been put down, multiply the first terms, 14 and 16, together; do the same with the two 2d terms, 20 and 24, and that product by the third term, 56, and proceed as in Simple Proportion. COMPOUND PROPORTION. 101 Ex. 2. If 8 men can reap 32 acres in 6 days, how many acres can 12 men reap in 15 days. 8m.: 12n.:: 32 6d. 15d. 48 180 32 48)5760 120 acres ans.. Ex. 3. If 100 gain $6 in 12 months, what will $400 gain in 8 months? 100: 400:: 6 12 8 12 0 3200 6 1200)19200 $16.00 Ex. 4. If $100 gain $6 in 12 months, in what time will $400 gain $16? 400: 100:: 12 6 16 2400 1600 12 2400)19.200 8 months ans. Ex. 5. If 12 horses, in 5 days, draw 44 tons of stone from a qnarry, how many horses would it require to draw 132 tons in 18 days? no BOARDS. 44: 132:: 12 18 5 792 660 12 792)7920 10 Ex. 6. A garrison of 1500 men has provisions for 12 weeks, at the rate of 20 ounces per day to each man, how many men will the same provisions maintiu for 20 weeks, allowing each man only 8 ounces per day? 8: 20::.500 20 12 160 240 1500 160)360000 2250 men ans. BOARDS. RuLE.-Multiply the length in feet by the width in inches, divide the product by 12, the quotient will be the number of square feet. Boards or plank that tiper gradually, add the width of the two ends together, and -half theirJsum, multiplied by the length, will be the number of square feet. Ex.. 1. How many square feet in a stock of 15 botrds, 12 feet 8 inches long, 13 inches wide? See rule in Duodecimals. 10$ 12 8' 1 1 1 0' 8" 12 8' 13 8' 8" 15 205 10' ans. Ex. 2. How many square feet are there in a board 18 feet long, 10 inches wide? 18 10 12)180 sq. in. 15 sq. ft. Ex. 3. How many square feet are there in 660 boards, each 16 feet long and 6 inches wide? 16 feet long. 660 boards 6 inches wide. 8 ft. in a board. 12)96 5280 ans. 8 ft. in each board. Ex. 4. How many feet, board measure, are there in 1440 ft. of 1 1-4 inches thick? 4)1440 360 1800 t ans. Ex. 5. What length must be out of a board 8 1-2 inches broad to contain a square foot? RuLE.-Divide 144 by the inches in breadth, and the quotient will be the length of that board that will make a foot. 81-2 inverted 17)288 2 2X144=288 16 -7 11 II Bn16 - 17 17 17 Ans. 17 2 104 PLANK, JOISTS ANDT SCANTLINGS. Ex. 6. How many square feet are there in a board 18 feet long, 13 inches wide at one end, and 17 inches wide at the other. 13 18 17 15 2)30 12)270 15 221-2 ft. ans. PLANK, JOISTS AND SCANTLINGS. Ex. 1. How many feet, board measure, that is, one inch thick, are there in a stock of 15 inch plank; 12 ft. 8 inches long, 2 ft. wide and 2 inches thick? feet. inches. 12 8' 2 0' 25 4 of I inch thick. 2 inches thick. 50 8' of 2 inches thick. 15 plank. 760 0' ans. Ex. 2. How many feet, board measure, are there in 9 plank, 1 foot wide, 3 inches thick, length as follows: 1st method; 12 12 2d method. 12 3ps 3X12=12 ft long=108 14 2ps3X12=14 " = 84 14 lps3X12=-16 "' 48 16 l3ps X 12=18 " =162 18 -- 18 2d ans. 402 18 134 linear feet. 3 inches thick 402 feet 1st ans. JOISTS AND SCANTLINGS. 105 JOISTS AND SCANTLINGS. Ex. 1. How many feet, board measure, are there in 20 joists, 10 feet long, 6 inches wide and 2 inches thick? 10 ft. long. 6 inches wide. 60 2 inches thick. 12 inches a foot)120 10 ft. in each stick. 20 joists. 200 ft. ans. Ex. 2. How many feet, board measure, are there in 13 sticks of scantling, 13 feet long, 2X4. 13 ft. long. 4 inches wide, 52 2 inches thick. 12 inches a foot)104 8 8P 13 sticks. 112 ft. 81 ans. TIMBR, ER. Ex. 1. How mafty feet, board mteasure, are there in 12 stcks eof timber 12X12, lengths as follows, viz:12, 12, 14, 16, 16, 18, 18, 22, 22, 21 and 26, and 4 sticks 12X 14, lengths as follows:-16, 16, 16 and 16? 1st method. 2d method. 12X12 2 ts. 12X 12X 12-288 12 1" 12XI2X14X168 12 2" 12X12X16 —384 14 3" 12X12X18==648 16 2" 12X12X22= —528 16 1" 12X12X24=288 18 1" 12X12X26 — 312 18 4" 12X14Xl16 —896 18 22 2d ans. 3512 22 24 12X14 26 1; -- 16 218 linear feet. 16 12 inches wide. 16 2616 64 linear feet. 12 14 inches wide. 12)31392 896 12 inches thick. 2616 - 896 12)10752 3512 1st ans. 896 Ex. 2. How many feet, board measure, are there in 20 car sills, each 30 feet long, 5 1-2 by 10 1-2 inches, and how many feet, board measure, are there in 18 car sills, 5 by 7 inches, by 29 feet long? Ans. to the 1st, 2887 40-100 feet. " " 2d, 1522 44-100 feet. ORMA. IM 30 ft. long. 29 ft long. 5.5=5 1-2 inches thick. 5 inches thick. 165.0 145 10.5=10 1-2 in. wide. 7 inches wide. 12)1732.50 12)101.5 144.37 84.58 20 sills. 18 car sills. 2887.40 1522.44 Ex. 3. What is the solidity of a tapering square stick of timber, the largest end being 14 inches square, the lesser end 10 inches square, the length 40 feet? RuLE.-Square the two ends, add together the area of the two ends, and one-half their sum, multiplied by the length, and divided by 144, will give the solid contents. 14 10 14 10 195 100 148 100 40 feet long. 2)296 144)5920 41 1-9 feet ans. 148 Ex. 4. If a piece of timber be 8 inches square, what length of it will make a foot. RULE.-Multiply one by the other, and let the product be a divisor to 1728. 8 8 64)1728 27 inches long ans. 108 TIMBER. Ex. 5. How many cubic feet are there in a stick of timber 15 feet three inches long, 2 feet 4 inches wide, and 1 foot 8 inches thick? How many feet, board measure? 15 3' 35 7' 2 4' 20 inches thick. 5 1't 0" 71 8 ans. to the2d. 30 6' 35 7' 1 8t 23 8' 8" 35 7' 59 3' 8" ans. to the 1st. Ex. 6. How many feet, board measure, ir 41 sticks of timber, 20 feet long, 10' by 10'. 20 feet long. 10 inches wide. 200 10 inches thick. 12 inches a foot)2000 166,66-=1 66 66100 ft. in each stick. 41 sticks. 6833.06 CARPETING ROOMS. 109 CARPETING ROOMS. RULE.-Multiply the length in feet by the width in feet, and divide the product by 9, the quotient will be the number of yards if the carpet is one yard wide. If less than one yard wide, we first find how many pieces we want, then multiply them by.the width of each piece in inches the product will give the width of room in inches, and that product by the length of room in inches, and divide the product by the number square inches in a square yard, the quotient will be the number yards. Ex. 1. How many yards of carpeting, one yard wide, will it take to cover a floor 18 feet square. 18 18 9)324 36 yards ans. Ex. 2. How many yards carpeting, one yard wide, will it take to cover a floor 16 feet 5 inches long, and 13 feet 7 inches wide? 13 it'it wide. We add 1 " 5' to make full width of pieces. Making 15 " 0' width of room. 16" t' length of room. 9)246 " 3' 27 y 3 sq. ft. 3 inches. me PTKaTBERIN -ROOMS. Ex. 3. How many yards of carpeting, 3-4 yard wide, will it take to cover a floor 18 feet long and 15 feet wide? 15 feet wide. 12 inches a foot. Car. 27 in. wide.)180 62-3 To which we add 1.3 to make full width of piece. 7 0' pieces. Each piece, 27 inches in width. 189 inches width of room. 216 " length " 972)40924 42 yards ans. 18 ft. long. 1 yd. 36 in. long. 12 in. a ft. 27 in. wide. 216 972 square in's. in a square yd. PLASTERING ROOMS. Painting, plastering, paving and some other kinds of work are done by the square yard. If the contents in square feet be divided by 9, the quotient, is evident, will be square yards. Ex. 1. What will it cost to plaster a room 20 feet 6 inches long, 18 feet wide and 10 feet high at 12 1-2 ets. per square yard? Amn. $15.81 PFlTWO RhOW& 1* Overhead. 20 1. feet long. 201-2 feet long. 10 " high. 18 " wide. --, -- 205 369 2 sides. 