PJ^\t/^^/^^^r^^^«/5^t'^\^«^t/i^^?^'^^I/^•t/rvt/5^I/i\t/F^5^^^ OUR OWN PRIMARY ARITHMETIC. I BY KEV. S. LANDER, A. M., TRINCIPAL or LINCOLNTON FEMALE 8EMINARY. SECOND EDITION, GRElfiNSBORO, N. C: PUBLISHBD BY STERLING, CAMPBELL AMD ILBRIQHT RICHMOND, TA.: W. HARQRAVl IVHITl. CX)L\JMBI1, 8. C: TOWNSIMD AND KOKTU . ^//J\^^^t'l^^^l'W^^t''• ^^sv^^l4^4• J^l^>t^^^^'Tvl?^i4^t/^^ ^ >''' - George Washington Flowers Memorial Collection 1 DUKE UNIVERSITY LIBRARY ESTABLISHED BV THE FAMILY OF COLONEL FLOWERS ^£^-..7)^ V OUR OTV'N^ PRIMARY ARITHMETIC. BY REV. S. LANDER, A. M., PRINCIPAL OF LINCOLNTON FEMALE SEMINARY. -«d»- SECOND EDITION, GRESNSBOflO, N. C: PUBLISHED BY STERLING, CAMPBELL AND ALBRIGHT RICHMOND, TA.: W. HARGllAVlJ WHITE. COLUMBIA, S. Q^ TOWNSEND AND NORTH. PREFACE. The following pages are respectfully offered as an intro- duction to the author's School Arithmetic, in the h(jpe that they may in some sort supply a necessity which, has long been felt to exist. Entered according to Act of Congress, in the year 1863, BY REV. S. LANDER, In the Clerk's Office of the District Court of the^Con federate States, for the District of Cape Fear, '/ North Carolina. 'P. J. PEIMARY ARITHMETIC. -^♦^ PART -••#- ADDITION. § 1. One and one are how many ? + + ++ . One and two are how many 1 + ++ +++ One and three are how many ? + +++ ++++ One and four are how many % One and five are how many ? One and six are how manjt ? , One and seven are how many ? One and eight are how many ? One and nine are how many 1 1. John gave one cent for a slate pencil, and five cents for a lead pencil ; what did he give for them both ? Model. — One and five are six ; hence, he gave six cents for them both. • 3 §2 PRIMA&Y ARITHMETIC. • 2. Willie bought an apple for one cent, and some candy for four cents ; what did they both cost him ? 3. Mary gave one peach to Lizzie, and two to Emma ; how many did she give to them both? 4. A man gave one dollar for a pocket knife, and eight dollars for a vest^ what did he give for both ? 5. Father sowed one acre in turnips, and nine acres in oats ; how many acres did he sow in both ? 6. Mother gave Lucy one biscuit before dinner, and one before supper ; how many did she give her both times ? 7. James walked one mile in the ni' '.-ning, and two miles in the afternoon ; how far did he wall; i /I day ? 8. If a pencil cost one cent; and a shite cost six cents, what do both together cost ? § 2. Two and one are how many ? ++ + +++ - Two and two are how many ? -f+ ++ + + + -)- . . Two and three are how many ? Two and four .are how many 1 Two and five are how many ? Two and six are how many ? Two and seven are how many ? Two and eight are how many ? ' Two and nine are how many ? 1. Susan gave two cents to one beggar, and one to an other ; how many did she give to both ? Model. — Two and one are three ; hence, she gave three cents to both. 2. James had two books, and his father bought him two more ; how many had he then ? • ADDITION. 3. In the garden there are two apple-trees, and three pear-^rees; how many fruit trees are there ? 4. In a certain class there are two small girls, and four large ones; how many girls are in the class 2 5. I gave two dollars for a pair of shoes, and "five dollars for a silk hat; what did I give for them both ? 6. I pay two dollars a year for a weekly paper, and six df)llars for a daily ; how much do I pay for both 1 7. I had two apples, and brother gave me seven more ; how many had I then ? 8. If a Spelling Book cost two shillings, and an Arith- metic cost eight shillings, what do both together cost ? * § 3. Three and one are how many ? + + + -f- + + + + Three and two are how many ? +++ ++ +++++ Three and three are how many ? Three and four are how many ? Three and five are how many 1 • Three and six are how many ? ' Three and seven are how many ? Three and eight are how many ? Three and nine are how many ? 1. If I walk three miles one day, and two miles the next, day, how far do I walk both days ? Model. — Three and*two arc five; hence, I walk five miles in both dciys. 2. If I buy three pounds of butter from one man, and three pounds from an other, how many pounds do I buy from both ? 3. If Jane give a beggar three cents, and John give him four cents, how much do they botb give him ? 5 PRIMARY ARITHMETIC. 4. Mother gave three dollars for a calico dress, and five dollars for a muslin dress ; what did they "both cost her ? 5. John gathered three quarts of chestnuts, and James gathered six quarts'; how many quarts had they both ? 6. I earn three shillings a' day, and father earns seven shillings ; what do we both earn ? 7. I gathered three green apples, and eight r^d ones; how many of both kinds did I gather ? 8. Johnny is three years old, and his sister Sarah is nine years older ; how old is Sarah ? §4. Four and one are how many ? + -f + + + 4- -h + + + Four and two are how many ? • + + + + +-}- + + + + + + Four and three are how many ? Four and four are how many ? Four and five are how mar.\ ? Four and six are how many X Four and seven are how many ? Four and eight are how many ? Four and nine are how many ? 1. A man paid four dollars" for some hay, and eight dol- lars for som» oats ; what did he pay for both ? Model.— -Four and eight are twelve ; hence, he paid twelve dollars for both ? 2. Edward had four marbles, an-d Warren gave him three more ; how many had he then ? 3. Sallie gave four cents to a beggar, and spent two cents for candy ; how many cents did she spend in all ? 4. If a rocking chair cost four dollars, and a table cost five dollars, what do they both cost 1 6 ADDITION. §5 5. If I earn four dollars one week, and six dollais the next week, how much do I earn both weeks ? 6. A man gathered four bushels of apples from one tree, atid seven bushels from an other ; how many bushels did he gather from both trees ? 7. Jack caught four squirrels before dinner, and eight after dinner ; .how many did he catch all day ? 8. Lucy had four white roses, and nine red ones ; how many roses had she in all ? § 5. Five and one are how many ? + + + H--f + +-l--h4- + + Five and two are how many ? -f + -f + + +H- + + + + + + + Five and three are how many 1 Five and four are how many? Five and five are how many ? Five and six are how many ? Five aind seven are how many? « Five and eight are how many? Five and nine are how many? 1. There are five geese swimming on one side of the' pond, and one on the other ; how many are there in all ? Model. — Five and one are six ; hence, there are six geese in all. . / 2. Susan read five pages of history, and two pages oi poetry ; how many pages of both did she read ? 3. Emily had five picture books, and Clarence gave her three. more ; hoT7 many had she then? 4. In a certain. faniily there are five sons, and four daugh- ters ; how many children are there in the family ? 5.. Thomas hoed five rows 'of corn one day, and JoJ:eph hoed five rows ; how many rows did they both hoe ? 7 §6 PRIMARY ARITHMETIC. 6. There are five boys on one bench, and sis on an otTier ; how many are there on both benches ? 7. I gathered five apples from a tree, and left seven on it*; how many were there on it at first? 8. "Warren gave a beggar five cents, and George gave him eight cents ; how many cents did they both give him ] § 6. Six and one are how many ? + + + + + + + + + + + 4- + + ■ Six and two are how many ? + + + + + + ++ +-F + + -h-f + + Six and three are how many ? Six and four are how many ? Six and five are how many 7 ^ Six and six are how many ? Six and seven are how many t Six and eight are how many ? Six and nine are how many ? 1. I had six marbles, and my brother gave me one more ; how many had I then ? Model. — Six and one are seven ; hence, I had seven mar- bles then. 2. If I have six books in one hand, and two in the other, how many have I altogether ? 3. Charles gave six cents for an orange, and three cents Xor some nuts ; what did he spend for both ? 4. Emma said six good lessons one week, and four the next ; how masy did she say both weeks ? 5. Susan's father gave her six new books, and her teacher gave her five ; how many did she have then ? 6. Lucy gave six cents for a spool of thread, and seven cent^ for a dozen buttons ; how many cents did she give for both ? 8 ADDITION. §^7 7. William gathered six quarts of chincapins, and Samuel gathered eight quarts ; how many quarts did both gather ? 8. If an ounce of figs cost six cents, and a quart of chest- nuts cost nine cents, what will both cost ? § 7. Seven and one are how many ? +++++++ + ++++++++ Seven and two are how many ? +++++++ ++ +++++++++ Seven and three are how many ? • Seven and four are how many? Seven and five are how many ? Seven and six are how many 1 Seven and seven are how many ? Seven and eight are how many ? Seven and nine are how many ? 1. A farmer had seven cows, and bought two more ; how many had he then ? Model. — Seven and two are niae ; hence, he had nine cows then, 2. Alice had seven cents, and her brother gave her three more ; how many cents had she then ? 3. I gave seven dollars for my coat, and four dollars for my vest; what did both garments cost? 4. There are seven sheep in one lot, and five in an other ; how many are in both lots ? 5. I gave seven dollars for a calf, and six dollars for a pig ; what did I give for both animals ? 6. If a firkin of butter cost seven dollars, and a barrel of vinegar cost eight dollars, what do both cost? 7. A man paid seven shillings for a night's lodging, and seven shillings for his horse's food ; what did he pay for both ? 9 §8 PttlMAaY. AEJTHMETIC. 8, I paid seven dollars freight on a barrel of sugar, asd nine dollars on a barrel of molasses ; what did I pay on both ? § 8. Eight and one are how macy ? + + + -[- + + + + f +^-4- + + -|- + + + Eight and two are how many ? + + + + + + +■+ ++ + + + ^- + + + + + + Eight and three, are how many? Eight and.four are how many ? Eight and five are how many ? Eight and six are how many ? , Eight and seven are how many ? . Eight and eight are how many ? . Eight and nine are how many ? i , 1. John owes one man eight dollars, and another one dollar; what does he owe them both ? Model. — l^ight and one are nine ; hence, he owes^ theiii both nine dollars. ' . . ' '"' 2. Mary bought a slate for eight cents, and a pencil for two cents ; what did she give for them both ? 3. Jane has eight pins, and her sister has three; how many have they both ? 4. Harry had eight cent^^ and his brother gave him fonr more ; how many had he then? , . , . 5. James has eight apples, and John has five; how many have they both ? 6. Pinckney is spelled with eight letters,' and Sallie with six ; how many letters in both their names ? 7. Charles bought eight oranges, and James bought sev- en'; how many have they both 1 8. Sam gathered eight quarts of chestnuts, and Joe gath- ered nine ; how many quarts did they IBoth gather ? 10 ADDITION. § 9. Nine and one are bow luanj ? + + + +.+ + + + + H- + + + -h + + H- + -h + * Nine and two are how many 1 + + + + + + + + + ++ H- + + -I- + + + 4- + + + Nine and three are bow many f Nine and four are liow many ? Nine and five are how many ? Nine and six are how many ? Nine and seren are how many ? Nine and eight are how many 1 Nine and nine are how many ? 1. Mattie is nine years old ; how old will she he one year from this time ? Model. — Nine and one are ten ; hence, she will then he ten years old. 2. A farmer picked nine bushels of apples from one tree, and three bushels from an other ; how many hiishels did he pick from both ? 3. A man can earn nine dollars in a week, and his son can earn four dollars ; how much can they both earn ? 4. Father gave nine dollars for a set of chairs, and five dollars for actable ; what did she give for them both 1 5. Joshua is nine years old, and Joseph is six years older than he ; how old is Joseph ? . ■ 6. A man gave nine dollars for a barl-el of flour, and seven dollars for a keg of lard ; what did he give for both ? 7. James gathered nine quarts of walnuts, and Alpheus gathered eight quarts ; how many quarts had they both ? 8. In a waiter there arc liine red- apples, and nine green ones; how man}" arc there in all? 9. Robert, bought a shot-gun for nine dollars, and a dog for five dollars; how much did she give for them both ? 11 §10 PRIMARY ARITHMETIC. SUBTRACT ION. § 10. One from two leaves how maray 1 (x)x X One from three leaves how many ? (x)x X XX One from four leaves how many ? One from five leaves how many ? One from six leaves how many ? One from seven leaves how many ? One from eight leaves how many ? One from nine leaves how many ? One from ten leaves how many ? 1. John had two apples, and gave one to his sister Mattie ; how many had he left 1 Model. — One from two leaves one ; hence, he had one apple left. 2. A beggar had three cents^, and lost one ; how many cents had he left ? 3. I had four yards of cloth, but I cut off one yard to make a vest ; how many yards have I remaining ? 4. Joseph startfcd to school with five apples, but he ate one on the way ; how many had he when he got there ? 5. Annie made six houses on her slate, and then rubbed one of them out ; how many houses did she leave on her slate ? 6. Jennie had s.sven s^heets of paper, and gave Susan one of them ; how many sheets did she keep for herself? 7. Mother had ten chickens, but the cat killed one of them ; how many chickens has mother now ? 12 SUBTRACTION. §12 § 11. Two from tliree leaves how many ? ^ (X x) X X Two from four leaves how many ? (xx)xx XX Two from six leaves how many ? Two from seven leaves how many ? Two h'Om. eight leaves how many ? Two from nine leaves how many ? Two from ten leaves how many 1 Two from eleven leaves how many ? , . 1. Agnes had five roses, and gave Ella two of them ; how many did she keep for herself? Model. — Two from five* leaves three ; hence, she kept three roses for herself. 2. Alice had six dollars, and lent two dollars to Ida ; how many dollars did she retain for her own use ? 3. Mr. Jones had seven tin pans, and sold two of them ; how many had he left ? 4. There were eight birds on a tree, and two of them flew away ; how many were •left on the tree ? 5. There were nine passengers in the stage, but two of them got out ; how many remained in the stage ? 6. Johnny found ten eggs, but broke two before he brought them to his mother ; how many did he bring to her ? 7. "Warren found a tree with eleven apples on it, and pulled them all but two ; how many did he pull ? § 12. Three from four leaves how many ? (x X x)x X Three from five leaves how many ? (xxx)xx XX Three from six leaves how many ? Three from seven leaves how many ? 13 ^13 PRIMAJLY ARirnMETIC. • Three from eight leaves how many ? Three from nine leaves how many ? Three from ten leaves liow many ? Three from eleven leaves how many ? Three from twelve leaves how many ? 1. If I make five marks on my slate, and rub out all but three of them, how many do I rnb out ? Model. — rThreo from five leaves two ; hence, I rub out two marks. 2. I gave six cents for a lead pencil, and sold it for three cents ; how much did I lose on it? 3. Father had seven pigs, but a bad boy killed three of them ; how many has father now 1 4. Angus caught eight fish, and gave three of them to the miller's wife ; how many did he keep for himself? .5. Carlos gathered nine quarts of hazel nuts, and sold three, quarts of them ; how many quarts did he bring honiQ? 6. Carrie found a bush with ten roses on it, and pulled them all but three; how many did she pull 1 7. Susun had twelve apples. And gave her sisters all but three ; how many did she give away ? § 13. Four from five leaves how laauy ? (x X X x)x X Four from six leaves how many ? (x X X x)x X XX Four from seven leaves how many ? Four from eight leaves how many f Four from nine leaves how many ? Four from ten leaves how many 1 Four from eleven leaves how many 1 Four from twelve leaves now many ? Four from thirteen leaves h«w many f 14 SUBTRACTION. §14 1. Mr, Jacobs had six acrea of larni, and gave four acres to his sons ; how many Acres did he keep for himself ? Model. — Four from six leaves two; hence, he kept two acres for himself. 2. Mr. Carpenter made seven gallons of vinegar, aud sold four gallons ; how many gallons had he left ? 3. Mr. Kamsour ground eight barrels of flour, and sold all but four barrels ; how many barrels did he sell ? 4. Mr, Rhyme brought nine bushels of potatoes to town, but sold only four bushels ; how many bushels did he take home ? 6. Mrs, SQhrom made ten pounds of butter, and kept only four pounds for her own use ; how many pounds did she dispose of? 6, Mr, Stowe had eleven yards of homespun, and sold four yards ; how much did he retain for his own use ? 7. Mr, Plonk had eleven bushels of .wheat, and sold all but four bushels ; how much did he sell ? § 14. Five from six leaves how many ! (xxxxx)x X Five from seven leaves how many ? (xxxxx)xx XX Five from eight leaves how many ? Five from nine leaves how many ? ' Five from ten leaves how many ? Five from eleven leaves how many ? Five from twelve leaves how many ? Five from thirteen leaves how many ? Five from fourteen leaves how many ? 1. Mr, Wingate had eight gallons of sorghum syrup, and sold five gallons ; how much did he keep ? 15 §15 PRIMARY ARITHMETIC. Model. — Five from eight leases three ; hence, he kept, three gallons. 2. Mr. Collier had nine tons of coal, and retained five tons for his own use ; how many tons did he sell ? 3. Mr. Miller had ten children, five of whom were sons ; how many daughters had he ? 4. Mr. Tillett had eleven slaves, five of whom were wo- men ; how many of them were men ? 5. Mr. Jenkins bought twelve bushels of sweet potatoes, and sold five bushels ; how many bushels did he keep ? 6. Mrs. Sumner went shopping with thirteen dollars, and brought five dollars home ; how much did she spend ? 7. Mr. Shuford hauled fourteen loads of wood, and sold five of them ; how many loads did he keep.? § 15. Six from seven leaves how many ? (xxxxxx)x X Six from eight leaves how many ? (xxxxxx)xx XX Six from nine leaves how many? Six from ten leaves how many ? • Six from eleven leaves how many 1 Six from twelve leaves how many ? Six from thirteen leaves how many ? Six from fourteen leaves how many ? Six from fifteen' leaves how many ? 1. A tallow-chandler made seven boxes of candles one day, and sold six boxes ; how many boxes did he keep 1 Model. — Six from seven leaves one ; hence, he kept one box. 2. A grocer bought nine casks of soda, and sold six casks ; how many casks had he left ? 16 SUBTRACTION. §16 3. A cutler made ten cases of knives and forks, and sold six cases ; how many cases had he left ? 4. A shoemaker made eleven pairs of shoes one week, and kept six pairs for his ownTamily ; how many pairs did he sell ? 5. A hatter had twelve wool hats, and sold six of them-; how many did he keep ? 6. A coachmaker had thirteen buggies, and sent six. oft' th-em off to market ; how iftany did he keep at home i 7. A peddler bought fifteen pieces of calico ; after, he had" sold six pieces, how many had he left ? §16. Seven from eight leaves how many. ? (xxxxxxx)x X Seven from nine leaves how many I (xxxxxxx)xx XX Seven from ten leaves how. many ? Seven from eleven leaves how many 1 Seven from twelve leaves how many ? Seven from thirteen leaves how many ? Seven from fourteen leaves how many ? Seven from fifteen leaves how many ? Seven from sixteen leaves how many ? 1. John had ten walnuts, and gave his sister seven of them ; how many'had'he left ? Model. — Seven from ten leaves three , hence, he had three waliluts left. 2. James gathered eleven quarts of filberts, and sold seven quarts ; how many quarts did he keep 1 3. Thomas caught twelve fish, and they were all cat-fish but seven ; how many of them were cat-fish ? 4. Edward killed thirteen robins and larks together ; seven of them were robins ; how many were larks ? 17 B .§17 PRIMARY AaiTHMETlC. 5. Rufus found fourteen eggs, and they were all guinea- eggs but seven ; how many of them were guinea-eggs ? 6. Lawson caught fif teen j-abb Its in his traps, but seven of them got away ; how many did he have then 1 7. Joseph was sixteen years old ; Benjamin was seven years younger than he; how old was Benjamin ? ,§17. Eight from nine leavee how many ? (xxxxx,xxx)x X Eight from ten leaves how many ? (xxxxxxxx)xx XX Eight from eleven leaves how many ? ♦ Eight from twelve leaves how many ? Eiglit from thirteen leaves how many? Eight from fourteen leaves how many 1 Eight from fifteen leaves how many ? Eight from sixteen leaves how many ? Sight from seventeen leaves how many ? 1. A man brought home eleven books, and gave eight of them to his children ; how many xlid he keep ? Model. — Eight from eleven leaves three ; hence, he kept three books. 2. There were twelve girls in a class, and eight of them were sustained ; how many were di^pprDved? 3. There were thirteen girls in a class, and all left school but eight ; how many of them left school ? 4. If there are fourteen little girls in school, and all but eight have the hooping ccfugh, how many have it ? 5. If Susan brings fifteen apples to "school, and gives eigbt of them away, how many htis she left ?^ 6. Laura has read sixteen pages, all poetry but eight ; ..how many pages of poetry has she read 1 18 SUBTRACTION. §18 '§18. Nine from ten leaves liow many 1 (xxxxxxxxx)x X Nine from eleven leaves liow many? (xxxxxxxxx)xx XX Nine from twelve leaves how many ? Nine from thirteen leaves how many ? • Nine from fourteen leaves how many ? « Nine from fifteen leaves liow many ? Nine from sixteen leaves how many 1 Nine from seventeen leaves how many ? Nine from eighteen leaves how many 'r' i. Arthur found ten pnrtridge-eggs, and brought home nine of them ; how maUy did he leave in the nest ? • Model. — Nine from ten leaves one; hence, he left one eirff in the nest. * CO ■ 2. Benjamin bought eleven postage-stamps^ and used nine of them ; how many had he left? 3. Charles's father gave him ^twelve shillings, and he bought a knife for nine shillings ; how many shillings had he left? 4. David made thirteen tops, and kept nine of them ; liow many tops did he dispose of? 5. Edward earned fourteen shillings one week, but spent nine shillings before the end of the we^k ; how many shil- lings had he Saturday night ? 6. Frank gathered fifteen quarts of chincapins, and gave ^ine quarts to his little brothers and sisters ; how many quarts had he left ? 7. George bought sixteen peaches, and sold ther!i all but nine ; how many did he sell ? 8. Daniel" had eighteen little lambs, but the dogs killed nine of them ; how many had. he left? 19 §l9 PRIMARY ARITHMETIC. MULTIPLICATION. g 19. Twice one are two. Tvrice six are twelve. Twice two are four. Twice seven are fourteen. Twice three are six. ^ Twice eight are sixteen. Twice fo'ur are eight. Twice nine are eighteen* Twice five are ten. Twice ten are twenty. 1. If one apple is worth tliree cents, what are two apples worth 1 Model. — Twice three are six; hor<:p^ two apples are , worth six cents. Explanation. — Two apples ar» woiiii twice as much as one apple, that is, twice three cents, or six cents. 2. John bought two oranges at four cents apiece ; what did he give for them both ? 3. Henry* gave his sister five cents, and Isaac gave her twice as much ; how many cents did Isaac give her ? « 4. If flour sells at six dollars a barrel, what can I get for two barrels ? • 5. What is the cost of two bilshels of wheat, at eight shillings a bushel ? 6'. Seven days make one week ; how many days are there in two weeks ? 7. What cost two dozen Arithmetics, at nine dollars a dozen 1 § 20. Three times one are throe. Three times six are eighteen. Three times two are six. Three times seven are twenty-one. Three times three are nine. Three times eight are twenty-four. Three times four are twelve. Three times nine are twenty-seven. Three times five are fifteen. Three times ten aro thirty. 1. What cost three yards of lace, at two cents a yard? Model. — Three times two are six ; hence, three yards cost six cents. 20 ■ . MULTIPLICATION. §2! 2. What cost three i)ranges,,at four cents apiece ? 3. If oneft)arrel of corn is wofth five dollars, what are three barrels worth ? 4. If one ream of paper is worth six dollars, what cost three reams I 5. James bold three quarts of chestnuts, at seven- cents a quart ; how much did he get for them all ? • G. What cost three pounds of mutton, at eight cents a pound y ^ . ■ 7. A merchant sold three pairs of boots, at nine dollar a pair : what did he get for them all ? §21. Four times one are four. Four times Rix are twenty-four. Four times two are eight. Four times seven are twenty-eight. Four times three are tvelvo. Four times eight are thirty-two. Four times four are sixteen. Four times nine arc thirty-six. Four times five are twenty. Four times ten are fort3\ 1. If I walk three miles an hour, how far will I walk in four hours? Model. — Four times three are twelve; hence, I will walk twelve miles in four hours. 2. If I give. four dollars apiece for four hats, what do I give for them all ? ^ 3. What will cost four barrels of flour, at five dollars a barrel ? 4. How many boys are there or^ four benches, if there are six boys on each bench ? 0. How much will four yards of broajl cloth cost, at seven dollars a yard ? 6. What cost four quarts of beer, at eight cents a quart-? § 22. Five times one are five. Five times six are thirty. Five times two are ten. Five times seven are thirty-five. Five times three are fifteen. Five times eight aie forty. Five times four are twenty. Five times nine arc forty-five. Five times five are twenty-five. Five times ten are fifty. 21 §23 PRIMARY ARITHMETIC. , • 1. A man gave his five children'two shillings apiece; how much did he give them all ? ^ Model. — Five times two are ten ; hence, he gave them all tea shillings. 2. Mother has five rose-bushes with three roses on each ; how many roses are there on them all ? 3. If one bushel of wheat is vrorth four yards of domes-' tics, how many yards of domestics are five bushels of wheat worth ? '^ 4. How much will five head of sheep cost, at Q.ve dollars a head ? » 5. At six shillings apiece, iiwit will five Geographies • cost ? 6. At seven'dollars a cord, what will five cords of wood cost ? 7. Eight quarts make one peck ; how many qu.art;s are there in five pecks ? §23. Six times one are six. Six tiDia^i ;nx are thirty-tiix. . . Six times two are twelve. Six times seven are forty-two. Six times three are eigbteoa. Six times eight are forty-eight. Six times lour are twenty-fonr. Six times nine are fiftj'-four. Six times five are thirty. Six times ten are sixty. 1. If a family eat one bushel of corn every weokj liov; many bushels will last them six weeks ? Model. — Six times one are six ; lience, six burdcls v/ili last them in six weeks. . , 2. What will wx bushels of wheat cost, at tv70 dollars; a bushel ? ' 3. I bought six lead pencils, at three cents tipiece; what ' did I give for them all ? 4. What will six sheep^cost, at six dollars a head ? 5. If I get fo.ur head-marks a day for six days, bow many will I have then ? 22 MULriPLICATION. * §25 6. Susan reads five hours every day ; how many hours does she read in six days ? ' 7. We have six classes iu school, and six girls in each class ; how many girls are there in school ? 8. What will six pounds of sugar cost, at tea cents a pound ? ■^ 24. Seron times ono aro seven. Seven times six are forty-two. Seven times two are fourteen. Seven times seven are forty-nine. Seven times three are twenty-one Seven times eight are fifty-six. Seven times fonr are twenty-eight. Seven times nine are sixty-three. Seven times fivo aro thirty-five. Seven times ten are seventy. 1. Seven boys went chestnut hunting, and gathered three quarts apiece ; how many quarts Iiad they all ? Model. — Seven times three are twenty-one; hence, they all had twenty-one quarts. 2. John earns four dollars a week ; how much does he earn in seven weeks ? 8. At fire dollars a head, what cost seven sheep 1 4. If a daily paper cost*six dollars a year, what will seven subscriptions to it cost? - 5. There are seven days in a week; how many days are there in seven weeks ? 6. At eight dollars a day, what will seven days' board amount to ? 7. What will seven yards of broadcloth cost, at nine dol- lars a yard ? 