410 18 ft. wide. 360 10 ft. high. 369 180 9)1139 2 sides - 126.55=126 55-100 sq. yds. 360.125-12 1-2 cts. $15.81,875 PAINTING ROOMS. Solid bodies being frequently painted, it is necessary to know how to find their superficiality. To find the superficial contents of a square or many sides, or round pillar, multiply the sum of the sides, or circumference, by the height in feet, and the product, divided by 9, will be square yards. Proper Directions for Joiners, Painters, Glaziers, etc. Rooms being varied in their form,.take this general rule in all cases, viz: Take a line and apply one end of it to any corner of the room; then measure the room, going into every corner with the line till you come to the place where you first began; then see how many feet and inches the string contains, and set down for the compass or round; then.take the height by the same method. 112 PAPERING ROOMS. All kinds of work, such as cornice, mouldings, etc., are measured by running measure. Ex. 1. A man painted the walls of a room 8 feet 2 inches in height, and 72 feet 4t in compass, (that is, the measure of all the sides); how many square yards did he paint? See rule in Duodecimals. 72 4' 8 2' 12 0' 8" 578 8' 9)590 - 81 8"f 65 yds 5 sq ft 8"f PAPERING ROOMS. Ex. 1. How many yards of papering that is 30 inches wide, will hang a room that is 65 fect circuit 12 feet high, deducting 1-4 for doors and windows? 30 inches wide. 65 86 " long=1 yard. 12 in a foot. 1080 780 144 sq. inches sq. ft. 4)112320 28080 1080)84240 78 yards ans. FLOORING ROOMS. 11$ FLOORING ROOMS. There is a house containing 2 rooms, each 16 feet by 15 feet 4 inches, a hall 24 by 10 feet 6', 3 bedrooms each 11 feet 4t by 8 feet, a pantry 7 feet by 9 feet 6', a kitchen 14 feet 2f by 18 feet, and two chambers, each 16 feet by 20 feet 8'; what did the work of flooring cost at 2 cents per square foot? 16 0' 24 0' 11 4' 15 4' 10 6' 8 0' 5 4' 0" 12 0' O" 90 8' O Cr 240 3 rooms. 245 41 252 0' 272 0' 2 rooms. 16 0' 490 8t 20 8' 14 21 10 8' 18 0t 320 0' 255 0' 30 8' 2 rooms. 7 0(f 661 4' 9 6t 2.55 0t 66 6t 3 Cq 0" 490 8t 63 C' 252 0' 272 0' 666' - 1997 a.02 cts. per sq foot. $39.95 ans. W4 ILATUTEG LOOMn. LATEING ROOMb. Lathing is done mostly by the squnare yard. A Ilneh of lathing generally contains from b50 to 100 strips, each 4 leet long and 1 1 2 inches wide, makiag 10 feet, (allowing 100 strips to a bunch) will spread,. after they are ailed on, about 63 feet, which makes 7 square yards. - Ex. 1. How many feet in a bnneh of lathing containing 100 strips each, 4 feet long and 1 1-2 inches wide? 4 feet long. 1 1-2 inches wide. 6 square inches. 100 strips. 12)600 square inches. 50) square feet ans. Ex. 2. How many bmnches of lathing 4 feet long 1 1-2 inches wide, (containing 100 strips t, will it take to lath a room 20 feet 6 inches long, 18 feet wide and 10 feet high, allowing 63 feet to a bunch? 18 feet wide. 20 1-2 feet long. 10 feet high; 10 feet high. 180 205 2 sides. 2 sides. 360 410 length. 360 width. 20 1-2 feet long. 369 overhead. 18 feet wide. 63)1139 869 18 5-63 ans. GLAZIEIS WOf:K. 1its GLAZIERS WORK. RvIm. —To find the dimensions of their work, multiply the height of windows by their breadth. Glaziers are to take the depth and breadth of their work, multiply one by the other, dividing by 1414. Glass being measured as boards. If the windows are arched or have a curved form, no allowance is made by reason of the extraordinary troubtle and waste of time, expense, or waste of glass, etc. Dimensions taken from the highest part of the arch down to the bottom of the windows from the height or length which, multiplied by the breadth, the product will be the answer in feet, etc. Ex. 1. There is a house which contains 22 windows, each window has 12 lights of 13 inch by 10 inch -glass; what will the glazing work come to at 12 cents per square foot? Ans. $28.59. 13 inches long. 10 " wide. 130 12 lights in a window. 15ti0 22 windows. 144) 4s320 238,33,12 cents per square foot. $28,59,96 Point off from the last product the same as Ex. 8, p. 3. 116 TO MEASURE ROUND TIMBER. TO MEASURE ROUND TIMBER. RULE.-Multiply the length in inches by the square of 1-4 the girth in inches, and the product divided by 1728 will give the contents in cubic feet. If a tree or timber is tapering, girt it about 1-3 of the way, at the two ends, and divide the sum by 2 to obtahil the mean girth. Allow on:account of hbark, in oak 1-10 or 1-12 of the circumference; beech, ash, etc., should be less. Ex. 1 A stick of tenmber is 18 feet long and 56 inches girt; how many cubic feet does it contain? 4) 6 14 - 14 14=14 the girt. 196 216 inches long. 17'28)42336 24 1-2 feet ans. TO FIND THE BOARD MEASURE IN A LOG. RULE. —Subtract 4 from the diameter in inches, (which is takenl at the smaller end), multiply by onehalf the difference, and that product by the length in feet, and divide by 8. Ex. 1. If the diameter of a log is 16 inches, and I:t length is 20 feet, how many feet, board measure, does it contain' 16 inches in diameter. 4 12 6=half the difference. 72 20 feet long, 8)1440 180 feet ans. o o SIZE OF SLATE MANUFACTURED BY THE EAGLE SLAt' E COMPANY. Z ~ C, = Q Q = X s.5 X - = a C, _ C. o - z ct = CD s cs d = Et *- - *- _J a O * | O z 0 _- _ C 14X 7 874 t6X 8 277 I8X 9 213 20X10 169 22X11 137 24X12 114 5 14X 8 8'37 16X 9 296 18X10 192 20Xll 154 22X 12 126 24X13 105 8 - 14X 9 290 16XX10 221.[18Xll 174 20X12 141 22X1 116124X14 98 14X10 261 18X12 160 24X16 85. s Z 12X 8 400 o 12X 7 457 Co __ -....O a m o11 9 1E18 CUBIC NZEASURE. SLATING ROOFS. Ex. 1. How many slates, 10X10, will it take to cover one square, (that is 100 square feet). 144 in. in a squire foot. 100 square feet. 65)14400 221 7-13 slates ans. 16 inches long. Deduct 3 inches for underlap. 2)1:3 6 1-2 inches to the weather. 10 " wide. 65 square inches. Ex. 2. How many squares are there on both sides of a roof whose ridge is 30 feet long and rafters 20 feet long; how many slates, 18X10 i:,ches, will it take to cover both sides of the roof; including the undercourse? Ridge, 30 feet long. 12 inches a foot. Slate 18 in. long.)360 sdes. 20 slates for undercourse oln!&13th) 2 sides. 40 slates for undercourse oi( 1,otlh) Ridge 30 feet long. 20 " long, rafters. 600 2 sides. 100)1200 12 squares, ans. to first. '0VlW UlzsUnaa. fi 192 slates to a square by the table. 12 squares. 2204 40 slates for undercourse. 2244 Ans. to the last. SHINGLES FOR I SQULRIE. Ex. 3. How many shingles, 4 inches wide, and laid 3 1-2 inches to the weather, will it take to lay a square? 4 144 inches in a square foot. 3 1-2 100 square feet. 14 square inches. 14)14400 1028 4-7 shingles, ans. PERCHES IN CELLAR WALL. Mason's work is sometimes estimated by the perch of 16 1-2 feet in length, 1 1-2 feet in width and 1 foot in height. A perch contains 25.75 cubic feet. If any wall be 1 1-2 feet thick, its contents, in perches, may be found by dividing its superficial conte*ts by 161-2 feet, but if it be any other thickness than 1 1-2 feet, its cubic contents must be divided by 24.75 (24 34) to reduce it to perches. Joiners, painters, plasterers, bricklayers and masons sometimes estimate their work by the girt; that is, the length of the wall on the outside. Ex. 1. The side walls of a cellar are each 32 feet M6 long, the end walls 24 feet 6t, and the whole 7 fel; high and 11-2 feet thick; how many porches of stone 120 CUBIC MEASURE. are required, allowing nothing for waste, and for how many perches must the mason be paid for? Ans., 45 9-11 perches in the work. The mason must be paid for 48 4-11 perches. Length of side walls on the outside. 