8. What will. seven yards of calico cost, at seven cents a yard ? § 25. Eight times one are eight. Eight times six are forty-eight. Eight times two are sixteou. Eight times seven aro fifty-.six. Eight times three are twenty-four. Eight times eight aro sixty-four. Eight times four aro thirty-two. Eight times nine are seventy-two. Eight times five aro forty. Eight times ton aro eighty. 1. What will eight peaches cost, at two cents apiece ? , 2o §26 PRIMARY ARITHMETIC. Model. — Eight times two are sixteen ; hence, they will cost sixteen cents. • . 2. What will eight dozen "buttons cost, at three cents a dozen ? 3. What will eight bushels of corn cost, at four shillings a bushel ? 4. Susan gave five cents apiece to eight beggars; how much did she give them all ? 5. How many roses are there on eight bushes, if there are six roses on each bush ? ^, A farmer sold eight tons of hay at seven dollars a ton; what did he receive for his hay ? 7. A lady sold eight pounds of butter at ten cents a ^ound ; what did she get for it all ? g26. Nine times one are nine. Nine times six are fifty-four. Nine times two are eighteen. Nine times seven are sixty-three. Nine times three are twenty-seven. Nine times eight are seventy-two. Nine times four are thirty- six. ' Nine times nine are eighty-one. Nine tin'ies five are forty-five. Nine times ten are ninety. 1. Susan bought nine dozen apples at three cents a dozen ; what did th^y cost her ? Model. — Nine times tliree are twenty-seven ; hence, they cost her twenty-seven cents. , 2. How many yards are there in nine pieces of cloth, if there are five yards in each piece 1 3. If I travel six milesr an hour, how far will I travel in nine hours? 4. What will nine barrels of flour cost, at seven dollars a barrel? •5. What will nine gallons of sorghum cost, at eight shil- lings a gallon ? 6. If nine yards of calico will make sister Mattie a dress, what will a dress cost her, at nine cents a yard ? 24 DIVISION. §27 DIVISIO'N, 1 27. Two in two, onco. Two in twelve, six times. Two in four, twice. Two hi fourteen, seven times. Two in six, tliree times. Two in sixteen, eight limes. Two in eight, four times. Two in eighteen, nine times. Two in ten, five times. • Two in twenty, ten times. When a number is divided into two equal parts, each ^art is called one half of the number. Let the above table be recited also as follows : — One is one half of two. ' Six is one half of twelve. Two is one half of four. Seven is one half of fourteen. Three is one half of six. Eight is one half of sixteen. Four is one half of eight. ' Nine is one half of eighteen. Five is one half of ten. Ten is one half of twenty. 1. At two cents apiece, how many peaches may be bought for eight cents 1 Model. — The number of peaches is equal to the number of times two cents is contained in eight cents: two in eight, four times ; hence, four peaches may be bought for eight cents. 2. A man divided fourteen marbles equally between hie two boys ; how many did he give them apiece 1 Model. — He gave each boy one half of fourteen marbles: seven is one half of fourteen ; hence, he gave them seven marbles apiece. 3. How n\any yards of ribbon at two cents a yard can I buy for six cents ? 4. Silas brought ten apples to school, and gave them equally to his two class-mates ; how many did he give to each ? . , 6. At two dollars a bushel, how much wheat cap be bought for twelve dollars? 25 m PR [ M AEY ARTTHM ETi C. G„ Last Christmas, mother 'divided qightG'ei equali}^ between si.-^tors Mary aiid Jane; how many oranpes em receive ?♦ did each of th Threo in eighteen, six timos. Three in twenty-one, seven times. Three in twenty-four, eight times. Three in twenty-seven, nine time?. Three in thirty, ten times. ? 28, Three in three, once. TJirec in six, twice. Three in nine, three times. Thro 9 in twelve, four times. .Three in fifteen, five times. When a number is divided into three equal parts, each part is called one third of tho number. Therefore, One is one third of three. Six is one third of eighteen. Two is one third if six. Seven is one third of twenty-one. Three is one third of nine. Eight is one third of twenty-four. Four is one third of twelve. Nine is one third of twenty-seven. Five is one third of fifteen. Ten is one third of thirty. 1. I spent fifteen dollars for corn at three dollars a bar- rel , how many barrels did I get ? Model.— The number of barrels is equal to the number of times three dollars is contained in fifteen dollars : three in fifteen, five tiines , hence, I got five barrels. 2. John, Andrew, and Peter gathered eighteen quarts of chestnuts ; how many quarts apiece did they gather ? 3. If a train of cars run one mile in three minutes, how far will it go in twenty-one minutes ? 4. If three girls in a class answer twenty- four questions^, how many does each one answer ? ,5. How many pounds of butter at three shillings a pound can be bought for twenty-seven shillings ? G. Joseph distributed thirty cents among thrte poor chil- dren ; how many cents did he give them apiece 1? [ 29. Four in four, once. Four in eight, twice. Four in twelve, three times. Four in sixteen, four times. Four in twenty, five times. 26 Four in twenty-four, six times. Four in twenty-eight, seven times Four in thirtj^-two, eight times. Four in tlurty-six, nine times. Four in forty, tea times. division:; iioO When a number is divided in four equal parts, each part is called one fourth of tKc number. Therefore, One is one fourth of four. Six is 030 fourth of twenty-four. Two is one fourth of eight. Seven is one foui'th of twenty-eight. Three is one fourth of twelve. Eight is one fourth of tliirty-two. Four is one fourth of eixteen. Nino is one fourtli of thirty-six. Five is one fourth of twenty. Ten is one fourth of forty. 1. How many classes, of four pupils each, can bo formed of twclva pupils? MoDii^L. — The iiumbei: of classes i.^ equal to the mimber of times four pupils is contained in twelve pupils : four in twelve, three times ; hence, three classes can be formed. 2. A olasK of four pupils made up twenty dollars to bu)' a present for their teacher; liow much was that apiece? 3. A farmer distributed eight bushels of potatoes equally among four poor families : how many bushels did he give to each family ? 4. How many primers, at four cents apiece, can you buy for twenty-four cents ? 5. HoW' many books, at four dollars a dozen, may you buy for twenty-eight, dollars? 6. A laborer received thirty-six dollars foi- four wcck.^' work; how much was that each week? §30. Five in five, once. Five in thirty, six times. Five in ten, twice. Five in thirty-live, seven timcs^ Five in fifteen, three times. Fiye in forty, eight tiE\ps. Five in twenty, four tiniea. ' Five iu furty-five, nine times. Five in twenty-five, five times. Five in fifty, ten times. When a number is divided into five equal parts, each part is called one fifih of the number. Therefore, One ia one fifth offivo. . Six is one fifth of thirty. Two is one fifth of ten. Seven is one fifth of thirty-five. Three is one fifth of fifteen. Eight is one fifth of forty. Four is one fifth of twenty. June is one fifth of for<-y-five. Fire is one fifth of twsuty-fivc. Ten ia one fifth of fifty. 1. How many dozen eggs, at five cents a dozen, can you buy for fifteen cents ? 27 '§31 PRIMARY/ ARITHMETIC. Model. — The numbe;- of dozen is equal to the number of times five cents is contained in fifteen cents : five in fifteen, three times ; hence, three dozen eggs can be bought for fif- teen cents. '2. How much broadcloth, at five dollars a yard, may be got for twenty dollars? Ji. How many kegs, each holding five gallons, will be re- quired to hold twenty-five gallons of vinegar? 4. At what price per barrel vrould thirty dollars buy five barrels of flour ? 5. A gentleman divided thirty-five picture books equally among his five Sunday -.school scholars ; how many did each one get? 6. I gave forty-five cents for five^ spelling books; how much did I give apiece ? * 2 31. Six in six, once. Six in thirty-six, six times. Six in twelve, twice. " Six in forty-two, BeventimeB. Six in eighteen, three times. Six in forty-eight, eight times. Six in twenty-foiir four times. Six in fifty-four, nine times. Six in thirty, five times, Six in sixty, ten times. When a number is divided into six eijual parts, each part is 'called one sixth of the number. Therefore, One is one sixth of six. Six is one sixth of thirty-six. Two is one sixth of twelve. Seven is one sixth of fortj^-two. Three is one sixth of eighteen. Eight is one sixtli of forty-eight. Four is one sixth of twenty-four. Nine is one sixth of fifty-four. Five is one sixth of thirty. - Ten is one sixth of sixtj'. 1. John earned thirt}^ shillings in six days ; how much diel he earn each day ? ■ "■ Model. — He earned each day one sixth of thirty shil- lings : five is one sixth of thirty; hence, he earned five shillings each day. 2. How long would it take to go twenty-four miles, at six miles an hour ? ?>. If stfirch sells at six cents a pound, how much may be bought for forty-eight cents? 28 « DIVISION. 4. If you read six chapters, of the Bible every day, how long would you be in reading forty-two chapters ? 5. A good little girl memorized fifty-four stanzas in six weeks ; how many stanzas did she memorize each week ? G. Mattie requires six yards of gingham to make a dress* she paid sixty cents for a dress pattern; what was it a yard? 232. Seven in seven, once. Seven in forty-two, six times. Seven in fonrteen, twice. Seven in forty-nine, seven times. Seven in twenty-one, three times. Seven in fifty-six, eight times. Seven in twenty-eight, four times. Seven in sixty-three, nine time». Seven in thiHy-five, five times. Seven in seventy, ten times. When a number is divided into seven eq^ual parts, each part is called one seventh of the number. Therefore, One is one seventh of seven. Six is one seventh of forty-two. Two is one seventh of fourteen. Seven is one seventli of forty-nine. Throe is one sovcnth of twenty-one. Eight is one seventh of fifty-six. Fonr is one seventh of twenty-eight. Nine is one seventh of sixty-three. Five is one seventh of thirty-five. Ten is one seventh of seventy. 1. If seven boys sit on a bench, how many benches will be required for twenty-one boys? Model. — The number of benches is equal to the number of times seven boys is contained in twenty-one boys: seven in twenty-one, three times; hence, three benches will be req'uired for twenty-one boys. 2. If seven yards of ribbon cost forty-nine cents, what does one yard cost ? 3. Mr. Goodman gave thirty-five marbles to his seven children ; how many did he give them apiece? 4. A stage-coach runs forty-two miles in seven hours ; how many miles an hour does it run 1 5. In a school of fifty-six pupils, there are seven pifpih in each class ; how many classes are there ? 6. I gave seventy cents for seven yards of domestics ; what was that a yard ? ^ ^ 29 j33 ' primIry* arithmetic. g 33. Eight in eight, once. Eight in forty-eight, six times. Eight in sixteen, twice. Eight in fifty-six, seven times. Eight in twenty-four, three times. Eight in sixty-four, eight times. Eight in thirty-two, four times. Eight m seventy-two, nine timee. Eight in forty, five times. Eight in eighty, ten times. When a DTiiiiber is divided into eight equal parts, each part is called one eighth of the number. Therefore, One is one eighth of eight. Six is one eighth of forty-eight. Two is one eighth of sixteen. Seven is one eighth of fifty-six. Three is one eighth of twenty-four. Eight is one eighth of sixty-four. Four is one eighth of thirty-two. Nine is one eighth of seventy-two. Five is one. eiglith of forty. Ten is one eighth of eighty. 1. If eight head of sheep cost twenty-four dollars, what does one sheep cost? Model. — One sheep costs one eighth of twenty four dol- lars: three is one eighth of twenty- four; hence, one sheep costs three dollars. . '2. If eight work hands eat sixteen pounds of meat in a day, how much does one hand eat ? §34. Nine in nine, once. Nine in fifty-four, six times. Nine in eighteen, twice. Nine in sixty-three, seven times. Nine in twenty-seven, three times. Nine in seventj'^-two, eight times. Nine in thirty-six, four times. Nine in eighty-one, nine times. Nine in forty-five, five times. Nine in ninety, ten times. When a number is divided into nine equal parts, each part is called one nintli of the number. Therefore, One is one nJnth of nine. Six is one ninth of fiftj'^-four. , Two is one ninth of eighteen. Seven is one ninth of sixty-three. Three is one ninth of twenty-seven. Eight is one ninth of seventy-two. Four is one ninth of thirty-six. Nine is one ninth of eighty-one. Five is one ninth of forty-five. Ten is'' one ninth of ninety. 1. At nine dollars a yard, how much cloth will cost tvcen- ty-seven dollars? Model. — The number of yards is equal to the number of times nine dollars is contained in twenty-fEeven dollars : nine in twenty-seven, three times ; hence, three yards will cost twenty-seven dollars. 2. If I divide forty-five apples equally among nine girls, how many apples will each girl receive ? 30 BART U. . — — .*»»- NOTATION AND^ ADDITION. § 35. Numbers are represented by figures. The number one is represented by the figure 1 « (( two u o « u three « ti 3 (( <. four " a 4 <( « five (( <;• 5. « ;< SIX t f( u ■ 6 « c> seven « (1 7 <; « eight « « 8 172. ii 185. ii 199. NOTATION AND SUBTRACTION. §48 Model. — 9 from 113 leaves 104 ; hence, he spent 104 dollars. 2. A farmer raised 127 bushels of wheat, and reserved 11 bushels for seed ; how much had he besides ? 8. A man bought a buggy for 135 dollars, and sold it at a loss of 13 dollars ; how much did he get for it ^ 4. Miss Sallie Brown went off to a boarding school with 145 dollars, and had only 8 dollars left at the end of the session ; v/Lat were the session's expenses? 5. Little Johnny's book has 166 pages, and he has read all but 9 pages ; how many pages has he read 't 6. Mr. Planter raised 180 bushels of ground peas, and kept 15 bushels for his own use ; how many bushels did he dispose of ? g 43. Tw» hundred is denoted 200. Two hundred and one " 201. Two hundred and five '• 205. Two hundred and ten '' 210. Two hundred and fifteen » '• 215. Two hundred and twenty-five " 225. Two luindred and thirty-seven '' 237. Two hundred and forty-nine • " 249. Two hundred and sixty-six " 2CG. Two hundred and seventy-five •• 275. Two hundred and eighty '• 280. Two hundred and ninetj'-eight " 298. Write two hundred and three, two hundred and eleven, two hundred and twenty-two, two hundred and thirty,»two hundred and fifty-five, two hundred and seventy-seven. Read 207, 214, 228, 235, 244, 258, 297. 1. Mr. Smith sold a horse for 225 dollars, and gained 10 dollars by the bargain ; what did the horse cost him ? 2. Mr. Coulter raised 200 bushels of corn, and paid 9 bushels tax ; how mucb had he left ? 37 §44 PRIMARY ARITHMETIC. 3. Mr. Finger made 215 gallons of sorghum, and lost II gallons by leakage ; how many gallons had he left f 4. Mr. Carpenter raised 100 bushels of wheat on one field, and 125 bushels on an other ; he paid 20 bushels for having it threshed ; how much had he remaining? §■44, I'hree hundred is denoted 300. Three hundred and three " . 303. Three hundred and fifteen a 315. Three'hundred and twenty-one " 821, Tkree hundred and thirty-three " 333. Three hundred and fifty-six '« 356. Three hundred and eighty niiic '■ 359, Write three hundred and one, three hundred and ten, three hundred and seventeen, three hundred and thirty, three hundred and forty-three, three hundred and sixty ^six. Read 308, 313, 327, 349, 352, 390, 399. 1. I had 325 dollars, but I had to pay 12 dollars tax on it ; how much money Had I left ? 2. A traveler, whose journey wa.s 350 miles, has finished it all but 20 miles ; ^how far has he gone ? 3. Susan hnp rend a.i but 15 pages of a book of 368 pages ; how many pages has she read ? 4. A grocer bought a barrel of sugar weighing 376 pounds gross; the barrel weighed 14 pounds; how many pounds of sugar did he buy ? 2 45. Four linudred Four hundred and four Four hundred and seven Four^hundred^and fourteen " Four hundred and forty. Four hundred and forty four Four hundred and fifty-four Write four hundred and seventeen, four hundred and ts deuottd 400. 404. 407. 414. 440. 444. 454. NOTAriON' AND SUBTHACriON. §4G twenty- eight, four liundi-ed and thirty-nine, four hundred and eighty, four hundred and ninety-six. Read 418, 422, 430, 449, 450, 478, 487. 1. A farmer raised 420 bushels of corn, and sent 25 bushels to his pastor ; how many budiels ha4 he left ? 2. ^ man took 450 dollars to town, hut spent only 16 dollars; how much did he bring home ? o. A butcher killed a beef weighing 418 poundp, and kept 16 pounds for his own use ; how much did he gell ? 4. A trader sold a pair of horses for 435 dollars, and gained 15 dollars by the trade ; what did the horses cost hi m % 2 46. Fivo hundred is denoted 500. Five hundred and fivo y 32 pages of being through it ; how many pages have I studied ? 4. I sold a carriage f'or 550 dollars, and thereby gained 47 dollars ; what did it cost me I 39 U7 PRIMARY ARITHMETIC. 2 -47. Six hundred -, is denoted 600. Six hundred and six <( 606. Six hundred and sixteen (. 616. Six hundred and ninety-nine ii 699. Seven hundred " 700. Seven hundred and seven <.' 707. Seven hundred and soventj'-eeven (( 777. Seven hundred and eighty-four It 784. Write six hundred and tliirty-fourj six hundred and for- ty-,three, six hundred and fifty-seven, six hundred and sev- enty-five, seven hundred and fifty-six, seven hundred and sixty-five, seven hundred and ninety-nine. Read 626, 662, 638, 683, 741, 714, 729, 792. 1. I am reading a Historyjn two volumes; the first vol- ume has 400 pages, and the second has 350 ; I am within 45 pages of being through the second -^olume; hcnv many pages have I read ? 2. Brother John is reading the same History, and has 30 pages of the first volume yet to r^ad ; how many pages has he to read in all ? 3. James gathered 425 chincapins yesterday, and gaT« away 25 ; to-day he has gathered 300 more; how many has he now ? 4. Mr. Sykes sold 47 acres from a tract of 650 acres ^ how much land had he remaining ? 148. Eight hundred Eight hundi ed and one Eight hundred and eight Eight hundred and eighteen Nine hundred Nine hundred and nineteen Nine hundred and ninety Nine hundred and ninety-nine is denoted 800. li 801. « 808. a 818. a 900. (( 919. (( 990. t< 999. Write eight hundred and fifteen, eight hundred and fifty- one, eight hundred and forty-seven, eight hundred and tev- 40 NOrATJON AND MULTiriUCATlON. §49 ent}'*four., nine hundred and fiixtj-thr^e, nine hundred and seventy-nine, nine hundred and ninety-seven. Read 823, S82, 849, 894. 948, 984, <)57, 975. 1. There arc 929 chapters in the Old TcL-tament; Zechariah has 14 chapters, and Malachi 4; bitter Susan has read all bub thci^e two books; how many chapters has she,, read ? 2. There are 150 Psalms in the Bible; how many cha'p- ters are there lu the Old Testament besides the Pi^alnisi' 3. The New Testament has 260 chapters-; the Revelation bas 22 ; how many chapters are in all the other boohs t 4. Mattie has ro«id the book of Matthew, which has 28 chapters ; how many more chapters has she to read ? -«♦»- NOTATI0.N AND MULTIPLICATION. is dev oted 1000. 1001. 1011. 1101. 1110. 1211. 1717. 1999. 4 49. Cue thousand One thousand and ono One thousand and el*vcn * One thousand one hundred and one One thousand one hundred and ten One thousand two hundred and eleven One thousand seven hundred and seventeen , On* thousand nine hundred and ninety-nine "Write one thousand one hundred and forty, one thousand two hundred and twenty-five, one thousand four, hundred and sevQuty-nine, one thousand and ninety seven, one thou- sand six hundred and sixty-one, one thousand one hundred and sixty-six, one thousand six hundred and sixteen. . Read 1007, 1207, 1220, 1203, 1033, 1330, 1429, 1492. '1. What cost 7 yards of lace, at 3 cents a yard ? n §50 PHI.MARY -VRITHrvIETIG Model. — 7 times 3 arc 21 ; heocGj 7 yards cost 21^8uts, Explanation. — 7 yards cost 7 tiaies as mucli as one yard, that is, 7 times 3 cents, or 21 cents. ;^n'fl.. — r>o carofal not tn alifi'.r f.he pupil to say 3 ti'iic- 7, for 7 tirrjes o 2. What cost 3 quarts of chestnuts, at 8 cents a quart ? 3. If 1 yard of dloth cost 5 dollars, what will 5 yards eost? 4. I bought 4 barrels of flour, at 7 dollars a barrel ; what did T pay for the four ? is denoted 2000. li 2001. u 2002. ii. 2020. ii 2022. i. 9220. li 2325. li 2436. ^50. Two thousand Two thousand and one Two thousand and two Two thousand and twenty Two thousand and twenty-two Two thousand two hundred and twenty Two thousand three hundred and twenty-five Two thousand four hundred and thirty-six Write two thousand five hundred and forty, two thou- sand sis hundred, two thousand and sixty, two thoMsand seven hundred and ninety-five, two thousand eight hundred and fifty, two thousand nine hundred and seventy- seven, two thousand seven hundred and twenty^seven. Read 2037, 2203, 2:^09, 2902, 2092, 2370, 2437, 2307. 1. What cost 4 yards of calico, at 8 cents a yard 1 2. Wliat cost 7 quarts of chestnuts, at 5 cents a quart? 8. Bought 9 dozen apples, at 4 cents a dozen ; 'v;hat did tlaey cost ? 4. I gave 5 dollars a yard for G yards of cloth; what did I give for it all ? 5. What should 1 give for 4 Primary Arithmetics, at 9 cents apiece ? 42 NOTATION AND MULTIILICATION. §52 2 51. Three thousand Three thoufland and three • Three thousand and thirty Three thousand tliree hundred Three thousand three hundred and three Three thousand three hundred and thirty-throe Three thousand six hundred and thirty-nine Three thousand tight liundnvl and twenty-seven 1*3 denoted sooo. <( 3003. a 3030. 3300. '• 3303. 333^. 3039. 3827. Write three thousuDd four hundred niid eighty-seven, .three thousand five hundred and five, three tlior.snnd and seventy, ihrco thou.sand and nine, three thousand two hun- dred and ninety-nine, three thousand one hundred and four, three thousand nine hundred and ninety-nine. Read 3456, 3645, 3564, 3465, 3329, 3932, 3093, 3009. 1. Laura bought 4 .^peHing hooks, at 10 cents apiece; what did the four cost? 2. James gathered 7 quarts of chestnuts every day for G days ; how many quarts had he in all ? 3. Su:^an bought 5 dresses, of 9 yards each ; how many yards were in them all ? 4. Joseph read 7 chapters in the Bible every day for a week; how many chapters did he read in all 1 5. Saul wa.s-sick 7 whole weeks; how many dayji was he sick ? ? 52. Four thousand l''our thousand and four Four thousand aad ten Four thousand and forty Four tkouoaud five liundrcd and fiJty . Four tliousand and fiity six Four thousand and cighty-uinu Four thousand seven liuiylrcd P.rd soventy-.six is doioted 400'), " 4004. ;( 4010. ii 4040. ti . 4550. a 405C. i( 40S9. a 477G. V/iitx:: four thousand and nine, four thousand three liun- dred, four ihousand and seventy^ four thousand and seventy- nine, four thou.°and seven hundred and eight, four thou- 43 S53 PRIMARY ARITHMETIC. sand three hundred and sis, four thousand one hundred and one, four thousand seven hundred and seventeen. Read 4007. 4014, 4125, 4236, 4247, 4458, 4569, 4670. 1. A man jj;ave iiiw 7 children 8 apples apiece ; how many did lie ^ive them all ? . 2. If our school fills 8 benches with 7 girls on a bench, how many girls are there in schooH o. Lucy gave 9 cents a yard for 6 yards of calico ; how much did she give for it all? g53. rire thoiisand is denoted 5000. Five thousand and one "'■ 5001. Five thousand and eleven " 5011. Five thousand and twehtj' , " 5020. Five thousand one hundred " 5100. * Five thousand five hundred and fifty " 5550. Five thousand and fifty-five " 5055. Five thousand six hundred and eighteen " 5618. Write five thousand three hundred and seventy-five, five thousand seven hundred and nine, five thousand six hun- dred and eighty-nine, five thousand seven hundred and twelve, five thousand three hundred and. forty-eight, five thousand eight hundred atid seventy. Read 5516, 5716, 5671, 5167, 5890, 5089, 5908, 5895. 1. Joseph bought 6 copy-booh.^, at 10 cents apiece ; what did he give for them all ? 2. Lawrence sold 10 quarts of blackberries, at 6 cents a quart ; what did he receive for them all ? 3. Father bought 7 yards of broadcloth, at 7 dollars a yard ; what did it all cost him ? 4. Mother gave 7 cents a dozen for 9 dozen eggs; what did she give for them all ? 5. Jonathan bought 5 Primers, at 11 cents apiece; how much did he pay for them all ? 44 NOTATION AND MULTIPLICATION. S5'5 is denoted 6000. (( eooi. 6006, CO-22, 7103, 7232. 7787. §54. Six thousand Six thousand and one Six tliousand and six Six thousand and twenty-twp Seven thousand one hun(h-ed and three Seven thousand two Inindrcd and thirty-two Sovon thousand ecv6n-hundred and eighty-soven Write six thousand two huixdred and seventy, six thou- i^nnd three hundred and eight, six thousand one hundred nnd ten, six thousand and ninety-nine, seven thousand five hundred and seventy- five, seven thousaud and seventy, seven thousand seven hundred, seven thousand eight hun- dred and eighty-nine. t Head 0125, 6250,, 6361, 6472, 7132, 7243, 7354, 7465. 1. If 7 boys gather 10 quarts of chestnuts apiece, how many quarts do they all gather 1 2. Susan bought a calico dress containing yards, at 8 cents a yard ; what did her dress cost ? . 3. Thomas traveled 8 hours at 9 miles an hour ; hov/ far did he travel ? 4. How many persons are there in 10 families, if there are 7 persons in each ? is denoted sooo. a 8008. a soso. a ii075. a 9100. a 9201. a 9312. f • 9423. §58. Eight thousand Eight thousand and eight Eight thousand and eighty Eight thousand and seventy-five Nine thousand one hundiyd • Nine thousand two hundred and one Nine thousand three hundred and twelve Nine thousand four hunSred and twenty-three Write eight thousand one hundred and two, eight thou- sand two hundred and thirteen, eight thousand three hun- dred and twenty-four, eight thousand four hundred and thirty-five, nine thousand five hundred and forty-six, nine thousand six hundred and fifty-seven, nine thousand seven 45 m PKIMARY ARITHMETIC. Inindred and f-ixty- eight, cine thousand eight hundred and i^evciity-riine. Road 8947,. 883G, 8725, 8G14, 9503, 9492, 9381, 9270. 1. If I v/ork 9 hours a 'day for 9 days^, how' many hoars do I work ? 2. John sold 8 quarts of ground-peas, at 10 cents a quart; what did he receive for tl;em ? 3. What pay does a man receive for 10 days' service, at 8 dollars a day '^ 4. What will 9 nionlbs' board auiount to, at 10 doUars a month ? * 5. What cost 10 dozen Arithmetics, at 9 dollars a dozen y inOtation and division f;0. Tea thousand Ten thousand and one Ten thousand and ten Ten thousand one hundred Eleven thousand Twelve thousand one hundred ^ Thirteen thousand two hundred and ten I'ourteen thousand three hundred and tweutj-one is (.u'lioted 10001. »10i)10. luioo. 11000. 12100. 13210. 14321. Write nineteen thousand and ninety -eight, eighteen thou- sand seven hundred and eighty-seven, seventeen thousand five hundred and seventy-six, sixteen thousand three hun- dred and sixty-five, fifteen thousand one hundred and fifty- four, fourteen thousand nine hundred and forty>three, thir- teen thousand seven hundred and thirty-two,, twelve thou* sand five hundred and twenty. Read 12345, 15878, 10102, 11435, 14768, 17091, 10324. 1. At 6 dollars a yard, how much cloth can be bought for 24 dollars? 46 .NOTATION J^XTi JjlVL-il §57 ■ Model. — The number of yards it- c([^t'j] to ihc uwmhcr of times dollars is cciitained 171 24 (dollars: (5 in 24. 4 times ; hence, 4 jards can be bought for 24 (iOiUir,-\ 2. A lady divided 21 apples ccjually aii)on(r iun- 7 oImI- dren ; how many apples did each child receive? Model — Each child received one ^evouth of 21 apples: ?> is one seventh of 21 , hence, each child received 3 apples. o. At 8 dollars a barrel, how niany*barre!s of flour may be bought for 24 dollars? 4. I spent 27 dollars for Latin Gra!n'Mars, nt 9 dollars a tlozen ; how many dozen did I fret ? f). If I give 28 dollars for v cords of wood, how much dn I give per cord 1 6. If 5 barrels of corn c.'st 25 dollars; ^\hatdoes 1 barrel cost ? is (lonotcJ 20000. a 20200. >t 22.101. .< 23513. (> 34625. " 35737- '• G6S49. a 37950. 