32 6' Ler gth of end walls 7 0' on the outside. 24. 6 227 6' 7 0' 2 sides, 171 6t 455 0 2 ends. 343 343 0' 16.5)7980 24 6' length of end walls. 48 4-11 Deduct 3 (t fbr thickness. 21 6' 7 0' 150 6' 2 ends. 301 (0 455 16.5)7560 45 9-11 ans. CUBIC YARDS IN CELLAR WALL. Ex. 1. The side walls of a cellar are each 32 feet 60 long; the end walls in the inside are 22 feet long, and the whole 7 feet high and two feet thick, and for how many cubic yards must the mason be paid for? Ans. 56 51-100 cubic yards. CUBIC MEASURE. 121 32 6' ft. long, side walls. 22 (I ft. long, end walls. 7 O' ft. high. 7 0' 227 61 154 0' 2 0' feet thick. 2 ft. thick 455 C( 308 0' 2 sides. 2 ends. 910 c( 616 0' 910 0 27 cu. ft. in a yd.)1526 56.51 How many cubic yards in the above walls, extending the length of the end walls to the center of both side walls. Ans. 58 59-100 cu. yds. 32 C' long, side wlIls. 22 0' long, end walls. 7 C' high. 2 C' which is the center of side walls. 227 {' 24 0' 2 al ft. thick. 7 C0 feet high. 4~55 0' 168 0' 2 sides. 2 0f thick. 9'0 0 336 0 672 2 ends. 27)1582 672 O' 58.59 cu. yds. ans. Note. —lhe masons are sometimes allowed to the center of the side walls. BOARDS TO COVER A HOUSE. Ex. 1. How many feet of boards will it take to cover the walls of a house 40 9-12 feet long, 30 1-2 feet wide, and 20 feet high, allowing 5 per cent. waste? ne w OUBTC` X;StIRU. 40 3-4 feet long. 30 1-2 feet wide. 20 feet high. 20 feet high. 815 610 2 sides. 2 sides. 1630 1220.0.5 per cent. 1630 81.50 2850 81 2931 feet, ans. BRICKS FOR THE WALLS OF A HOUSE. Ex. 1. How many bricks, 8 inches long, 4 inches wide and 2 inches thick, will it take to build the walls of a house which is 80 tAet long, 40 feet wide and 25 feet high, the wall to be 12 inches thick'? Ans. 159300 bricks. 40 feet wide. Deduct 2 feet for thickness of wall. 38 960 in. long 12 in. a foot. 300 in. high. 456 in. wide. 288000 300 in. high. 2 sides. 136800 576000 2 sides. 12 in. thick. 273600 6912000 12 inches thick. 3283200 6912000 1728 cu. in. in a cu. ft.)10195200 5900 cubic feet. 27 bricks in a cubic foot. 159300 bricks. Some masons allow 23 bricks in a cu. ft. in mortar. CUBIC MEASURUI 1' BRICKS FOR FLOORING ROOM. Ex. 1. How many bricks, 9 inches long, 4 inches broad, will it take to floor a room 20 feet square? 9 inches lon1g. 20 feet long. 4 " broad. 20 " broad. 36)144 in. a sq. ft. 400 4 bricks in a sq. it. 4 bricks in a sq. ft. 1600 bricks, ans. BUSHELS IN BIN. RULE.-Reduce the cubic feet to cubic inches, then divide by the number of cubic inches in a bushel, which is 2150.4; the quotient will be the answer. Ex. 1. How many bushels of grain will a bin hold 48 feet long, f16feet wide and 14 feet deep? 48 feet long. 16 feet wide. 768 14 feet deep. 1075'2 1528 cu. in. in a cu. ft. 2150.4)18579456.0 8640 To find the number of bushels, heaped measure, divide the number of cubic inches by 2747.7. GALLONS IN A BARREL. Ex. 1. How many wine gallons in a cistern, which is 6 feet long, 5 feet wide and 4 feet deep. Ans. 897 gals., 2 qts., 1 pt., 1 gill. 124 VULGAR FRACTIONS. 6 feet long. 1728 cu. in. in a cu. ft. 5 " wide. 120 cu. ft. 30 231)207360(897 4 feet deep. 1848 120 2256 2079 1770 1617 153 4 qts. gal. 612(2 462 150 2 pts. qt. 300(1 231 69 I gills pint. 276(1 231 VULGAR FRACTIONS. A fraction is a part of any thing and is represented by two numbers, one above the other, and the oilier below it; thus, 2 3 read one-half, two-thirds and three-fourths. The figure above the line is called the numerator; the figure below the line is called the denominator. VULGAR FRACTIONS. 125 The fraction 4-5 read four-fifths, the four is the numerator and the five is the denominator. The denominator makes the number of equal parts into which the whole number is divided; the numerator shows the number of those intended to be expressed by the fraction thus: if we say that if we have 2-3 of an apple, we mean that the apple was divided into three parts and that we have two of those parts. A proper firaction is that which its numerator is less than its denominator, as - 2 4 An improper fraction is that which has its numera37 8 tor greater than its denominator, as 2 4 5 A compound fraction is a fraction of a fraction, as is expressed by 2 or more fractions, as or3f 2 of 4 A mixed number is a whole number with a fraction annexed, as 21-2, 4 2-3, 16 4-5. Any whole number may be made a fraction of by writing a 1 under it. A complex fraction is one which has a fraction in its numerator or denominator or both, as 2 1-2 4 2 1.3 5 51-3 83-4 ADDITION OF FRACTIONS. RuLE.-Multiply each numerator by all the denom. inators, except its own, for a numerator, aud all the denominators together for a common denominator. ift A.DDIlX10 Or PRACfTL1O. Ex. 1. What is the sum of 3-5 and -6? 8 5 3X0=-"18 43 new numerator 5X6 — 30 new denominator. Ex. 2. What is the sum of 1-2, 2-5, 3-4 and 2-3? 1X5X4X3= 60 the numerator for 1 2. 2X2X4X-= 48 " " 2-.5. 3X5X2X3= 90 it " 3-4. 2X4X5X2- 80 " " "2-3. 278 120)278 2X5X4X3=120 - 2 19-60 Ex. 3. What is the sum of 1-20 and 1-35? 1X35= 35 1X20-= 20 5)55 (tl red'd to its lowest terms. 20X35= 700 140 Note.-The numerator cannot be divided by the denominator. The two numbers are reduced to its lowest terms, that is 5 will divide them without a remainder. WHOLE NUMBER AND MIXED MUMBER. RULE. —Reduce them to improper fractions and then proceed as before. Ex. 4. What is the sum of 12 and 1-2? 41-2 9X 12 2 2 1 9 red'd to an improper fraction. 9X)1 — 9 2 12X2 —24 2)33 33 16 1-: ans. - ADirn ON io TFRaCTIOnS. TWO MIXED NUMBERS. Ex. 5. What is the sum of 41-2 and 51-2 9 4 1-$ 51-2 9X2=18,2 2 11 X2 —22't, 1 1 40 4)40;02 2X2= 4 10 ans. COMPOUND FRACTIONS. Ex. 6. What is the sum of 2-3 of 1-8, 3-5 of 6-3 and 8-7? 2 of 1=2 -3 of 6=18 2 18.8;3 24 5 3 15 24 15 7 2X15X 7= 210 18X24X 7=3024 8 X 15X24=2880 2520)6114 6114 2; 179-420 ans.;1X 15X 7= —-520 Ex. 7. How many feet are there in 6 sides of leather measured as follows: 81-4 ft., 6 1-2.f., 7 3-4 t., 8 3-4 ft., 91-2 it. and 14 3-4 ft? 8 feet 1= 8 1-4 feet. 6 " 2:=612.. 7 " 3= 734 8 " 3= 83-4 " 9 " 2 —9 1-2 " 14 " 3=1434 " 55 2" -— 5 1-2 " In the 1st column there are 14 quarters —3 1-2 feet, which we carry the 3 feet to the column of feet, maklug 55 1-2 feet, ans. 198 ADDITION OF FRACTIONS. TO FIND THE GREATEST COMMON DIVISOR:. RULE.-Divide the greatest number by the less; then divide the divisor by the remainder, and so on, dividing always the last divisor by the last remainder until nothing remains. A common divisor of two or more numbers is a number which will divide each of them without a remainder. Thus, 3 is a common divisor of 9, 15 and 18. The greatest common divisor of two or more numbers, which divide each of them without a remainder; thus, 24, 36, {8, can be divided by 2, 3 or 4, but their greatest common divisor is 12. Ex. 1. What is the greatest com. div. of 69132 ~ Operation. 3132)6912(2 6264 648):3132(4 2592 540)648(1 540 108)540(5 Ans., 108 is a divisor common to both terms. SUBTRACTION OF FRACTIONS. 129 SUBTRACTION OF FRACTIONS. RULE.-Subtract their numerators, where they have a common denominator, otherwise they must first be reduced to a common denominator. Ex. 1. From 3-5 take 14. 3tX4=12 1 x<5= 5 3*-1 7 5 4 20 ans. Ex. 2. From 12-15 take 8-5. 12-8=-' ans. 15 15 15 IEx. 3. From 18-27 take 3-9. 18X 9=162 3X2= — 81 81) 81(1-3 27X 9 —-243 ans., WHOLE NUMBER AND A. FRACTION. Ex. 4. From 20 take 3-5. 