257. Twenty tbousanci TAventy thousand two hnndred Twent)'-two thousand four hundred and ojie Twenty-three thousand five hundred and thirteen Thirty-four thousand six hundred and twenty-five Thirty-five thousand seven hundred and thirty-seven Thirty-six thousand eight hundred acd forty-nine Thirty-seven thousand nine hundred and fifty. Write twenty- nine thousand six hundred and forty-five, twenty-eight thousand five hundred and thirty-four, twenty- .seven thousand three hundred and twelve, twenty-five thou.- sand one hundred and ninety, thirty-six thousand two hun- dred and ten, thirty-four thousand and ninety-five, thirty- three thousand nine "hundred and seven ty-t^ree, thirty-one thousand seven hundred and fifty- one. Read 20125, 21286, 22347, 23458, 35469, 36570, 37681, 38792, 34975, 37384. 1. At 10 cents apiece, how many oranges can you buy for 40 cents ? 47 §58 PRIMARY ARITHMETIC. 2. At 8 cents a yurd, how many yards of calico can you^ buy for 40 cents'? 3. At 5 miles an hour, hoar long will it take to go 35' miles? 4. At* 4 dollars a cord, how many cords of wood can you buy for 32 dollars ? 5. At 9 dollars a month, how long could you board for 36 dollars ? §58., Forty thousand is denoted 40000. Forty thousand and forty " 40040. Forty thousand four hundred " 40400. Forty-four thousand and four . " 44004. Fifty tliousand one hundred and five ■ '' 50105. Fifty-one thousand two hundred and sixteen " 51216. Fifty-two thousand tliree hundred and twenty-seven " ' 52327. Fifty-four thousand five hundred and forty-nine. " 64549. Write forty thousand three hundred and twenty one,, forty-three thousand six hundred and fifty-four, forty-six thousand nine hundred and eighty- seven, forty-nine thou- sand two hundred and ten, fifty-two thousand five hundred and forty-three, fifty-five thousand eight hundred and sev- enty-six, fifty-eight thousand one hundred and nine, fifty- one thousand four hundred and thirty-two. Read 41482, 44765, 47098, 40321, 53656, 56987, 59210. 1. How long would it take to travel 40 miles, at 5 miles an hour ? 2. How many yards of broadcloth, at 9 dollars a yard,, may be bought f^r 45 dollars? 3. If 7 cords of wood cost 42 dollars, what does 1 cord cost? 4. If 6 Spelling Books cost 48 cents, what does one cost?' 5. If a boy divides 49 apples equally among his 7 class- mates, how many does he give them each ? 48^ POTATION AND DIVISION* §60 ii5 denoted GOOOO. ■ li 62000. n 64100. a C632Q. " 78543. '• 70765. a 72987. a 741C9. g59. Sixtj'^ thouj^and Sixtj'-two thousand Sixty-four thousand ono hundred Sixty-six thousand three hundred and twenty Seventy-eight thousand five hundred and forty-three Seventy thousand scveu hundred and sixty-five - Sevonty-two thousand nine hundred and eighty-seven Seventy-four thousand ono htmdred and nine Write sixty-five thousand four hundred and thirty-two, sixty-six thousand five hundred and forty-three, sixty-seven thousand six hundred and fifty-four, sixty-eight thousand seven hundred and sixty-five, aeventy-nipe thousand eight hundred and seventy-six, seventy thousand nine hundred and eighty-seven, sevfenty-one thousand and ninety-eight, seventy- two thousand one hun^dred and nine. Read 6357D, 64680, 66802, a7913, 78024, 79135, 70246V 1. Sallie gave 50 cents to 10 poor children equally • how much did she give them apiece ? 2. A school of 54 girls is divided into 6 equal classes •. how many girls are in each class ? 3. A farmer made 56 bushels of corn from 7 eq^al'rowfi^, how many bushels did he make from each row ? 4. If 8 boys gather 56 quarts of hazel nuts, how many quarts does each boy gather ? §60. Eighty thousand * Eighty-two thousand and two Eighty-four thousand ono hundred and six. Eighty-six thousand and twenty-eight Ninety-seven thousand three hundred and forty. Ninety-nine thousand five hundred and sixty-on© Ninety-five thousand six hundred and nineteen Ninety-six thousand one hundred and ninety-ftvo. Write eighty-one thousand two" hundred and five, eighty- three thousand and fifty-one, eighty thousand five hundred and thirteen, eighty-five thousand one hundred and thirty, ninety-six thousand two hundred and forty-one, ninety-two 49 D ia denoted 80000. a 82002. a 84106. ii. SC028. (i: 97340. «' 99561. '- 95619.' ii 96195. §60 PRIM AE.Y ARITHMETIC. thousand four hundred and sixteen^, ninety-four thousand one hundred and sixty-two, ninety-one thousand six hun- dred and twenty-four. Kead 80246, 82460, 84602, 86024, 97135, 91357, 93571. 1. At 6 shillings a bushel, how many bushels of apples can be bought for 60 shillings ? 2. At 7 shillings a yard, how many yards of cloth can be bought for 63 shillings ? 3. At 8 cents a yard, how many yards of •ribbon can be bought for 64 cents ? 4. If a father divide 70 marbles equally among his 7 sons, •how many marbles will each receive ? 5. If a gallon of milk cost 9 cents, what number of gal- lons will cost 72 cents ? 6. A planter wishes to make 10 equal fields to contain 80 acres in all ; how many acres will each field contain 1 7. His neighbor wishes to divide 81 acres into fields of. 9 acres each ; how many fields will he have ? 8. At 10 cents apiece, how many lead pencils can you buy for 90 cents ? 50 PART III. WEITTEN ARITHMETIC. NOTATION. § 61. Aritlimetic is the science of numbers. § 62. A unit is any single thing. § (33. A number is a collection of units. § 64. Numbers are denoted bj figures. For this pur- pose the following ten figures are used : naught, 1 one 2 two, 3 three, 4 four, 5 five, G six, 7 seven, 8 eight, 9 nine! ^ The figure is used simply to fill vacant places, and is aiways omitted in reading. § 6'5. 10 units make 1 ten, 1^ *^^s " 1 hundred, 10 hundreds « 1 thousand, 10 th6usands « 1 ten-thousand, 10 ten-thousands ^* 1 hundred-thousand, 10 hundred-thousands " ' 1 million 10 millions u 1 ten-million, 10 ten.millions " i hundred-million, 10 hundred-millions « 1 billion, &c. 51 \6S PRIMARY ARITEMETICr. » A unit is called a unit of the first order, A: ten . " a unit of the second order, A hundred *' a unit of the third order, A thousand " a unit of the fourth order,. A ten-thousand " a unit of the fifth order, A hundred-jbhousand " a unit of the,sixth order, &c. Thus, ten units of any or'^er make one of the next higher. § 66. Any number less than ten is denoted by one fig- ure, as in § 04. § 67. To denote a number between nine and one hun- dred, two figures are placed side by ri^e, the one on the' right denoting simple units, and the "fher denoting tens. Thus, twenty-one, (that is, two tens aud one unit), is de- noted 21 ; thirty-two is denoted S2 ; forty-three 43 ; fifty- four 54 • sixty -five 65 ; seventy-six 76 ; eighty-seven 87. In 23, how many units, and how many tens t How many of each in 29? In 34? In 45 ? In 50 ? In 61 ? In 16 ? In23? In 49? In94?.In86? In 68 ? In 40 ? In 27 ? Read 14, 25, 52, 3&, 63, 10, 26, 62, 37, 73, 25, 53, 3(>, 64, 47, 75, 58, 86, 69, 97, 78, 86, 67, 56, 45. Write seventeen, twenty-six^ thirty-five, forty- six, fifty- five, sixty-four, seventy-three, eighty-two, ninety-eighty seventy-one, .sixty-two, fifty-three, forty-four, thirty-four, twenty-five, thirty-six, eighteen, nineteen, ninety, § 68. .To denote a number between ninety-nine and one thousand, three figures are placed side by side, the one on- the right denoting units, the next denoting tens, and the other denoting hundreds. Thus, five hundred and twenty-six, (that is, five hun- dreds, two tens, and six units), is denoted 526 ; one hun- dred and twenity-three is denoted 123 ; two hundred and thirty-one 231 , three hundred and twelve 312. 52 NOTATION. In 127, liow maDy units, how many tens, und how many hundreds? How many of each in 271 ? In 7121 In 172? In 246? In 357? In 579 ? In 480? In 591 ? In 602? In 369 ? In 470 ? In 259 ? In 350 ? In 503 ? In 507 ? Read 147, 238, 367, 478, 589, 690, 701, 812, 923, 134, 245, 358, 467, 578, 689, 790, 801, 912, 129, 230, 341, 452, 563, 674, 785, 896, 907, 108, 219, 320, 435. Write 2 hundreds and 4 tens, 3 hundreds and 5 units, 4 hundreds 1 ten and 6 units, 5 hundreds 2 tens and 8 units, 6 hundreds 3 tens and 9 units, 7 hundreds and 4 tens, 8 hundreds and 5 units. Write 4 units of the 1st order and 5 of the 3rd ; 3 units of the 2nd order and^4 of the 3rd ; 7 units of the, 1st order, ^ of the 2nd, and 5 of the 3rd ; G units of the Srd. order, 4 of the 2nd, and S of the 1st ; 2 units of the 3rd order .and 9 of the 2nd ; 8 units of the 3rd order and 4 of the 1st.* Write one hundred and twenty-seven, two 'hundred and thirty-eight, three hundred and forty-nine, foiir hundred and sixty, five hundred a»d se-^ienty-one, {?ix hundred and eighty-two, seven hundred and ninety -three, eight hundred and four, nine hundred and fifteen. § 69. To denote a number larger than 999, more than three figures are used ; and these figures are separated into periods of three figures each, beginning at the right. § 70. The names of the periods in their order frogi right to left are as 'follows : 1st, units; 2nd, thousands; 3rd. •millions; 4th, billions ; 5th', trillions ; 6th, quadrillions,* 7th, quintiilions; 8th, sextillions; 9th, seplillions ; 10th. octillions, &c. § 71. In each period, the figure on the right denotes units, the next tens, and the other hundreds, of that period. Thus, 123 in the 2nd period denotes one hundred and 53 §72 PRIMARY ARITHMETIC- twenty-three thousand ; 245 in the 3rd period denotes two hundred and forty-five millions ; 102 in the 4th period de- notes one hundrgi and two billions. §72. The 1st, 2nd5 and 3rd orders constitute the. Isfc period ; the 4th, 5th, and 6th orders constitute the 2nd period; the 7th, 8th, and 9th orders consbitute the 3rd period, &c. § 73. 1000 units make 1 thousand, 1000 thousands i( 1 million. 1000 millions a 1 billion, 1000 billions iC 1 trillion, 1000 trillions >£ 1 quadrillion, 1000 quadrillions k i 1 quintillion. Thus, one thousand units of any period make one of the next higher. § 74. Rule for Reading NuxMbers. — Sepanite the fi'j- ures into periods of three figures each, beginning at the right ; then, beginning at the left. ?-^'; ? each 'period as if it stood alone, and pronounce the nuuie of the period after reading it. * Read the following numbers -. •3462 9077 5435- 6428 4005 8611 J 776 1864 ' 26408 31597 72410 47400 98780 40862 57913 42701 109875 151903 168024 753812 210986 382014 409135 864923 1421097 44i)3125 5510246 7975034 7142109 5449312 6551024 4797503 19012417 21394455 54301556 43057974 20123529 32405467 65312605 54168085 20345630 976453240 653126075 541680854 12034563 197615325 54 165311565 5416808540 NOTATION. §74 Write the following numbers in figures : 49. Six thousand, four hundred and eight. 50. Seventy thousand, and twenty-eight. 51. Eight hundred and fifty-one thousand, nine hundred and, fifty-two. 52. Nine millions, eighty-one thousand, an(!f ninety. 53. Sixty-three millions, twenty-seven thousand, five hundred and twenty -five. 54. Four hundred millions, and four. 55. Three millions, three thousand, and three. 56. Twenty millions, twenty thousand, and twenty. 67. One hundred millions, one hundred thousand, one hundred. 58. Two billions, three millions, four thousand, and five. 59. Sixty billions, seventy millions, eighty thousand, and ninety. 60. Six hundred billions, eighty millions, ten thousand, and nine. "61. Seventy-five billions, seventy-five thousand. 62. Ten billions, one hundred millions, and one. 63. Twenty-nine billions, and ninety-nine. 64. Six hundred and fifty billions, forty-three millions, twenty-one thousand, nine hundred and eighty-five. 65. Seventy-nine trillions, seven hundsed and seven mil- lions, eight hundred and eighty. Write, and then read, the following : • QQ. 25 units of the 1st period, 75 of the 2nd, and 10 of the 3rd. 67. 17 units of the 2nd period and 23 of the 3rd. 68. 175 units of the 3rd period and 715 of the 1st. 69. 225 units of the 1st period and 25 .of the 4th. 70. 23 units of the 1st period and 225 of the 3rd. 55 §75 PRIMARY ARITHMETIC. 71. 321 units of the 3rd period, 32 of the 2nd, and H of the 1st. 72. 123 units of the 1st period, 45 of the 3rd, and 6 of the 5th. 73. 7 units of the 1st period, 8 of the 2nd, -90 of the 3rd, and 100 of tUe 4th. 74. 230 units of the 4th period, 45 of the 3rd, and 19 of the 1st. 75. 25 in the period of units, 3 in that of thousands, 47 of millions, and 127 of trillions. 76. 135 in the period of quadrillions, 790 of billions, and 59 of thousands. 77. 264 in the period of trillions, 80 of millions, and 68 of units. 78. 147 in the period of billions, 25 . : • thousands, and 40 of units. 79. 400 in the period of millions, 40 of thousands, aad 4 of units. Note. — Let the teacher extend suck exercises until the class seem to be perfectly familiar with tiio principles of Notation. • • ADDITION. § 75. *Addition is the operation of jB.ndiDg one number equal to several other numbers put together. §76. The result of addition is called .the sum of the numbers added. Thus, 10 is the sum oi 6 and 4, because 10 is equal to 6 and 4 put together. Before proceeding' further, let the pupil thoroughly memorize the following Table. 56 • ADDITION. §78 J\.13I31TION T:_4lI3LE:. 2 nnd are 2 and 1 .".re 2 and 2 are 2 and 3 are 2 and 4 are 2 t.nd 5 are 2 and 6 are 2 and 7 are 2 and 8 arc 10 2 and 9 are 11 f? and 3 and 3 and 3 and 3 and 3. and 3 and 3 and 3 and 3 and nrc 3 1 are 4 2 arc 5 3 are 6 4 are 7 5 arc 8 G are 9 7 are 10 8 are 11 9 are 12 n 4 and afe 4 and 1 are 4 and 2 are 4 and 3 are 4 and 4 are 4 and 5 are 4 and 6 are 4 and 7 are 4 and 8 arc 4 5 (S 7 8 9 10 11 4 and 9 are 13 5 and are 5 5 and 1 nve '*> 5 and 2 arc 7 5 and 3 are 8 5 and 4 are 9 5 and 5 are 10 5 and 6 are 11 5 and 7 are 12 f) and 8 are 13 r^ and 9 arc 14 6 and 6 and 1 6 and Q 6 and 8 6 and 4 G and 5 G and 6 and 1 G and S G and 9 are 6 are 7 are 8 are 9 are 10 are 11 are 12 are 13 are 14 arc 15 7 and 7 and 7 and 7 and 7 and 7 and 7 and 7 and 7 and 7 and are 1 are 2 a^e 8 are 4 are 5 are 6 are 7 are 8 arc 9 are 8 9 10 11 12 13 14 15 16 8 and 8 and 8 and 8 and 8 and 8 and S and' 8 and 8 and 8 and are 1 are iiare 3 are 4 are 5 are G are 7 are 8 are 9 are 10 11 12 13 14 15 16 17 9 and 9 and 1 9 and 2 9 and 3 9 and 4 9 and 5 9 and G 9 and 7 9 and 8 9 and 9 arc 9 are 10 are '11 are 12 are 13 are 14 are 15 are 16 are 17 are 18 § 77. Two or more numbers can not be added "or put together, unless they are similar. We can not say that 2 apples and 3 peaches make 5 a^pples or 5 peaches. So, 4 dollars and 5 cents make neither 9 dollars nor 9 cents. In the sanie way, 2 simple units and 6 tens make neither 8 units nor 8 tens. Ex. 1. Add 2, 3, and 4. 