20X5-100 20-3 3X1= 3 1 5 97 5)97 X5 — 5 19 2-5 ans. TWO MIXED NUMBERS. RULE.-When one mixed number is to be subtracted from another, we may reduce both numbers to an improper fraction, and then to a common denominator. * —Sign of subtraction. tx sign of multiplication. 9 130 MULTIPLICATION OF FRACTIONS. Ex. 5. From 9 1-4 take 7 34. 91-4 7 3-4 4 4 37-31 37 31 red'd to an improper frac. 4 4 4 4 37X4=148 31 X 4 —124 24 16)24 16 1 1-2 ans. WHOLE NUMBER AND A MIXED NUMBER. Ex. 6. From 5 take 4 1-2. 4 1-2 5 X 2 —10 2 5-9 9X1= — 9 9 1 2 1 ans. 2 1X2- 2 MULTIPLICATION OF FRACTIONS. RULE.-Prepare the fractions as previously required, multiply the numerators together for a new numerator, and denominators together for a new denominator. MULTIPLY A FRACTION BY A FRACTION. Ex. 1. Multiply 4-5 by 7-8. 4-X7-4)2( 7 ans. 5 X8 40 10 MULTIPLY A FRACTION BY A WHOLE NUMBER. RuLE.-Multiply the numerators of the fraction by the whole number and write the product over the denominator. *Sign of multiplication. MULTIPLICATION OF FRACTIONS. 131 Ex. 2. Multiply 21-30 by 15. 21X15 —315 30)315 30 1 30 101-2 ans. WHOLE NUMBER AND A MIXED NUMBER. RULE.-Multiply the whole number by the denominator of the fraction, and to the product add the numerator, then set that sum above the denomator. Ex. 3. Multiply 50 by 4 1-2. 41-2 2 9 50X9-450 21450;2 1 2 2 225 ans. TWO MIX NUMBERS. Ex. 4. Multiply 125 1-2 by 7 3-4. 125 1-2 7 34 2 4 251 31 2451 X31=7781 8)7781 2 4 2 4 8 972 5-8 ans. 33x. 5. If one yard broad cloth cost $4 50, what will 1-8 of a yard cost? What will 1-16 cost? Ans. to the 1st, 56 1-4 cts. Ans. to the 2d, 28 1-8 cts. 1X450=8)450= —- 56 1-4 cts. 8 1 8 1 X 450 —16)450 16 28 1-8 cts. 132 DIVISION OF-FRACTIONS. DIVISION OF FRACTIONS. RULE.-Prepare the fractions as in multiplication; then invert the divisor and proceed as in multiplication. DIVIDE A FRACTION BY A FRACTION. Ex. I. Divide 42-54 by 24-35. 42 -:2 inverted thus, 42X35 1470 54 35 54 24 1296 1295)1470 129-216 ans. Ex. 2. Divide 4-7 by 3-5. 3-5 inverted thus, 4X5=20 7 3 21 COMPOUND FRACTIONS. When compound fractions occur in the divisor or dividend, they must be reduced to simple ones, and mixed numbers must be reduced to an improper fraction. Ex. 3. Divide 3-4 of 2-3 by 21-3. 2 1-3 3 3 of 2 —6 reduced to 7 4 3 12si'le ones, improper frac. 6X7 inverted thus 6X3=6)18(3-14 ans. 12 3 12 7 84 DIVISION OF, FRACTIONS. 138 WHOLE NUMBER AND A MIXED NUMBER. Ex. 4. Divide $28 by 3 1-2. 1st method. 3 1-2 2800 2 2 7 -7)5600 2 $8.00 ans. 2d method. 28X7 inverted thus, 28X2 —56 7)56 1 2 1 7 7 8 ans. TWO MIXED NUMBERS. Ex. 5. Divide 8 2-3 by 3 1-2. 8 2-3 3 1-2 3 2 26 7 inverted thus, 26X22=-52 26 7 S 2 3 7 21 3 2 21)52 2 10-21 ans. The numerator represents the dividend and the denominator the divisor. DIVIDE A FRACTION BY A WHOLE NUMBER. RULE.-There are two ways; 1st, divide the numerator by the whole number (if it will contain it without a remainder), and under the quotient write the denominator. Otherwise multiply the denominator by the whole number, over the product write the numerator. Ex. 6. Divide 21-25 by 7. 7)21 3-25 ans. 134 ADDITION OF DECIMAL ]BRACTIONS. DIVIDE A WHOLE NUMBER BY A FRACTION. RULE.-Multiply the whole number by the denominator, and divide the product by the numerator. Ex. 7. Divide 75 by 5-9. 75 9 5)675 135 ans. Ex. 7. Divide 120 by 10 3-4 120 10 3-4 4 4 43)480 43-4 11 7-43 ans. ADDITION OF DECIMAL FRACTIONS. RULE.-Write the numbers so that the same order may stand under'each other; placing tenths under tenths and hundredths, etc. Begin at the right hand or lowest order, proceed in all respects as in adding whole numbers. The decimal point in the answer will always fall directly under the decimal points in the given number. Ex. 1. What is the sum of 3,5; 25,467; 125,4 and 2,466? 3,5 25,467 125,4 2,466 156,833 ans. ADDITIro ot D0CIMAL fRaCTtOS, 135 Write the units under units, tenths under tenths, hundredths under hundredths, etc.; then beginning at the right hand or lower order, proceed thus: 6-thousandths and 7-thousandths are 13-thousandths. Write the 3 under the column added and carry the 1 to the next column, as in addition of whole numbers; one to carry to 6-hundreths makes 7-hundreths, and 6 are 13-hundreths, set the 3 under the column and carry the 1 as before; 1 to carry to 4-tenths make s 5 and 4 are 9-tenths, 4 are 13-tenths and 5 are 18-tenths or 1 and 8-tenths. Set the 8 under the column and carry the 1 to the next column. Finally, place the decimal point in the amount directly under that number added. Decimal fractions are commonly expressed by writing the numerator only, with a point (.) before it, called the decimal point, thus: 9-10 is written thus,.9 99-100 " ".99 999-1000 " ".999 The denominator to a decimal fraction, although not expressed, is always understood, and is 1 with as many ciphers annexed as there are places at the right hand of the point, thus:.99 is a decimal of two places, consequently 1, with 2 ciphers annexed, (100), is its proper denominator. 136 SUBTRACTION OF DECIMAL FRACTIONS, SUBTRACTION OF DECIMAL FRACTIONS. RULE.-Write the lower number under the greater with units under units, tenths under tenths and so on. Subtract as in whole numbers. Ex. 1. From 26,467 subtract 14,18 26,467 14,18 12,287 Having written the less number under the greater, units under units, etc.; thus, 0-thousandths from 7-thousandths, leaves 7-thousandths, with the 7 in the thousandths place; as the next figure in the lower one is larger than the one above it, we borrow 10. Now 8 from 16 leaves 8; set the 8 under the column and carry 1 to the next figure. Proceed in the same manner with the other figures in the lower number; place the decimal point in the remainder under that in the given numbers. Ex. 2. From 16 take 1.5 16.0 1.5 14.5 ans. Ex. 3. From 1 take.125. 1 0125.875 ans, Ex. 4. From.56078 take.40003..56078.40003.16075 ans. MULTIPLICATION OF DECIMAL FRACTIONS. 137 MULTIPLICATION OF DECIMAL FRACTIONS. RULE.-We multiply as in whole numbers and point off as many decimals in the product as there are decimal figures in both factors. Ciphers on the left of decimals do not effect their value. The 0 may be omitted. Ex. 1. Multiply.48 by.5..48.5.240 Ex. 2. Multiply 8.46 by.25 2.1150 Ex. 3. Multiply.045 by.03..045.03.00135 In the example No. 3, there are 5 decimal places in the factors and only three figures in the product, therefore two ciphers are placed at the left of the product to make the number of decimal places equal to those in the factors. DIVISION OF DECIMAL FRACTIONS. RULE.-Divide as in whole numbers. Point off as many decimal places in the quotient as the dividend has more than the divisor. When the decimal places in the divisor exceed those in the dividend, make them equal by annexing ciphers to the right of the dividend, and the quotient'will be a whole number. 138 DIVISION OF DECIMAL FRACTIONS. When there is a remainder, the quotient may be carried to any degree of exactness by annexing ciphers to the remainder. Ex. 1. Divide 4.7614 by 3.8. 3.8)4.7614 1.253 Ex. 2. Divide.7644 by.42. 42).7644.0182 In the first example the decimals in the dividend exceed those in the divisor by 3; three figures are, therefore, marked off in the quotient. And in the second example the decimals in the dividend exceed those in the divisor by 4; one cipher is therefore prefixed in the quotient to make four decimal places. Ex. 3. Divide.289 by 2.4. 2.4).289.12+ans. The decimal places exceed those in the divisor by 2; we point off two decimal places in the quotient. When there is a remainder the sign (+) of addition should be annexed to the quotient to show that it is not complete. Ex. 4. Divide.063 by 9. 9).063.007 ans. In this example the dividend has 3 more places of decimals than the divisor; the quotient must have 3 places of decimals. We must therefobre prefix 2 ciphers to the quotient. DECIMAL FRACTIONS. 139 TO READ A DECIMAL FRACTION. Beginning at the left hand, read the figures as if they were whole numbers, and the, last one, add the name of its order. Thus,.7 is read 7-tenths..36 " 36-hun dreths..475 " 475-thousandths..6342 " 6342-ten thousandths..57834 " 57834-hundred thousandths..284648 " 284648-millionths..8913629 " 8913629-ten millionths. All the figures which come before the point are whole yards, pounds, acres, etc., as the case may be. All which come after the point are fractions of the same. Thus, 1.7 pounds stands for 1 pound and 7-tenths of a pound; 12.3X yards stand for 12 yards, 3-tenths of a yard and 4-hundredths of a yard, or 12 yards and 34-hundreths of a yard. 140 DUODECIMALS. DUODECIMALS OR CROSS MULTIPLICATION. This rule is particularly useful to glaziers, masons, marble and slate dealers. One foot is divided into 12 equal parts, called inches or primes, and marked (). Each is again divided into 12 equal parts called seconds, and marked ("). Each second is again divided into 12 equal parts called thirds, and marked ("'). Each third is again divided into 12 equal parts called fourths, and marked ("N) DUODECIMALS. Under the multIplicand write the corresponding denomination of the multiplier. Multiply each term of the multiplicand by each term of the multiplier in succession, beginning at the lowest denomination, observing to carry a unit for every twelve from each denomination to the next higher. The sum of these partial products will be the answer required. By this rule, also may be calculated the superficial DUODECIMALS. 141 and solid contents of bodies, having the measurea of their different sides. The more easily to comprehend the ruleFeet multiplied by feet give feet. 94" " inches " inches. " " seconds " seconds. Inches " inches " " " " seconds " thirds. Seconds" " " fourths. Ex. 1. Multiply 8 feet 5' by 7 feet 3', or how many superficial feet. Ans. 61 ft. 0' 3"t. We begin on the right hand and multiply each denomination of the multiplicand, first by the inches of the multiplier and by the feet of the multiplier as follows: Feet. Inches. 8 5' 7 3' 2 11 3"1 58 11t 61 0' 3"1 super'l ft. ans. 3'X515ftt —1t 3t we write down the 3"t and reserve the 1' for the next product. Again, 8 ft. X3'==adding in the 1' which was reserved from the last product, we have 252 —2 ft. 11, which we write down entire. Again, we have 7 ft.X5-__35==2 ft. 11t; we write down the 11 under the primes of the former line, and 142 DUODECIMALS. reserved the 2 ft. for the next product; 8 ft. X7 ft. —56 ft. to which, adding the 2 ft. reserved from the last product, we have 58 feet, which we place under the feet of the former line; taking the sum we have 61 ft. 0t 3" for the answer. Ex. 2. Multiply 8 feet by 3 feet 4 inches, by 4 feet 2 inches. Feet. Inches. 8 0' 3 4' 2 8' 0"i 24 0' 26 8' 0o" 4 2' 4 5' 4"/ 0't 106 8' 0" 111 1' 4"r 0o"' Multiply as follows:-4X0=0tt we write down the 0"tt Again, 8 ft. X4=32-=2 ft. 8t, which we write down entire. Again, we have 3 ft. X —— 0; we write down the 0' under the inches of the former line; 8 ft.X3 ft.=24 ft. we place under the feet of the former line. Taking the sum we have 26 ft., 8' 0"f; again, 2'XO" =0, we write down the 0"'t; 2X8-=16 —l. / 4I, we write down the 4t and reserve the 1' for the next product. Again, 26 ft.X2' —52', adding in the 1' which was reserved from the last product, we have 53= —4 ft. 5t, which we write down entire. DUODECIMALS. 143 Again, 4 ft.X0Ot=0Ot, we write down under the seconds of the former line. Again, we have 4 ft.X8'=32_=2 ft. 81; we write down the 81 and reserve the 2 ft. for the next product. Again, 26 ft.X4 ft.=-104 ft., adding in the 2 ft. reserved from the last product, we have 106 ft. which we place under the feet of the last former line. Taking the sum, we have 111 ft. 1' 0 for the answer. Ex. 3. Multiply 7 feet, 3 inches, 2 seconds by 1 foot, 7 inches and 3 seconds. Feet. inch. seconds. 7 3' 2I" 1 7' 3" 1' 9" 9i/ 6/"1 4 2' 10"i 2/i 7 31 2i" 11 71 of/ 11mf 6Btii Multiply as follows: V2/X3t/ —=6li; we write down 6mil. Again, 3"X3'=9"'; we write down 9I"'. Again, 7 ft.X3 —=21-=-1' 9/"; we write down entire. Again, 72X2'=-14;ff-1/ 2m; we write down the 2"' and reserve the 1"t for the next product. Again, 3'X7'=211", adding in the 1" reserved from the last product, we have 22"1=1' 10"; we write down 10" and reserve 1t for the next product. Again, 7 ft.X7'-'49', adding in the 1I reserved from the last product, we have 50" —_4 ft. 2', which we write down entire. Again, 1 ft.X2t= —2/, we unite 2/t under the last former line. 144 DUODECIMALS. Again, 1 ft. x3'=3', we write down under the primes of the former line. Again, 7 ft.X1 ft.=7 ft., we write down under the feet of the last former line. Taking the sum, we have 11 ft. 7t, 9tt, 111t, 6t/1', the answer. Ex. 4. Multiply 2 feet by 11 inches by 6 inches. 2 0' 11 1 10' 0f 6t 11' Of" 0o" Multiply as follows: 11'XO'0 —"(t; we write down 0it. Again, 2 ft.X11-22'-1 ft. 10'; we write down entire. Again, 6'X0"-0"'; we write down 0"' under the last former line. Again, 10X6't=60tt — -5 0tt; we write down 0"t and reserve the 51 for the next prodoct. Again, 1 ft.X6'-6t, adding in the 5t reserved from the last product, we have 11 inches the answer. Ex. 5. Multiply 2 ft. 2 inches byl foot by 6 inches, 2 2t 1 0' 2 2 6t 1 It 0"f WDtODECIMlLS. 145 Multiply as follows: 1 ft.X2f —'; we write down 2. Again, I ft. X2 ft 2 ft; we write down. Again, 2'XX6 —12"l-l 0"; we write down the 0". Again, 2 ft.X6'12', adding in 1t which was reserved from the last product, we have 13=1 ft. 1 inch, the answer. Ex. 6. How many cubic feet are there in 3 ps. slate 2 feet by 10 inches by 6 inches? 2 2' 10W 1 9' 8"r 6' 10' 10" (Y" 3 piece s 2 8W 6" 0" ans. Multiply as follows: 2'X1O1=t0-~?Y=1' 8?"; we write down 8" and reserve the 1t for the next product. Again, 2 ft.X1O' —20, adding in the 1 reserved from the last product, we have 21-=1 ft. 9', which we write down entire. Again, 6'X8" —— 48t44" Y0"'; we write down Ot and reserve V4 for the next product. Again, 6'X9=-54", adding in 4" reserved from the last product, we have 58 —-4! 10"; we write down the 10" and reserve the 4' for the next product. Again, 1 ft.X6 ——', adding in the 4! reserved from the last product, we have 10' which we write down. Again, 3 ps.&X( —-— 0I, we write down. 10 .14 TRIANGLES TO FIND THE THIRD SIDE. Again, 3 ps.X10O" —-30'_-2 6r"; we write down the W6 and reserve the 2' for the next product. Again, 3 ps. X10' —30, adding in'2 reserved from the last product, we have 32 —2 ft. 8', which we write down entire for the answer. TRIANGLES TO FIND THE THIRD SIDE. RULiE.-First add together the square of the base and of the perpendicular, and the square root of the sum is the hypotenuse or longest side. RULE 2d-Add together the hypotenuse and any one side, multiply the sum by their difference, and the square root of the product equals the other side. Ex. 1. A wall, 36 feet high, and a ditch before it is 27 feet wide; what is the length of a ladder that will reach to the top of the wall from the opposite side of the ditch. 