9 -J • 3 § 78. MoDEL.^4 and 3 are 7, and .2 are 9. • 4 The sum is 9'. • 9 Explanation. — These three numbers can evidently be added together, because each of them is some number of • ' 57 • ■ §79 PRIMARY ARITHMETIC. Simple units, and henee they are all similar. Beginning afc the foot of the column in which they are arranged, and going up itj as in the Model, we readily find that 9 is equal to the three numbers pat together : and henoo V7^ GODclude that their sum is 9. Note. — Let the teacheT seo (.o it that the pupil recites prf cisely according to the mode! both here and wherever a model is given. Ex. 2. Add 1, 3, and 5. ' Sum, 9. 3. What is the sum of Ij 2, and 8 ? Ans. 6. 4. What is the sum of 2, 3, and 2 ] , Ans. 7. 5. Find the sum of 1, 3, i*id 4. Sum, 8. 6. Find the sum of 2, 4, and 2. - Sum, 8. . 7. Add 10, 20, and 40. 10 • 20 § 79. Model. — ; 4 and 2 are G, and 1 are 40 7. The sum is 70. 70 Explanation. — Since each of these numbers is a num- ber of tens, they can be added together. The is written at the right, to keep the 7 in its proper place, v.. Ex. 8. Add 10, 50, and 20. . >Sum, 80. . 9. What is the sum of 30, 20, and 10 ? Ans. (50. 10. What is the sum of 3Q, 20, and 20 ? Ans. 70. 11. Find the sum of 40, 30, and 10. Sum, 80. 12. Find the sum of 40, 20, a^nd 20. Sum, 80. 13. Add together 23 aiid 84. 2^ §80.. Model.— 4 and 3 are 7.^ 8 and 2 are 51 5. The sum is 57. 57 Explanation. — Each of these numbers consists partly of units and partly of, tens. The units and the tens can not be added all togetlier, as we learned in § 77 ; but the - 58 ADDITION. S81 units can be added together in one sum, and the tens in an other, and these'two sums may be placed side by side, each in i'js proper place. By this means the two given" numbers arc added together. The numbers are arranged for con- venience with units under units, and tens under tens. la like manner, numbers expressed by more than two figures may be" added by taking the sum of the nnit;^, tlien the sum of the tens, and then the sum of the hundreds, &c., from rio-ht to left. Ex. 14. Add together 123, 231, and 115. Sum, 469. 15. Add 1023, 2031, and 1105.. Sum, 4159. 16. Find the sum of 113.402 and 5321 J5. Sum, 655527. 17. Find the sum of 10321, 34102, and 12321. 18. What is the sum of 2742, 1034, and 4211 ?• 19. Add 123, 456, and 633. • . ]'-^^ §81. Model.— 3 and 6 are 9, and 3 are 12 ; 1 and 3 are 4, and 5 are 9, and 2 are 11 ; 1 and. 6 are 7, and 4 aro 11, and 1 are 12. 456 633 1212 The sum is 1212. Explanation. — After arranging the numbers as in §80, v/e find the sum of the column of units to be 123 12 units. Sine:; this is expressed by two fig- 456 ures, it can not be placed under that column. 633 We may, however, place 2 under the column ]2 of unit?, and 1 on its left, or under the col- 10 umn o1^tcD.«. It v/e add the column of tens, ]X we find 10 tens for its sum; and this can not Y^-pj be placed under the column of tens, for the "''■'"' same reason : but we may place the under the tens, and the 1 on its left, or under the hundreds. In like mann-jr, the 11 hundreds, which we get fi'oifL the third column, may be written partly under hun- dreds and partly still further left. By adding these partial sumS; we obtain 1212, the same as in the Model. In pracfcicQ it is'unnecessarv to write the several partial 59 mi PRIMARY ARITHMETIC. BUD.1S in tliio way, if we are careful to add the left hand fig- ure of eacli partial sum to the numbers in Ihe next column on the left. In the Model, this figure is taken in first in ^ adding, for fear of its beiitg forgotten. We may now give the following Rule fo& Addition. — Arrange the numhcrs iclth units of the mme order in the same column. Beginning at the right, find the sutn of each column ; if this sum is exjjressed hy one figure^ set it doion under flic cilamn f hiU^ if it is expressed hy more thiin one figure^ yet the "right hand figure imd^r this column^ and add the re- inaining figure or figures in loith the next cohiinu. JSet down the whole sum of the If st col(i77i7i. PiiooF.* — 1. Add as before, but begin at the top of eacli column. Or, 2. Find the sum of all the numbers but one, and ^o this sum add the number excepted. Ex. 21. Add 246, 157, and 290. 22. Add 1234, 4507, and 1752. 23. Add 2461, 5729, and 1207. 24. Add 1864, 8641, and 4681. 25. Add 1864, 18645, and 186456. 2Q. Add 1G23, 10234, and 102349. . 37. Add 1020, 30405, and 607080. 28. Adda234, 5678, and 90807. 29. Add 13057, 12304, and 10509." 30. Add 27903, 72903, and 30927. 31. What is the sum of 38014, 83014, 32. What is the sum of ,49125, 52149, Sum, 693j Sum. , 7493. Sum, 9397. Sum, 15186, Sum, 206965. Sum, 113606. Sum, 638505. Sum, 97719. Sum, 35870. Sum, 131733. and 41838 ? « . Ans. 162866. and 51949? An*. 153223, ADDITION. §81 33. What is the sum of 53236, 63254, and 02051 ? Alls. 178541. 34. What h the sum of 63307, 74365, and 73162 ? Ans. 21083-1, 36. What is the sum of 75418, 85476, and 84273 ? Ans. 245167, 36. What is the sura of 86529, 96587, and 95384 ? Ans. 278500. 37. What is the sum of 97630, 70698, nn^l 60495 ? Ans. 228823. 38. What is the sum of 80741, 81709, and 70506 '^ ■ Ans. 232956. 39. What is the sum of 91852, 92810, and 81617 ? ' . Ans. 266279. . 40. What is the sum of 302983, 92728, und 3921 ? Ads. 399612, 41. Find the sum of 413074, 103829, and 31032. Sum, 547935. 42. Find the sum of 513185, 2149310, 31145, and 42143. Sum, 2735783. 43. Find the sum of U23295, 32510421, 43256, and 53254. Sum, 33230226. 44. Find the sum of 7345106, 43621532, 54367, and 64375 Sum, 51085380. 45. Find the.sum of 8457216, 54732043, 65478, and 75386. Sum, 63330723, 46. Find the sum of 9568327, 65843754, 75689, and 86497. Sum, 75^74267. 47. Find the sum of 10679438, 76954865, 867910, and 975108. * Sum, 89477321. 48. Find the sum of 217810549, 871065976, 9781021, and 1086219. Sum, 1099743765. • 49. Add 3189216510, 982176087, 10892132, and 21973210. Sum, 13043842939. 61 PRIMARY ARITHMETIC. 50. Add 4291032, 76211003, 2872198, 20910324,332108, and 431194321. Sum, 535811076. 51'. Add 5926873, 3927591, 4389217, 6431279, 3326981, and 5678901. Sam, 29680842. 52. Add 20065321, 67754826, 83332716, 2176534498, and 3222110097. Sum, 5569796958. 53. Add 327, 916, 424, 326, 917, ISO, 232, 316, 419, 550, 613, 222, and 311. Sum, 6693. 54. Add 2160, 6120, 1260, 1620, 2610, 1234, 4321, 1200, 1020, 3156, and 2150. Sum, 26S51. 55. Add 2175, 1750, 2318, 9129, 6312^ 2120, 3816. 4505, 3216, 7888, and 3200. Sum, 46429, 56. Add 36, 22, 20, 19, 43, 16, and 10. Sum, 166. 57. Add 50, 60, 70, 81, 18, 91, and i9. Sum, 389, -«<5»- SUBTRACTION. §82. Subtraction is the operation of finding the differ- ence between two numbers, by taking tlie less from the greater. §83. The number to he subtracted is called the subtra- hend. § 84. ' The number to be diminished' is called the minu- end, § 85. The result of subtraction is called the remainder or the difference. Before proceeding further, let the pupil thoroughly? memorize the following Table. 62 SUBTRACTION, sujsxn^vcxioi^ x..-^sL"ii:. 1 from 1 from from from fi^m from from from 1 from 1 from 1 leaves 2 leavog 1 3 leaves 2 4 leaves 3 5 leaves 4 6 leaves 5 7 leaves 6 8 leaves 7 9 leaves 8 10 leaves 9 2 from 2 from 2 from 2 fi'om 2 from 2 from 2 from 2^ from 2 from 2 from 2 loaves 3 leaves 1 4 leaves 2 5 leaves 8 6 leaves 4 7 leaves 6 8 leaves G i> leaves 7 10 leavep 8 11 leaws 3 from S from 3 from 8 from 3 from 3 from .3 from 3 from 3 from 8 from 3 lenvfs 4 leaves 1 6 loaves 2 leaves 3 7 leav 8 from 8 from 8 from 8 from 8 from 8 from 8 from 8 from 8 leaves 9 leaves 1 10 leaves 2 11 leaves 3 12 leaves 4 13 leaves 5 14 leaves 6 15 leaves 7 16 leaves 8 17 leaves 9 9 from 9 from 9 from from 9 from 9 from 9 from 9 from 9 from 9 from 9 leaves 10 leaves 11 leaves 12 leaves 18 leaves 14 leaves 15 loaves IG leaves 17 leaves 18 leaves § 86. The difference between two numbers can not be found, unless they are similar. We can not say that 2 apples from 5 peaches leaves 3 apples or 3 peaches. So, 5 cents from 7 dollars leaves neither 2 cents nor 2 dollars. 63 PRIMARY ARlTIlMEIlC. In the same way, 3 simple units from 7 tens leaves neither 4 units nor 4 tens. % § 87. The difference between two numbers is not changed by increasing those numbers equall}^ Thus, The difference between 8 and 3 is 5 : now, add 4 to each of these numbers, and the difference between 12 and 7 is 5 still: again, add 6 to each of these last, and the differo^ice betvv'cen 18 and 13 is 5 still : and so on. - Ex. 1. Subtract 25 from 48. • 48 25 . § 88. MoDSL.— 5 from 8 leaves 3 : 2 from 4 23 leaves 2. The remainder is 23. Explanation. 7— We arrange the, two numbers with units under units^ and tens under tens, placing the subtrahend under the minuend. We then take the .units of the sub- trahend from those of the minuend, leaving 3 units for the remainder^; and we then take tfiie tens of the subtrahend from those of the minuend, leaving 2 tens for the remainder. In the same way we would proceed if the numbers were composed of more than two figures each, taking the differ- ence ; first of the units, next of the tens, then of the hun- dreds, &c., from right to left. Ex. 2. Subtract 123 from 369. Rem. 246. 3. Subtract 1024 from 2158. Rem. 1134. 4. Subtract 1203 from 7894. Rem. 6691. 5. Subtract 2345 from 5689. Rem. 3344. 6. From 98575 take 34543. . Rem. 64032. 7. From 575898 take 364032. Rem. 211866. 8. From 568759 take 203203. cRem. 365556. 9. From 679868 take 1^2302. Rem. 5775G6. ■ 10. From 789977 take 123456. Rem. 666531, 11. From 2561 take 836. 64 SUBTRACTlOx\. §{)0 ^5G1 §89. Model.— G from 11 leaves 5; .4 836 from G leaves 2 ; 8 from 15 leaves 7; 1 from 1725 2 leaves 1. The reuiaiuder is 1725. Explanation. — After arranging the niimljers as in ^ 88,. we are required to take 6 units from 1 unit: this, of cou^rse,. we can not do. But (§ 87) the difference between two num- bers is not changed by increasing those numbers equally. So we add 10 units to the 1 unit of the minuend, making 11 units, from which we subtract the 6 units of the subtra- hend, getting 5 units for the remainder. Then, since we increased the minuend 10 units, we must indrease the sub- . trahend the same amount : aod do this by adding 1 ten (equal to 10 units) to the 3 tens of the subtrahend. Hence we say,- ♦4 from 6 leaves 2." In the column of hundreds we meet the same difficulty, and avoid it by adrding 10 hun- dreds to the minuend, and afterwards 1 thousand (equal to 10 hundreds) to the subtrahend. Ex. 12. From 123456 take 9876. 123456 §90. Model.— 6 from 6 leaves 0; 7 9876 from 15 leaves 8 ; 9 from 14 leaves 5; 10 113580 from 13 leav.es 3 ; 1 from 2 leaves 1 ; fr^m 1 leaves 1. The remainder is 113580. We may now give the following RuLy FOR, Subtraction. — Place the subtrahend under the minuend, with units of the same order in the same column. Beginning at the right, take each figure of the subtrahend from the corresjyonding figure of the minuend. If an?/ figure of the minuend is less than the correspond-^ ing figure of the subtrahend, add 10 to this minuend figure, and add 1 to the suj^trahend figure in the next column. PnooF. — -J. Add the remainder to the subtrahend ; the- sum will be equal to the minuend. , 65 E §y^ PRIMARY ARITHMETIC. Or, 2. Subtract the remainder from the minuend ; the difference will be equal to the subtrahend. Ex. 13. From 270 take 195. 14. From 381 take 18G. 15. From 492 take 275. 16. From 5104 take 386. 17. From 6215 take 497. 18. From 7326 take 5108. • 19. From 8435 take 6229. 20. From 9326 take 6340. 21. The minuend is 10437 ; what is the remainder ? 22. The minuend is 21548 what is the remainder ? Rem the subtrahend is Eem the subtrahend is Rl^i. 12861 ■ Rem. 75. Rem. 195. Rem. 217. Rem. 4718. Rem. 5718. Rem. 2218. Rem. 2206. 2986. 7465; 2972. 8887: 23. The minuend is 30435 ; the subtrahend is 9798 ; what is the remainder? Rem. 20637. 24. The minuend is 49324 ; the subtrahend is 10899 ; what is the remainder ? Rem. 38425. 25. The minuend is "58213; the subtrahend is 21911; what is the remainder? Rem. 36302. 26. The minuend is 67102 ; the subtrahend is 32823 ; what is the remainder 1 , Rem. 34279. 27. The minuend is 78901 ; the subtrahend is 41723 ; what is the rema^inder ? Rem. 37178. 28. The minuend is 891012 ; the subtrahend is 50612 ; what is the remainder ? , Rem. 840400. 29. The minuend is 9102123 ; the subtrahend is 61501 ; what is the remainder? Rem. 9040622. 30. The minuend is 10213435 ; the subtrahend is 76522; what is the remainder? Rem. 10136913. 31. The subt'd is 10213435 ; what is the remainder 1 the minuend is 53431201 . Rem. 43217766'. 66 SUBTRACTION. §90 32. The subt'.d is 21345647 ; the minuend is 534312010 ; what is the remainder? Eem. 512966363. 33. The subtrahend is 21345; the minuend is 312010: what is the remainder ? * " ' Eem. 290665. 34. The subtrahend is 121345; tlie minuend is 312010 ; what is the remainder ? ^ Rem. 190665. 35. The subt'd is 6121345 ; the minuend is 31201016; what is the remainder ? Rem. 25079671. 36. The subt'd is 5431216; the minuend is 31201016; what is the remainder ? . Rem. 25769800. 37. The KubtM is 6320105; the minuend is -42315427 ; what is the remainder'/ Rem. 35995322. 38. The subt'd is 7210094; the minuend is 53426739; what is the remainder? Rem. 46207645. 39. The subt'd is 8321125; the minuend is 42115628; what is the remainder ? Rem. 33994503. 40. The subt'd is 9432167 ; the minuend is 31204517; what is the remainder? Rem. 21772350. 41. What is the difference between 24680 and 86042 2 Ans.- 61362. 42. What is the difference between 25 and 25000 2 Ans. 24975. 43. What is the difference between 9000000 and 9 ? Ans. 8999991. 44. What is the difference between 95000 and 950 ? Ans. 94050. 45. What is the difference between 13579 and 97531 ? Ans. 83952. 46. What is the difference between 24680 and 8642 ? Ans. 16038. 47. What is the difference between 35791 and 9753 ? Ans. 26038. 48. What is the difference between 1000000 and 1 ? Ans. 999999. 67 §90 PRIMARY AUITIIMETIC. 