36 2025(45 feet ans. 36 27 16 27 1296 -- 85) 425 729 729 425 2025 Note. —A figure of the sides like that formed by the wall, the ditch and the ladder, is called a right angle triangle, of which the square of the hypotenuse, or slanting side, (the ladder), is equal to the sum of the square of the other two sides that the height of the wall and the width of the ditch. CImRCLE~. 14 Ex. t A line of 86 yards will exactly reach from the top, of a fort to the opposite bank of a river, known to be 24 yards broad; the height of the wall is required. 720(26.83 36 46)20 24 t36 276 - 24 60 - 528)4400 12 12 4224 720 5363) 17600 16089 Ans. 26 yards and 83 hundredths of a yard. CIRCLES. RULE.-To find the length of the diameter, multi. ply the length of the diameter by 3 1-7, the product will be the circumference. To find the diameter, divide the circumference by 31-7, and the quotient will be the diameter. To find the area or surface of a circle, multiply the square of the diameter by.7854, the product will be the area. Ex. 1. If the diameter is 231 feet, what is the circumference? 7)231 31-7 693 33 726 feet ans. 148 SQUARE ROOT. Ex. 2. If the circumference is 726 feet, what is the diameter? 3 1-7 726 7 7 22 )5082 231 feet ans. Ex. 3. What is the area of a circle whose diameter is 6 inches' Ans. 28 it. 6.7854 6 36 86 28.2'44 SQUARE ROOT. RULE WITH EXA.wPLE.-Divide the given number intQ periods of two zgures each by placing a point over the unit figure, and every alternate figure toward the left. Ist, Find the square root of 3 of the first period, 10, and place it in the quotient. Subtract the square of it, 9, froni the first period, and to the remainder annex the next period, 69, for a dividend. Double the root already found, 3, for a divisor, and supposing the unit figure 9, omitted, find how often 6 SqUARE gOOT. 149 is contained in the dividend. It is containtd 2 times; place the 2 in the quotient and the divisor; multiply by 2 the divisor 62, ar d subtract the product 124 from the dividend. 2d, Double the figures already found in the root for a new divisor, (or bring down your last divisor for a new one, doubling the right hand figure of it), and from these, find the next figure, in the root, as last directed, and continue operation in the same manner till you have brought down all the periods. If the divisor is not contained in the dividend, place a cipher in the root; also, on the right of the divisor, and bring down the next period. If there is a remainder after the periods are brought down, periods of ciphers may be annexed, and the figures of the root thus obtained will be decimals. Ex. I. What is the square root of i06929(327 9 proof. 62) 169 327 124 327 647) 4529 10i6929 4529 Ex. 2. What is the square root of 164? 164(12.8 ans. 22)64 44 248)2000 1984 1o0 SQUARE ROOT. Ex. 8. What is the square root of 10308921894001? Ans. 3210751. 160309sA89060(3210751 9 1st divisor 62)I30 124 2d " 641) 689 641 3d " 64207) 482198 449449 4th " 642145) 3274940 3210725 5th 6" 6421501) 6421501 6421.501 Ex. 4. What is the square root of 4-25? Ans. 2-5. 4(2 25 4 5)25 2)0 Ex. 5. What is the square root of 201-4? 20 1-4 2025(4.5=41-2 ans. 4)81 4 4)16 20.25 81 85) 425 425 4 CUBE Root. 151 CUBE ROOT. RULE WITH EXAMPLE.-Divide the given numbers into periods of three figures, beginning at the place of units. Place the cube root of the first period 2, in the quotient, and subtraet its cube, 8, from the first period, and bring down the next period for a dividend, which is 4812. To find a divisor, multiply the square of the figure placed in the quotient by 300=1200; find how often this is contained in the dividend, viz: 3 times; place the 3 in the' quotient for the second figure of the root. Multiply the part of the root formerly found, viz: 2, by the last figure placed in the root, viz: 3, and the product by 30=180; add this and the square of the last figure placed in the root to the divisor, viz: 1200. Multiply the sum of these, 1389, by the last figure placed in the root 3, and subtract the product, 4167, fiom the dividend. 4812; bring down another period for a new dividend and proceed in the same manner. Ex. 1. Find the cube root of 12812904(234 2X2 —-4X300=1200 8 2X:3=6X 30= 180 _ proof. SX3= 9 4812 234 13 9X3= 4167 234 23X23=529X300=158700 645904 54756 23X 4- 92X 30= 2760 234 4X 4= I-t= 16 -- 161476X4 —=6459044 Proof.-Multiply the root into itself twice, and if the last product is equal to the given number, the work is right. 152 CUBE ROOT. When there is a remainder, periods of eiphers may be added, and the figures of the root thus obtained, will be decimals. If the right hand period of decimals is deficient, this deficiency must be supplied by ciphers. When there are decimals in the given example, find the root as in whole numbers; then point off as many decimal figures in the answer as there are periods of decimals in the given number. If the divisor is not contained in the dividend, place a cipher in the root; also, two ciphers on the right of the divisor, and bring down the next period. In finding the cube root of a common fraction, first reduce the fraction to its lowest terms, then extract the root of its numerator and denominator. When either the numerator or denominator is not a perfect cube, the fraction should be reduced to a decimal, and the root of the decimal be found as above. A mixed number should be reduced to an improper fraction. Ex 2. What is the cube root of 27-64 Ans. 3-4. 27(3 numerator. 64(4 denominator. 27 64 Ex. 8. What is the cube root of 13 2-3? 13 2-3 3)41000000000 - 13666666666 41 3 1366666 ((2.3908 ans 8 2X2 —4 X 3001200 5666 2X3 —6X 0= 180 3X3= 9 1389X3=4167 1499666 CUBE ROOT. 153 23X2.3=59 300 —158700 23X 9207X 30= 6210 9X 9= 81 1649391 X9-1484919 147476660 239 X 239 —=57121 X 3001713300 239X 0= 239X 30= 7170 8X8 64 17143534 X 8=137148272 Ex. 4. The dimensions of a round bushel measure are 18 1-2 inches wide and 8 inches deep; what will be the dimensions of a similar measure that will hold 8 bushels? Ans. 37 inches wide, 16 inches deep. 18.5 8 18.5 8 342.25 64 18.5 8 6331625 50659(37 512 8 bu. 27 8 bu. 50653000 23653 4096 3XO-3= 9X300-2700 3X7=21X 30= 630 7X7- 49 3379X7 —23653 1X-1X= 300=300 1X6 —-X 30-180 4096(16 6X6 — 36 1 516X6= 3096 3096 3096 154 ZBMEASUREMENT OF SURFACES. MEASUREMENT OF SURFACES. How many acres are there in a farm 416 rods long and 170 rods wide? 416 170 160 rods an acre)70720 442 acres ans. Ex. 2. How many square feet are there in a lot which is laid out in a right angle triangle, the base measuring 49 feet, and the perpendicular 30 feet? 49 30 2)147,) 735 anls RULE.-Multiply the base by the perpendicular, and divide the product by 2; or multiply the base by onehalf of the perpendicular. Ex. 3. There is a lot 75 feet wide and 8 rods long, how many square rods does it contain? Ans. 36 36-100 rods. 272 1-4 sq. ft. 1 sq. rod. 16 1-2 ft. rod. 1 8 rods long. 1089 quarters. 132 75 feet wide. 9900 4 1089)39600 quarters. 36.36 MEASURBEMENT OF SURFACES. 155 Ex. 4. There is a lot of land 25 feet long and 75 feet wide, and was sold for $6575; what did it cost per square foot? 75 25 1875)6575.00 1875 sq. feet. $3.50.6 ans. Point off in the quotient the same number of decimals as Ex. 3, p. 27. Ex. 5. How many acres in a tract of land 20 miles broad and 250 miles long? 250 20 5000 640 acres in a square mile. 3,200,000 Ans., three million two hundred thousand acres. Ex. 6. What is the area of a garden which is 18 rods long and 15 rods wide? 18 15 270 rods ans. Ex. 7. How many feet in 200 yards? 200 3 feet a yard. 600 feet the ans. Ex. 8. How many acres in 21181651-2 yards? 21181651-2 2 -- inverted. 4236331 X 4 = 16945324 2 121 242 156 DENOMINAT9 NUMBERS. 242)16945324 30 1-4 sq. yds a sq. rod. 4 16 rods an acre.) 70022 - -- 121 437.63 4 Four hundred, thirty-seven acres and sixty-three hundredths of an acre. DENOMINATE NUMBERS. STERLING MONEY. 4 farthings make 1 penny, marked d. 12 pence a shilling, " s. 20 shilling make a pound, " ~ 21 " " guinea, " g. TROY WEIGHT. Troy weight is used for weighing gold, silver, jewels, etc., and for ingredients used in philosophical experiments. marked 24 grains (g) make a pennyweight, pwt. 20 pennyweights make 1 ounce, oz. 12 ounces " 1 pound, lb. AVOIRDUPOIS WEIGHT. By this weight, coarse bulky goods are weighed and, all the common necessaries of life. marked 16 drams (dr.) make 1 ounce, oz. 16 ounces make 1 pound, lb. 25 pounds make 1 quarter, qr. 4 quarters (or 100 lbs.) hundred weight, cwt'. 20 hundred weight I ton, T. DENOMINATE -NUMBERS. 157 Apothecaries and chemists use this weight in mixing medicines, but drugs are bought and sold by avoirdupois weight. marked 20 grains (g) make 1 suruple, sc. 3 scruple make 1 dram, dr. 8 drams make 1 ounce, OZ. 12 ounces make 1 pound, lb. LONG MEASURE. marked 12 inches (in.) make 1 foot, ft. 3 feet make 1 yard, yd. 51-2 yards, 16 1-2 ft. 1 rod, perch or pole, r. or p. 40 rods make 1 furlong, fur. 8 furlongs, or 320 rods make a mile, mi. 3 miles make on league, lea. 60 geographical miles or 69 1-2 statute miles make 1 degree, deg. 160 degrees make a great circle, or circumference of the earth. CLOTH MEASURE. Cloth measure is used in measuring cloth, carpeting', ribbons, etc. marked. 1-4 inches (in.! make 1 nail, na. nails, or gin, 1 quarter yard, qr. L quarters make 1 yard, yd. I qrs, 3-4 of a yard, 1 Ell Flemish, Fl. qrs., or 1 1-4 makes 1 Ell English, Ewe. i qrs., or 1 1-2 yards make 1 Ell French, F. %15 DENOMINITE NUMBERS. SQUARE MEASURE. Square measure is used for measuring surfaces, such as land, paving, flooring, plastering, boards, etc. marked. 144 square inches (sq. in.) make 1 sq. ft. sq. ft. 9 square feet make 1 square yard. sq. yd. 301-4 square yards, or 272 1-4 feet, 1 sq. rod, perch or pole, sq. r. 40 square rode 1 square rood, R. 4 roods, or 160 square rods, 1 acre, A. 640 acres 1 square mile, M. CUBIC MEASURE. Cubic measure is used in measuring solid bodies or spaces; that is, things having length, breadth and height, or thickness, such as earth, stone, timber, boxes of goods, the capacity of rooms, etc. marked 1728 cubic inches (cu. in.) make a cubic foot, cu. ft. 27 cubic feet make a cubic yard, cu. yd. 40 feet of round timber, or 50 feet of hewn make 1 ton or load, T. 42 cubic feet I ton of shipping, T. 16 cubic feet 1 foot of wood or cord foot. ft. 8 cord feet, or 128 cubic feet, 1 cord, c. BEER MEASURE Is used in measuring beer, ale and milk. marked 2 pints make 1 quart, qt. 4 quarts make 1 gallon, gal. 36 gallons make 1 barrel, bbl. 1 1-2 barrels, or 54 gallons, 1 hogshead, hhd. DENOMINATE NUMBERS. 159 LIQUID MEASURE. The standard gallon of the United States measures 231 cubic inches, and containts 833888 pounds avoirdupois of distilled water. The British imperial gallon contains 10 avoirdupois of distilled water and measures 277 1-4 cubic inches. marked 4 gills (gi.) make 1 pint, pt. 2 pints make 1 quart, qt. 4 quarts make 1 gallon, gal. 31 1-2 gallons make 1 barrel, bar. 63 gallons make 1 hogshead, hhd. 2 hogsheads mlake I pipe, pi. 2 pipes make 1 ton, ton. 16 large tablespoonfuls are 1-2 pint. 8 " " 1 gill. 4 " " 1-2 gill. 2 gills make 1-2 pint. A common sized tumbler is 1-2 pint.' 1" teacup is 1 gill. "' " wine glass is 1-2 gill. A large wine glass, 2 ounces. A tablespoonful makes 1-2 an ounce. 40 drops are equal to one teaspoonful. 4 teaspoonfuls are equal to one tablespoonful. 160 MISCELLANEOUS TABLE. MISCELLANEOUS TABLE. 12 individual things make a dozen. 12 doz, 144 units, make 1 gross. 12 gross, 1728, make 1 great gross. 20 individual things make 1 score. 56 pounds make 1 ferkin of butter. 100 pounds make 1 quintal of fish. 196 pounds make 1 barrel flour. 200 pounds make 1 barrel pork. 18 pounds make 1 cubit. 80 pounds make 1 bushel salt. 24 sheets of paper make 1 quire. 20 quires make I ream. 4 inches 1 hand-used to measure horses. 6 feet a fathom-used to measure depths at se& 3 miles a league-used reckoning distances at sea. 1 cubic foot marble will weigh 180 pounds. Marble 2 inches thick 31 1-2 lbs. for every foot. Marble 1 1-4 in. thick will weigh 20 lbs. for every foot. Marble 1 1-2 in thick will weigh 24 lbs. for every foot. Heaped bushels, anthracite coal, weighs 80 lbs. Marble 1 inch thick will weigh 15 Ibs. for every foot. 14 pounds of iron or lead make 1 stone. 21 1-2 pounds of stone make 1 pig. 1760 yards, 5280 ft. or 83 chains, make 1 mile. 5760 grains, Troy, make 1 pound Troy. 7'i00 " " " 1 pound avoirdupois. 437 1-2 " " " 1 ounce " 2711-32" " " 1 dram " 27 cubic feet for a ton of 2000 lbs. hard coal. Wheat flour, 1 pound is 1 quart. Indian meal, 1 pound is 2 quarts. Butter, when soft, 1 pound is 1 quart. WEIGUTS OP A BUSHEL PRODUCE. 161 WEIGHTS OF A BUSHEL PRODUCE. Clover seed, 60 Corn on cob, 70 Beans, 62 Barley, 48 Buckwheat, 48 Flax seed, 45 Indian corn, 56 Oats, 32 Timothy seed, 44 Peas, 60 Potatoes, 60 Sweet Potatoes, 56 Rye, 56 Wheat, 60 NUMERATION TABLE. Numeration is the art of reading numbers when expressed by figures. H Hundreds of trillions, tr Tens of trillions, - Trillions, o Hundreds of billions, T l'ens ot' billions,. Billions,.* Huudreds of millions, c Tens of millions, u Millions, v Hundreds of thousands, q Tens of thousands, 2 Thousands, cA hundreds, o* Tens, m Units. Tihe above numbers will read nine hundred and twenty-four trillions, six hundred and seventy-ono billions, eight hundred and sixty-two millions, four hundred and seventy-nine thousand, five hundred and thirty-eight. 11 162 BANKRUPTCY. BANKRU PTCY. A banlikrupt is a person who is insolvent or unable to pay his debts. Assets is effects of an insolvent person-stock in trade. Ex. 1. The liabilities of a bankrupt are $63240, and his assets are 12648; what per cent call he pay on the dollar. 12648 100 63240)1264800 20 per cent. ans. Ex. 2. A bankrupt compromises with his creditors at 64 cts on thle dollar; how much did B receive on his debt of 2563.50? 2563.50.64 $1640.64.00 Point off from the product the same as Ex. 8, p. S. Ex. 3. A man fidlcd in business owes A $1.56.45, B 256.40 and C $360.40, and his effects are valued at $317; how much will each receive? 156.4.5 773.25: 156.45:: 317 256.40 317 360.40 773.25) 49594.65 64,137 GOODS BOUGHT AND SOLD BY THE TON. 163 773.25: 256.40:: 817 773.25: 360.40:: 317 317 317 773.25) 81278.80 773.25)114246.80 -05,113 147,749 A's 64,138 nearly. 105,113 147,749 $317,000 Ex. 4. How much can a banlkrupt pay on the dol lar who has $6540 real estate, anld owes $56CC0? Ans. 11 cts., 6 mills. 6510 100 s6000)654000 11.6 Point off in the quotient in the same manner as Ex. Il, in assessment of taxes, p. 96. GOODS BOUGLIT AND SOLD BY THE TON. RULE. —Multiply the number of pounds by onehalf tile price* and divide the product by 1000, that Will point off 3 figures from the product, and two more for cents; all the figures at the l1ft hand will be dollars, and those at the right hand will be cents, To fiud the price per hundred, annex 2 ciphers to the price per ton, divide by two and point off in the quotient in the same manner as above. *Mnltiply hy one-half the price, because it cost double the price at 10U0 pounds, as it would at 2000 pounds. 