49. What is the difference betwceu 200000 aud 200 ? Aius. 199800, 50. What isjthe difference between 45000 and 45 ? Ans. 44955. " PROMISCUOUS PROBLEMS. 1. A farmer raised on one field 425 bushels of corn, or; an other 379 bushels, and on a third 10'^ otishels ; how iiiany . bushels did he raise on all three 1 An>\ 1002 bushels. 2. A man lent 2550 dollars to one fneuu, 3775 dollais to an other, and kept 1575 dollars for* his own use; how much money had he at first ? Ans. 7900 dollars. 3. A merchant bought a case of silk fur 3740 dollars, and sold it for 3387 dollars; how much did he lose on it ? Ans. 353 dollars. 4. The same man bought a quantity of linen for 2465- dollars, and sold it at a profit of 1233 dollars ; how much did he receive for it t • Ans. 3698 dollars.. 5. I bought 525 barrels of flour, and sold it all but 238 barrels ; how much did I sell ? Ans. 287 barrels. 6. I wish to. buy a tract of laud for 5000 dollars, and I have only 3775 dollars on ha'nd ; how much money do I lack ? Ans. 1225 dollars. 7. By selling a farm for 3000 dollars, I gain 875 dollars j what did I give for it? " Ans. 2125 dollars. 8. I bought 3 bales of Stowe's domestic, containing re- spectively 985 yards, 1063 yards, and 1187 yards; how maoy yards did I buy in all ? Ans. 3235 yards. 9.' I bought one lot of coffee for 786 dollars, and an other for 695 dollars, and sold one lot for 875 dollars, and the 68 SUBTRACTION. §90 other for 200 dollars less; bow much did I gain or lo&e in all ? Ans. I ^ined 69 dollars. 10. A merchant wont to market with 10000 dollars, and laid out 2569 dollars for dry goods, 2147 dollars for gro- ceries, 1728 dollars for hittdware,and 975 dollars for queens- ware ; 4iow ni'uch money did. he bring home, provided bis trip cost him 81 dollars? Ans. 2500 dollars. 11. A merchant made a collecting tour : in one town he collected 1075 dollars; in an other, 2128 dollars; in a third, 1357 dollars; and in a fourth, 809 dollars; he had 50 dollars with him when he started, and his expenies for the whole tour were 105 dollars; how much money did he bring home ? • Ans. 5374 dollars. 12. A dealer bought 25 bolts of cloth containing altogeth- er 700 yards ; aRer selling 18 bolts containing 578 yards, how many yards had he left ? Ans. 122 yards. J.O. .Four men contribute to the founding of a school r A gives 1000 dollars ; B, 245 dollars more than A ; C, 176 dollars less than B ; and D, 233 dollars more than C ; how much does J) contribute ? Ans. 1302 dollars. 14. A farmer raised 253 bushels of wheat, which is 149 bushels Ipss than he raised last year ;' how much did he raise last year ? ' Ans. 402 bushels. 15. I borrowed 1000 dollars from a friend ; since then I have paid him at different times 225* dollars, 239 dollars, and 397 dollars ; how much do I still owe him ? , Ans. 139 dollars. 16. A man who had 2465 acres of land, gave one of his sons 729 acres^ and an other oTS acres ; how many acres had he left ? Ans. 1163 acres. .17. A farmer raised 876 bushels of wheat, and sold 147 b ishels, and had 208 bushels ground into flour ; how many buhbels had he remaining.? Ans. 521 bushel.^. 69 §91 PRIMARY AaiTHMETIO. 18. If the mijijuend is 300300, and the remainder is 48729, what is the subtrahend? Ans. 251571. 19. If the subtrahend is 300300, and the remainder is 48729, what is the minuend ? Ans. 349029. 20. If the subtrahend h 0:/:784, and the minuend is 300300, what is the remainder? Ans. 207516. 21. If the subtrahend^is 568913, and the minuend is 891356, what is the remainder ? , An;,. 322443. 22. If the subtrahend is 123456789, and the minuend is 987654321, what is the remainder ? Ans. S64197532. MULTIPLICATION. §91. Multiplication is the operation of finding a Durn bef which shall contain one of two given numbers as mapy times as there are units in tJie otue:-. §92. The numher to he mulii'j/ '• I is called the muUi- plicand. § 93. The multipli/ing number is called tlie muItipUer. § 94. The result of multiplication is called the product. § 95. Either the multiplicand or the multrplier is called a factor of the product, and they both -ire called its factor.<. §96. An ahsiract ii\Vim.hQV is one whose unit is notsnec- ified ; as, two, forty, seven, twenty -seven. §97. A concrete number is one vfhose unit is specified ; as, five dollars, ten men, sixteen books. § 98. The product of any tv^o abstract factors is the same, no matter which is used as multiplier. Thus, 3 times 6, and 6 times 3, are each equal to 18; 4 times 5 is equal to 5 times 4. Before proceeding further, let tlic pupil thoroughly memorize the following Table. 70 MULTIPLICATION. §98 ]MU1L.TI1?'L.ICA.T10]?^ TJk]BL.3i]. Once is Twice are o •J times are Once 1 n 1 Twice 1 are 2 n timei' 1 arc 3 Once 2 IS 2 Twice 2 are 4 3 times 2 are () . Once 3 is 3 Twice 3 fvre 6 3 times 3 are 9 Odco 4 IS 4 Twice 4 are 8 3 times 4 are 12 Once 5 IS 5 Twice 5 are 10 3 times 5 are 15 Once G IS 6 Twice 6 are 13 3 times 6 are 18- Onoc 7 IS 7 Twice < are 14 3 times 7 are '21 Once 8 is 8 Twice 8 are IG S times 8 are 24 Once 9 is 9 Twice 9 are 18 3 times 9 are 27 Once W is 10 Twice 10 are 2U 3 times 10 are 30 Once 11 is 11 Twice n arc 22 3 times 11 are 33 One 3 12 is 12 Twice 12 are 24 3 times 12 are 36 4 times are are 5 times are ' G times aro 4 times 1 4 6 times 1 are 6 G times 1 are* G 4 times >) are 8 5 times 2 are 10 G times •t are 12 .■> •4 times 3 are 12 5 times 3 are 15 6 times 3 are IS 4 .times 4 are 16 5 times 4 are 20 G tiroes 4 are 24 4 times 5 are 20 5 times 5 are 25 6 times 5 are 30 4 times 6 are 24 5 times 5 are 30 6 times G are 3G 4 times 7 are 28 5 times 7 are 35 6 times 7 arc 42 4 times 8 are ^2 5 times 8 are 40 € times 8 are 48 4 times 9 are 3^ 5 times 9 aro 45 G times 9 aro 54 4. times 10 are 40 5 times 10 are 50 6 timea 10 are 60 4 times 11 are 44 6 times 11 are 55 G times 11 are GG 4 times 12 are 48 5 times 12 are GO G timws 12 are 72 7 limes nrc 8 times are 9 times are 7 times 1 are 8 times 1 are 8 9 times 1 are 9 7 times n are 14 8 times 2 j^re IG 9 times o are 18 7 times 3 are 21 8 times 3 are 24 9 times s are 27 7 times 4 are 28 8 times 4 are 32 9 times 4 are 3C 7 times 5 are 55 8 times 5 are 40' 9 times 5 are 45 7 times 6 are 42 8 times G are 48 9 times 6 aro 54 7 times 7 are 49 8 times 7 are 56 9 times 7 are 63 7 times 8 are 5G 8 times 8 arc G4 9 times 8 are 72 7 times 9 are OS 8 times 9 are 72 9 times 9 are 81 7 times 10 are 70 8 times 10 are 80 9 times 10 are 90 7 times 11 are 77 8 tiroes 11 aro S8 9 times 11 are 99 7- times 12 are 84 8 times 12 are 96 9 times 12 are 1G8 71 ;99 PRIMARY ARITHMETIC. 10 times 10 times 10 times 10 times 10 times 10 times 10 times 10 times 10 limes lOJtimes 10 times 10 times 10 times are 1 arc 2 are 3 are 4 are 5 are 6 are 7 are S are, 9 are 10 are 11 are 12 are 11 times are 12 times are (J 10 11 times 1 arc n 12 times 1 are 12 20 11 times r* are 22 12 time.? 2 are 24 30 11 times 3 are 33 12 times 3 are 36 40 11 times 4 are 44 12 times 4 are 48 50 11 time3 5 are 55 12 times 5 are 60 60 11 times 6 are 66. 12 times 6 are 72 70 11 times 7 are , 77 12 times 7 are 84 80 11 times 8 are 88 12 times 8 are 96 90 11 times 9 are 99 12 time^ 9 are 103 100 11 times 10 are no \l times 10 are. 120 110 11 times 11 are 121 12 times Ji are 132 12(7 11 timed 12 are 132 12 times 12 are 144 1^99. The multiplier must al^vays be an abstract num- ber, and the product is always like the multiplicand. Thus, to find the cost of 5 yards of cloth at 10 cents a yard, it is evident that we can not multiply 10 cents by 5yards; that is, we can not say, 5 yards times 10 cents : but we multiply 10 cents by 5, and this evidently gives 50 cents. Ex. 1. Multiply 2423 by 2. 2423 2 4846 SIOO. Model.— Twice 3 are 6; twice 2 are 4 ; twice 4 nrc 8 ; twice 2 are 4? The product is 4846. Explanation, — The smaller factor is placed under the larger. Then, beginning af the right, each figure of the upper number is taken twice, and each product is set under the figure which produced iit. For, since the product is always like the multiplicand, (§99,)^ twice 3 units are 6 units, twice 2 tens are 4 tens, &c, . ' . Ex. 2. Multiply 1203 by 2, 3. Multiply 130420 by 2. 4. Multiply 20301402 by 2. 5. Multiply 2030102 by 3. 6. Multiply 1203201 by 'i. 72 ^ Prod. 2406. Prod. 260840. Prod. 40602804. Prod. 6090306. Prod. 3609603. "^lU LTJ PL r CATION. §10! 7. Multiply 2310132 by 3. Prod. 6980396. 8. Multiply 21012 by 4. Prod. 84048. 9. Multiply 102120 by 4. - ^ Prod. 408480. 10. Multiply lOUOl by 5. Prod. 505505. 11. Multiply 12345 by 4. 12345 §101. MoDKL. — 1 time? 5 fire 20; 4 times 4 4 are 16, and 2 are 18; 4 times 3 are 12, 49380 ^^^ ^ ^^^ ^^ ' "^ ^^^'^^^''^ '^ ^^'^' '^' ""^^ l_are9 ; 4 times 1 arc 4. The product is 49380. , Explanation.— When we multiply 5 unit.?, by 4, we get '^:0 units; and, since this is expressed by two figures, it caii not be written in the place of units : lience, as»in addition, ^ 81, we set down the in the place of units, and reserve the 2 to be added to the 16 tens, which we get by multiply- . ing 4 tens by 4. Again, sinec 18 tens are equal to 1 hun- dred and 8 tenF,we .set^8in the place of ten^■, and reserve the 1 hundred to be added to the product of 3 hundreds by 4. - Ex. 12. Multiply 53706 by 3. Prod. 158118. 13. Multiply 27.95 by 2. ^ Prod. 5590. 14. Multiply 1684 by 3. Prod. 505?. 15. Multiply 3810G by.5.' * Prod. 190530. 16. Multiply 49217 by*6. Prod. 295302. 17. Multiply 510328 by 7. Prod. 3572296. .18. Multiply 621439 by 8. Prod. 4970712. 19. Multiply 7325410 by 9. Prod. 65928690. 29. Multipfy 8436521 by 10. o^ot'AoiA §102. MoDLiL. — Annex one naught to the 84365210 j^uuipiicaiid. The product is 84365210. Explanation.— Since'lO units of any order make one of the next order on the left, any number is multiplied by 10 by merely moving eiich of its figures ont3 place to the left, and puttin.^ a in the place of units. So, if the multiplier 73 1 103 prima;?y abithmetic. is cojiiposed of 1 with naugbts annexedj the produofc is ob- tained by simply aiinesing to the multiplicand as many naughts an there are a6 the right of the 1 in the multiplier. Ex. 21. Multiply 31597 by 10. Prod. 315970. 22. Multiply 426108 by 100. Prod. 42610800. 23. Multiply 537219 by 10. Prod. 5372190. 24. Multiply 6483210 by 100. Prod. 648321000. *25. -^lultiply 759432Kby 1000. Prod. 7594321000. 26. Multiply 12345 by 50. § 103. MoDiiL. — 5 times 5 are 25 ; 5 12345 times 4 a^e 20, and 2 are 22; 5 times 3 50 are 15, and 2 are 17 ; 5 times 2 are 10, and 617250 1 are 11 ; & times 1 are 5, and 1 are 6 : — annex 0. The product is 617250. Explanation. — We first multiply by 5, as in §101; and ihen, since 50 is 10 times 5, we multiply thi« product by 10, as in § 102, to get the true product. Ex. 27. Multiply 6172 by 20. Prod. 123440. 28. Multiply 7283 by 30. Prod. 218490. 29. Blultiply 8391 by 40. Prod. 335760. 30. Multiply 94105 by 500. Prod. 47052500. 31. Multiply 105216 by 60. Prod. 6312960. 32. Multiply 216327 by 700. Prod." 151428900. 33. Multiply 317438 by 80. Prod. 25895040. H. Multiply 428549 by 900. Prod. 385694100. 25. Multiply 246 by 35. § 104. Model. — 5 times 6 are 30 ; 5 Iflmes 246 4 are 20, and 3 are 23 ; 5 times 2 are 10, ana 35 2 are 12* — 3 times 6 are 18, set down B un- 1^0 der 3 ; 3 times. 4 are 12, and 1 are 13; 3 ygg times 2 are 6, and 1 are 7: — add the partial —j — products: 0; 8, and 3 are 11 ; land 3 are 4, ^^^^ and 2 are 6 ; 7 and 1 are 8. The product is 86J0. 74 "multiplication. 1^104 Explanation. — The upper number is inultiplied, first by 5. as in §*101, and then by -^0, aa in § 103, except tb.t the at the right is omitted, as being unnecessary, .^ince the ee\*feral figures can bo placed iu their proper columns without it. It must hf^ remembered, however, that the second partial product is not 738, but 7380. We may now give the following RULK FX>R MuLTIPrJCATION. — 1. When either factor contains hut one valual>Jc Jigure. Set the smaller factor un- der the larger. Beginning at the right, multiply each figure of the upper nvmher hy the lower number, set down, the right hand '^gure of the product, and add the remaining figure, if any, to the next 'product ; hut set down the tvhole of the last 2>i'odiict. 2. When tlie smaller factor Y 325. Prod. 6973200. 45. Multiply 32567 by 430. Prod. 14190212. 46. Multiply 43G78 hy 547. Prod. 23891866. 47. Multiply 54789 by C58. Prod. 30551162. -r. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. Q6. 67. 68. 69. 70. >- « / i. 72. 73. 74. 75. 76. 77. 78. 79. Multiply 658 109 by 769. Multiply 7692110 by 8710. Multiply 87103251 by 9'821. Multiply 98214 by 10932.. Multiply 109325"by 21104. Multiply 2110436 by 31254. Multiply 321547 by 42365. Multiply 342658 by 53476. Multiply 453769 by 64S7. Multiply 564760 'by 7598. Multiply 675671 by 86109. Multiply 786952 by 97210. Multiply 897063 bv 10832. Multiply 908174 by 20943. Multiply 108:195 by 31.054. Multiply 2092105 hj 42165. Multiply 31103216 by 5827. Multiply 42214327 by 6138. Multiply 1203450 by*9004. Multiply 9087061 by 56708. Multiply 8706544 by 67089. Multiply 4321209 by 12340j, Multiply 3456789 1^- 5G7C90. xMultiply 598750 ii)^ 32451. Multiply'5007631 by 43976. Multiply 423455 bj 3250. Multiply 536527 by 1864. Multiply 25876 by 2864. Multiply 47237 by 3526. Multiply 95423 by 8721. Multiply 58792 by 4587. Multiply 67813 by l-.'525. Multiply 243685 by 4372. 76 -*^ Prod. 506085821. Prod. G7075199200. Prod. 855441028071. Prod. 1073G>5448. Prod. 2307194800. P^od. 65959566744. Prod. 13623338655. Prod. 18323979208. Prod. 2913599503. Prod. 4291046480. Prod. 58181354139. Prod. 76499603920. Prod. 971G983416. Prod. 19019891082. Prod. 3362992930. Prod. 8y213o0V325. Prod. 165686831632. Prod. 271775837226. Prod. 40835863800. Prod. 5153>90551S8. Prod. 584113330416. Prod. 533276081481. Prod. 1960310474010. Prod. 19430036250. Prod. 220215580856. Prod. 1377499115. Prod. 100C086328. Prod. 74108864. Prod. 166557662. Prod. 832183983. Prod. 260G78904. Prod. 849357825. Prod. 1 065390820. DIVlSluW. §110 81. Mulriplj 89554S by 1028'G. Prod. 406800072^'. 8h Maltipiy ('65528 by 8765. Prod. 58333521)20. 8:1 Multip]}'^ 278963 by 7782. Prod. 2170890060. 84. Multiply 142986 by 0-17. Prod. 1317441112. 85. Multiply 111375 by 2242. Prod. 249702751). 