164 GOODS BOUGHT AND SOLD BY THE TON. Ex. 1. What will 960 pounds of hay come to at $15 per ton? 960 pounds. 750=1-2 the price. 7.20.000 Ex. 2 What will 48040 lbs. egg coal amount to at $15.50 per ton? Ans. $372.31. 48040 7.75-1-2 the price. 372.31000 Ex. 3. What will 60 pounds of sugar cost at $6.50 per ton? Ans. 19 cents. 3.25=1-2 the priee. 60.19.500 Ex. 4. What will 1252432 tons of coal amount to at $5 per ton? 1252432 5 6,262,160 six millions, two hundred and sixty-two thousand one hundred and sixty dollars the ans. GOODS BOUGHT AND SOLD BY THE HUNERED. 165 GOODS BOUGHT AND SOLD BY THE HUNDRED. RULE.-Multiply the number of pounds by the price, divide the product by 100; that will point off two figures fiom the product, and then point off two more figures for cents; the figures at the left hand will be dollars, and those at the right will be dollars and cents. Ex. 1. Wiiat will the fieight of a box of goods come to weighing 300 lbs., at 30 cents per hundred? Ans. 90 cents. 300 30,90,00 Ex. 2. What will 6075 lbs. of coal come to at 771-2 cents per hundred? Ans. 47.08. 6075,775=-77 1-2 47.08.125 We point off from the product 3 figures, then two more for cents; those at the left hand will be dollars. Ex. 3. What will 9 car loads of coal cost, weighing as follows, at $1.14 per hundred? Ans. $230.73. 3630 2:10 3700 1310 2010 ]810 1850 189(0 20240 1.14 230.M3.60 166 GOODS BOUGHT AND SOLD BY THE HUNDRED. Ex. 4. \What will the freight on 8 boxes-of sugar amount to, weighing 1685 lbs. at 55 cts. per hundred? Ans. $9.23. 1685.55 9.26.75 Ex. 5. If meal is $1.50 per hundred, how much can be bought for $75.45? 150: 7545:: 100 100 150)754500 5,030 ans. Ex. 6. How many tons are there? Ans. 2 103-200. 2,000)5030 2 103-200 Ex. 7. If meal is $1.60 per hundred, how much can be bought for 10 cents? Ans. 6 1-4 lbs. 160: 10 cts.:: 100 lbs. 10 160)1000(6 960 40 16 oz. pound. 160)610 4 GOODS BOUGHT AND SOLD BY THE THOUSAND. 167 GOODS BOUGHT AND SOLD BY TIlE THIOUSAND. RULE. —Multiply the number of feet or bricks, as the case may be, by the price, and point off fromn the product the same manner as tile rule on p. 163. Ex. 1. What will 822 feet of boards amount to at $7.50 per thousand? Ans. $6.16. 822 750 6,16.500 Ex. 3. What will 28 feet boards come to at $3.75 per thousand? Ans. 10 cents. 375 28,10,500 MISCELLANEOUS EXAMPLES. GOLD AT PnE.imuaUr.-You will have no difficulty in determining the discount on greenbacks to correspond ith tilhe premium on gold, if you will fix clearly in your mind the fiact that discount is always to be ascertained by dividing the amount in greenbacks by the price in gold. For example, 1st-when gold is worth 25 per cent. premium, so that a hundred dollars in gold is worth $125 in greenbacks, you have only to divide $100 by 1.00, increased by the rate per cent., and you get $80, which is the value in gold of the $100 in greenbacks, 168 MISCELLANEOUS EXAMPLES. and this gives a discount of 25 per cent. on greenbacks when gold is at 25 per cent. premium? 10') per cent. is written thus, 1.00 25 " " " ".25 125 " and 1.25 1.25)100.00 e $0 ans. Ex. 2. If you reverse the process and reckon up what $80 in gold is worth, 25 per cent. premium, you will find that it comes to just $100 in greenbacks. 125 per cent. is written thus, 1.2.5 80,00 100.0000 Ex. 3. If gold is 25 per cent. premium, and I have $100 in gold, how many dollars in greenibacks shall I get for it? Ans. $125. 1.25. 100.00 $125.00.00 Ex. 4. If gold is at 25 per cent. premium, what is $1 greenback worth? Ans. 80 cts. 1,25)1,00.00 0,80 ans. The decimal places in the quotient exceed those in the divisor by 2, counting the ciphers annexed, we point off two decimal places in the quotient for cents. Ex. 5. If flour is sold for $9 per barrel in greenbacks, and gold is 52 per cent. premium, what must it be sold for in gold to bring its actual value? YY yv~ir, CV- Cr bv~~ uu N~e) MISCELLANEOUS EXAMPLES. 169 100 per cent. is written thus, 1.00 52......52 152 " and " "1.52,',2 ~1.52)9.00 $5.92 ans. Ex. 6. If government bonds are 12 per cent. premium, what must I pay for a bill of $5786; what would be the amount at 2 per cent. discount? Ans to the 1st, 6480.32. " " 2d, 5670.28. 5786.00 112 per cent. is written thus, 1.12 $6480.32.00 5786.00 98 per cent. is written thus,.98 5670,28,00 Point off from the product the samne as Ex. 8, p. 3. Ex. 7. France once owed the United States 18,000,000 francs; what is the amount in federal money? 18.000,000.186=1 franc. 3,348,000,000 There are 3 decimal places in one factor; hence we point off from the product 3 decimal places; all at the left will be dollars-making three millions, three hundred and forty-eirght thousand dollars. Ex. 8. There are four concrete sidewalks, the first is 120 feet long, 51-2 feet wide. The second is 12 feet long and 4 teet wide, and 2 more, each 19 feet long 6~ ~~ie mrln 170 MISCELLANEOUS EXAMPLES. and 4 feet wide; what will they cost at 80 cents per square yard? 120 12 5.5-51-2 4 6:(;00 48 sq. ft. 48 1 52 _ — 19 9 ft. sq. yd.)860 4 95.55 76,80 S2 walks. $76.44.00 152 Ex. 9. If tea is worth 1.75 per pound, how much can be bought for 40 cents. Ans. 3 oz. 10 dr. Statement. 175:40:: 16 oz. a pound. 40 175)640(3 525 115 16 drams an ounce. lt40(10 1750 Ex. 10. There is a street 40 rods long and 4 rods wide; how rm.lny square yards does it contain? How many squares? 40 4 160 30 1-4 square yards 1 square rod. 1.00) 48.40 sq. yds ans. to the 1st. 48.40=18 2-5 squares, ans. to the 2d. MISCELLANEOUS EXAMPLES. 171 Ex. 11. If Brian Hill coal is selling for $8.50 per ton, how much can be bou-ght for $20? 850:2000:: 2000 2000 850)4000000 4705.8 ans. See rule in Simple Proportion, p. 96. Ex. 12 How imany cubic feet in a box 41-2 feet long, 2 1-2 feet wide and 2 feet deep? Ans. 22 1-2 ft. 4.5-=4 1-2 2.5= 1-2 11.25 2 22.5) Ex. 13. How many superficial feet are there in a piece of marble 5 feet 5 inches long and 3 feet I inches wide? Ans. 18 ft. 8 seconds. 5 5 3 4/ 1 v1 b" 16 83 18 O' 8" Ex. 14. How many cubic f cet, and how many feet, board measure, are there in a plank 2 feet 11 inches long, 1 foot 6 inches wide and 5 inches thick? 2 11' 1 6' 1 5' 0" 2 lii 4 4/' t 5' 1 9' I"t 6"' ans. to the 1st. 4 4' 6" 5 inches thick. 2i 10/ t )" ans. to the 2d 172 MISCELLANEOUS EXAMPLES. Ex. 15. How many feet of wood, at $4 per cord, shall be given for 50 cents? 400: 50:: 128 ft. 50 4.00) 64.00 16 ft. ans. Ex. 16. How many tiles, 9 inches square, will cover a hall 126X16 feet? 126 9 16 9 -- 2016 81 sq. inches. 144 in. sq. ft. 81) 290324 3584 tiles ans. Ex. 17. If a pole 16 feet long east a shadow 22 feet, what is the height of a steeple whose shadow is 216 feet? 22: 216:: 16 16 22)34.56 1571-11 ans. Ex. 18. How long must I keep $300 to balance the use of $500 which I lent a friend 4 months? 300: 500:: 4 4 3.00) 20.00 6 2-3 mos. ans. Ex. 19. How many times will a hind wheel of a MISCELLANEOUS EXAMPLES. 173 carriage 8 feet 6 inches in circumference, turn around 6 miles, 3 furlongs and 20 rods? 320 rods a mile. 6 miles. 1920 120 rods=3 furlongs. 20 rods. 2060 16..5=16 1-2 ft. a rod. 8.5) 83W90.0 399S.82 ans. Ex. 20. How many pounds of sugar shall be given for 13 cents per pound for $1? Ans. 7 lbs., 11 oz. I d. 13)100(7 91 16 oz. pound. 144(11 13 14 13 1 16 drams an ounce. 16(1 13