8C. Multiply 9.;97G3 by 8765. Prod. 8762022695. 87. Multiply 87G543 by 5462. . Prod. 4787G77860. $8. Multiply 275684 by 4827. Prod. 13307266GS. DIVISION. §105. Division is the operation of finding how mciny times one number is cont:iined in an other. Or, § 106. Division is the operation of separating a number into some number of equal part?. Thus, if I spend 15 cents for lace at 5 cents a yard, the work consists in finding how many times 5 cents is con- tained in 15 cents, and this number of times is equal to the number of yards I get. But, if I pay 15 cents for 3 yards of lace, the work con- sists in separating 15 cents into 3 equal pilrts, and each one of these parts is the price of a yard. § 107. The number to he divided is called the diifidcnd. § 108. The dividivj number is called the Jivisar. § 109. 'The result of division is called the quotient. §110. When the division is not complete, the undi- vided part of the dividend is called the remainder. Thus, 9 in 29, 3 times, with 2 over : here 29 is the divi- dend, 9 is the divisor, 3 is tho quotient, and 2 is the re- mainder. Before proceeding further, let the pupil tlioroughly memorize the following Table. • 77 §110 PRIMARY ARITHMETIC. I31VXfe!5IOINr 'X^JVBLJE. ] ir. 0, no time 2 in 0, no time 3 in 0, no time 1 in 1, o'ace 2 in ') once 3 in 3, once i iii "1 twice o in 4,' twice 3 in 6, tv;ice 1 ill 3, 3 times 2 in 0, 3 times 3 in 9, 3 times 1 in 4, 4 times o ill 8, > 4 times 3 in 12, 4 times 1 iu 5, 5 times 2 in 10, 5 times 3 in 15, 5 times 1 in 6, G times 2 in y-^, G time^ 3 in 18, times i in 7 7 times 2 in 14, 7 titpe-^ 3 in 21, 7 times 1 in 8. 8 times 2 in ^^ 8 times 3 in 24, 8 times 1 in 0, ii times in 18, 9 times 3 iu 27, 9 timec 4 in 0, no timo, i 5 in 0. no* time ! G in 0, no lime 4 in 4, onc;:i 5 in '^ 0!ice 1 '6 in G, once 4 in B, twice 1 * 5 iu 10, twice G in 12, twice 4 iu 12, 3 times ! h ia 15, 3 times I G in 18 3 times •1 in Ifi, 4 times. 5 in 20, 4 times j G in 24, 4 times 4 ia 20, 5 times 5 \n 25, 5 times ' 6 iu 30, 5 times 4 in 24, times 5 in 30, 6 times 6 in 36, G times 4 ill 28, 7 times* 5 in 35, 7 times 6 in 42, 7 times 4 in 32, 8 times T; in 40, 8 "limes 6 in 48, 8 times 4 in 36. 9 timed 5 iu 45, 9 times . 6 in 54, times 7 ia 0, no time 8 in 0, no time 9 in 0, no time 7 in 7, once 8 in 8. once 9 in 9, unce 7 in 14, twice 8 in 16, twice 9 in 18, twice 7 in 21, 3 timec 8 in 24, 3 times 9 in 27, 3 timei 7 in 28, 4 limes 8 in 32, 4 times 9 in 36, 4 times 7 in 35, 5 time§' 1 8 in 40, 5 times 9 in 4^\- 5 times 7 in 42, 6 times 8 In 48, C times 9 in 54, 6 times 7 in 49, 7 times 8 in 56, 7 times 9 in 63, 7 times 7 in* 56, 8 times 8 in 64, 8 times ' 9 in 72, 8 times 7 in dp, 9 times 8 in 72, 9 times 9 in 81, 9 times 10 in 0, no time 11 in 0, no time 12 in 0, no time 10 in 10, once 11 in 11, once 12 in 12, once 1.0 in 20, twice 11 in 22, twice 12 in 24, twice 10 in 30, 3 times 11 in oo. 3 times 12 in 36, 3 times 10 in 40, 4 times 11 in 44, 4 times 12 in 48, 4 times 10 in 50, 5 times •11 in 55, 5 times 12 in 60, 5 times 10 in 60, G times 1 11 in 66, 6 times 12 in 72, 6 times 10 in 70, 7 times M in 77, 7 times 12 in 84, 7 times 10 in 80, 8 times 11 in 88, 8 times 12 in 96, 8 times 10 in 90 9 trim6s 11 in 99, 9 tioles Vi in 108, 9 times 78 DIVISION. §112 SHORT DIVISION. Ex. 1. Divide 24608 by 2. 2V24608 '^ ^^^' ^^^^'^^^''- — -^ ^" ^- l____ over; 5 in 35, 7 times; 5 in 6, once, with 1713 1 over; 5 in 15, 3 times. The quotient is 1713. Explanation. — 5 is contained once in 5 ; so that there are 3 thousands still undivided. Now, 3 thousands are equal to 30 hundreds, and this added to the 5 hundreds of the dividend gives 35 hundreds, in which the divisor, 5, is contained exactly 7 (hundred) ti^es. Again, after getting the 1 ten of the quotient, we have 1 ten of the dividend undivided. This is equal to 10 units, which added to the 5 units of the dividend, makes 15 units, in which the divi- sor is contained exactly 3 times. 79 §llo I RI M.4 RY AlUTilMe r I C . Ex. n. Divide 578 by 6. § 118. Model. — G in 57, 9 timet?, with , 6j57o 3 over; G in 33, 5 times, with 3 over, set i^ 3 down 5 ill the quotient, and 3 as remain- der. The quotient is 95, and the remain- der 3. We may now give the following* RuLS FOR Short Divisiox. — Set the divuor on the left of the dividend, with a line between them, and one under the dividend. Beginning at thv, left, see hoio many times the divisor is contained in each figure of the dividend, and sat the result under the dividend. V/heneoer there is a remainder , prefix it to the next fig- ure of the dividend, before, dividing. If the divisor is not contained en any figure^ cxcfjpt the .first, set under such figure, and regard it as a remaiTider, Proof. — Multiply the q^iotient by the divisor: the prod- uct, increased by the remainder, if any, will be equal to the dividend. Ex. 13. Divide^684 by 2. 14. Divide 795 by 3. . 15. Divide 8016 by 4. 16. Divide 9127 by 5. 17. Divide 10238 by 6. 18. Divide 21349 by 7. 19. Divide 324510 by 8. 20. .Divide 435621 by 9. 21^ Divide 546732 by 10. 22. Divide 657848 by 11*. 23. Divide 768954 by 12. 24. "Divide 8791065 by 11. 25. Divide 98102176 by 10.' 80 ' - Quot. 342. « Quot. 265. Quot. 2004. .Quot. 1825, Rem. 2. Quot. 1706, Rem. 2. - Quot! 3049, Rem. 6. Quot. 40563, Rem. 6. Quot. 48402, Rem. 3.' Quot. 54673, Rem. 2. Quot. 59803, Rem. 10. Quot. 64079', Rem. 6. Quot. 799187, Rem. 8.. Quot. 9810217, Rem.,6. DIVISION. §114 ♦ 26. Divide 109213287 by 9. Quot. 1^134809, Rem. 6. 27. Divide 2110324398 by 8. Quot. 263790549, Rem. 6. 28. Divide 32214354109 by 7. Quot. 46020505872, Rem. 5. 29. Divide 433254652110 by 6. Quot. 72209108685. 30. Divide 5443657632215 by 5. Quot. 1088731526443. 31. Divide 6594768743324 by 4. Quot. 1638692185831. 32., Divide 766587985443 by 3. Quot. 255529328481 «83. Divide 118456974 by 9. Quot. 13161886.' 34. Divide 4546328 by 8. Quot. 568291- -♦©♦- LONG DIVISION. Ex 33. Divide 7527 by 92. §114. Model.— 9 in 75, 8 times ; mul- 7527192 tiply the divisor by 8; 8 times 2 are 16 ; 736 |g| 8 times 9 are 72, and 1 are 73 : subtract [^y the product from the dividend ; 7 ; 6 from 92 12 leaves 6 ; 4 from -5 leaves 1 : — 9 in 16, — ^ once ; multiply the divisor by 1 ; once 2 is 2 ; once 9 is 9 : subtract the product from the previous remainder ; 2 from 7 icavv^H ; 9 from 16 leaves 7. The quotient is 81, and the. remainder 75. Explanation. — The divisor is- now placed on the right of i i! dividend, for convenience in multiplying. The num- ber 9 I- used as a trial divisor. As one figure of the real ': ' )S thus omitted, one figure of each partial dividend .c imiicted also. Hence, since we use 75 as a trial 'd, the real first partial dividend is 752, and we set tir.st figure of the product under 2, one place to the riviii V 5. The 8 of the quotient stands for 80 ; and hence the fir t product is really 7360, and must be so regarded in snbtrtioiing. §115 PRIMARY ARITHMETIC^ Ex. 34. Divide 8932 by"29. § 115. Model. — 3 io 8, 3 times ; mul- 8932|29_ tiply the divisor by 3 ; 3- times 9 are 27, 87 |3()g 3 times 2 are 6, and 2 are 8 : subtract the 232 product from the dividend ; 3 ; 7 from 9 232 leaves 2 : — 3 in 2, no time ; . annex 2 : — 3 t: in 23, 8 times ; multiply the divisor by 8 ; 8 times 9 are 72 ; 8 times 2 are 16, and 7 are 23 : subtract the product from the previous Remainder ; 0. The quotient is 308. Explanation. — If the second figure of the divisor is less than 5, the first figure is the trial divisor , but, if the sec- ond figure is greater than 5, the trial divisor is one more than the first figure. This trial divisor will almost always give within 1 of the proper quotient figure,. and will usu- ally give it exactly. If, at any time, however, after multi- plying, a quotient figure is found to be too small, let it be increased a unit at a timq^ until the correct figure is found ; and, if it is found to be too large, let it be diminished in the same way. In this example, the first product is really 8700 ; but, after we begin dividing, every remaining figure of the divi* , dend must give a figure of the quotient. In subtracting, therefore, we do not begin *at the extreme right, as we usu- ' ally do ; but we begin only one figure to the right of the first partial dividend. We may now give the following ' Rule for Long Diyision. -^JSet the divisor on the right of the dividend, with a line between them, and one under the divisor. Beginning at the left, see how often the divisor is contained in the first part of the dividend : the result will he the first figure of the quotient. Multiply the divisor hy this quotient figure^ and subtract the product from that part of the divi- • 82 DIVISION. §115 dend which was used, annexing to the remainder the next Jlgure of the dividend. Take this remainder as a second partial dividend, and from it obtain the second quotient figure. Multiply the divi- sor hy this figure, and subtract the product from the previous remainder, annexing to the second remainder the next figure of the dividend. Continue this process till all the Jigures of the dividend have been used. If any partial dividend will not contain the divisor, set in the quotient, annex an other figtire of^the dividend, and divide again. ^ Proof. 1.— The same as in § 113, for short division. 01-52. Subtract the remainder, if any, from -the divi- dend ; divide this remainder bj the quotient, and the re- sult will be the divisor. Ex. 35. Divide 672 by 21. Quot. 32. 36. Divide 551 by 29. Quot. 19. 37. Divide 864 by 32. Quot. 27. • 38. Divide 1444 by 38. Quot. 38* 39. Divide 1008 by 42. Quot 24.' 40. Divide 3478 by 47. Quot. 74. 41. Divide 2091 by 51. Quot 41 42. Divide 49358 by 58. Quot. *85l' , 43. Divide 26596 by 61. Quot. 436. 44. Divide 27068 by 67. Quot. 404. 45. Divide 33361 by 73. Quot. 457 46. Divide 36506 by 78. * Quot. 468. 47. Divide 23534 by 82. Quot. 287. 48. Divide 43521 by 89. Quot. 489 49. Divide 98901 by 99. Quot! 99»! 50. Divide 98209 by 109. Quot. 901. 51. Divide 112924 by 218. Quot! 518 83 • 5115 PRIMARY ARITHMETIC. 52. Divide 199143 by 327. Quot. 609. 53. Divide 232824 by 436. Quot. 534. 54. Divide 5815550 by 598. Quot. 9725 PROMISCUOUS PEOBLEMS. 1. If a field of 56 acres produce 1232 bushels of vzneat, how many bushels does each acre produce ? « _ Ans. 22 bushels. 2. How many gallons will 205 bai;ry Mleasxire. Used for measuring grain, fruits, vegetables, salt, &c. 2 pints, pt. make 1 quart, qt. 4 quarts a 1 gallon, gal. 2 gallons a 1 peck, pk. 4 pecks a 1 bushel, bu. 'Also, 5 bu shels a 1 barrel, of corn. 8 bu shels a 1 quarter. 36 bu shels a 1 chaldron, 92 TABLES. • , §128 1. In 4 barrels of corn, how many bushels ? 2. In 20 bushels, how many pecks ? 3. In 80 pecks, how many gallons? 4. In 5 gallons,, how many pints ? * H27. Liquid IMeasure; or. Wine Mieasixre. Used in measuring liquids; as, molasses, spirits, wiiie, water, &c. -t gills, gi. make 2 pints 4 quarts 31^ gallons 2 barrels, or 63 gallons '^ '- hogsheads 2 pipes Also, 42 gaHons 2 tierces a a iC a ii i( 1 pint, 1 quarf, 1 gallon, 1 barrel, pt. qt. gal. bbl. 1 hogshead, hhd. i pipe, pi. 1 tun, tun. 1 tierce, 1 puncheon. 1 . What will 3 quarts of wine cost, at 2 dollars a pint ? t In 2 hogsheads, how many gallons?. In 3 gallons, how many pints ? ■a 1 gallon, how many gills ? V!*' seconds, sec. fiO minutes - I hours 365 j <'ays M' years V'' deuades Alwo, 7 days 30 or 31 days 12 months make 1 minute, 1 hour, 1 day, 1 year, 1 decade, 1 century, 1 week, 1 month, 1 year. u (< li (( li ii ii ii min. hr. da. dec. cent. wk. mo. •din^ to the table, 365^ days make a year. To avoid tiio aaticulty arising from the fraction, we reckon three 93 §128 Primary arithmetic. years of 365 days each, and one of 366 days. This long year is called leap year. The leap years are those whose numbers are exactly divisible by 4 ; except that the cen- tonniah years are -not leap years unless their numbers are exactly divisible by 400. Thus, 1860 and 1848' were leap years ; but 1900 will not be leap year, because it is not divisible by 400. The year is also divided into four seasons; Spring, Sum- mer, Autumn, and Winter. These consist of the following ufconths : — * Spiking, 3. March, . Mar. has 31 days. 4. 5. April, May, Apr. May 30 31 d 6. June, Jun. 30 ({ 7. 8. July, August, Jul.. Aug. 31 31 li « 9. 10. September, October, Sept. Oct. 30 31 a (I 11. November, Nov. 30 a 12. December, Dec. 31 a 1. 2. January, •February, Jan, Feb. 31 28 (i SUJIMEE, Autumn. Winter, Thirty days have September, April, June and November; All the rest have thirty-one, Except February alone, • . Which has but twenty-eight in fine, Till leap year gives it twenty-nine. 1. How many days are there in the three Spring months ? 2. Is 1865 a leap year or not ? 3. In 2 centuries, how many decades ? 4. In 50 years, how many decades ? * 94 TABLES. §1S0 §129. i>.A.i*id:3R,. 24 sheets, sh. make 1 ({uirc, qr. 20 quires " 1 ream, rm. 2 reams " 1 >)ur-dle, bdle. 5 bundles " 1 bale. 1. How many Blieets of paper in 1 ream ? 2. How many quires in 5 reams ? 3. How. many reams in 40 quires ? 4. How many sheets in 40 quires? § 130. i3XJOI>E;CI]M-A.lLiS. 12 units make 1 1J& dozen " 1 12 gross " 1 A'lso, 20 units '' ^1 1. In 1 gross, how many units? 2. In 24 dozen, how many gross ? 3. In 1 great gross, how many units ? 4. How many units in 3 score and 10? 95 dozen, doz gross, gr- great gross, score. ^"S. PART I.— MENTAL. Addition, •5" Subtraction. 10 Multiplication, 19 Division, ; 27 PAET^ II.—MENTAL. Notation and Addition,.'. 35 Notation and Subtraction, 42 Notation and Multiplication, ., 49 Notation and Division, 5(^ PART III.— WRITTEN. Notation, ,....,.. .CI Addition, ?'"> Subtraction, t^ S2 Promiscuous Problems, 90 Multiplication, , 91 Division, . . 105 Promiscuous Problems, .- 115 Tables.— Money, 117 Weights,..-./.; 120 Measures,.. 123 Promiscuous, 1'3S 98 Si' ^ Jur Own Series of School Books. PRSP^VRED BY I^ichavd i^terling, -A..M., & J. 33. Campbell, A..M.. OOxNSISTING OP X. Ouv Oav« X*ri?T".or. For the children. Stereotype edition; liand- ti'jmcJy illufitratoil; ptf/48, ll2aio. TI. <>u.v Own Spelling Book. Stereotype edition, illuf5trated,pp. a^8, 12mo. ^11. Our O-wn B^.irst Header. 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