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THE
AMERICAN PRIMARY  SCHOOL
ARITHMETIC:
DESIGNED
FOR THE USE OF PUPILS
IN
PRIMARY AND INTERMEDIATE SCHOOLS.
BY JAMES ROBINSON,
AUTHOR OF THE AMERICAN ARITHMETIC.
BOSTON:
PUBLISHED BY JOHN P. JEWETT & CO.
1851.




Entered according to Act of Congress, in the year 1851,
BY JAMIES ROBINSON,
In the Clerk's Office of the District Court of the District of Massachusctts.
STEREOTYE'Di BY
O3BA T'1' & ROBBINS,
NEW LECGLAN'D FTYPE AND STFEROTY'  E FOUNDJ'IR,
BOSTON.




PREFACE.
THE object of the author, in preparing this little work, has been
to furnish lessons in Arithmetic for young children suited to their
age and capacity.  To accomplish this desirable object, care has
been taken that they should be strictly progressive.
Commencing, therefore, with the simplest elements and combinations of numbers, the lessons advance by easy and gradual
steps, in the form of tables, interspersed with practical examples
and simple exercises to be performed on the slate, until they conduct the pupil through the various operations, with numbers as
high as 12, of Addition, Subtraction, Multiplication, and Division.
Having completed the tables, Addition, Subtraction, Multiplication, and Division, and their appropriate arithmetical terms
and signs, are clearly defined, and the methods of operation explained, and illustrated by appropriate examples.  The Rules
for their operation are also given, with exercises in larger numbers to be performed on the slate, followed by a few practical
questions. It is believed that these slate exercises will furnish
young children with pleasing employment, and facilitate, rather
than retard, their progress in mental and oral arithmetic, and be
found to be a valuable feature of the work.
Fractions, with appropriate exercises, have also been explained,
and introduced as extensively as would comport with the general
design of the book   Tables of money, weight, and measure, have
been added, which may be learned by pupils in primary and
intermediate schools.
With this brief explanation of the object and plan of the work,
the author commends it to the favorable notice of teachers, school
committees, and the friends of education.
J. R,
MAY, 1851.




TO TEACHERS.
IT is presumed that most children have learned to count, to
some extent, before they begin to attend school; yet it will be
necessary that young pupils should be shown how many thing
the name of each number denotes.  The most convenient apparatus for this purpose is the Numerical Frame.  The balls on the
wires are easily arranged, and may be seen by every member of
the class at the same time; and, with appropriate illustrations by
tile teacher, pupils will readily perceive'that every number is
composed of as many single things, or units, as its name indicates. If the school is not furnished with a numerical frame, the
teacher can make use of unit-marks upon the blackboard for
illustration.
The author would suggest to those teachers who have had but
little experience, that the introductory lessons should first be
explained to the class; and that each of the succeeding lessons,
in the order of their arrangement, should be given to the class,
previous to recitation, with such explanations as shall be found
necessary; and that the use of the book during recitation should
be strictly prohibited. Questions should be asked promiscuously,
and not in rotation; and no question should be asked or read
more than once by the teacher, if done slowly and distinctly.
The pupil should be required to repeat the question, and solve it,
without being interrupted by the teacher, unless it be to make
some criticism  or correction.  Care should be taken that the
language of the pupil be strictly accurate, and that the best
forms for the solution of problems should be carefully observed.
Pupils who have learned the first fourteen lessons will be able
to read and write the first one hundred and forty-four numbers.
Lesson XVI. may be omitted until CXVI. lessons have been
learned; then Lesson XVI. should be learned, before commencing
operations upon the slate with larger numbers.




THE
AMERICAN PRIMARY SCHOOL
ARITHMETIC.
INTRODUCTORY  LESSON.
_DefJnitions and Illustrations.
ARITHMETIC is the art of computing by numbers.
"Numbers are the expressions of one or more things
of the same kind."
Any whole thing is called a unit, or one; as, one book,
one slate, one pencil.
Every number greater than one is composed of units,
and each succeeding greater number contains one unit
more than the preceding number.
Thus: one and one more are two; two and one more
are three; three and one more are four; four and one
more are Jive; five and one more are six; six and one
more are seven; seven and one more are eight; eight and
one more are nine; nine and one more are ten; ten and
one more are eleven; eleven and one more are twelve;
and in this manner each succeeding greater number may
be formed.
One           * 1  Seven         -*****,  7
Two         ** 2  Eight            **8**,*,*        8
Three     *** 3  Nine            9***    ****   9
Four,***  4  Ten            ***-**X       ***  10
Five  * -***  5  Eleven   x**<, **,**  II1
Six' *,X<   *  6  Twelve * -*     *-,   **    * < 12
Th'e above illustrations are designed to show the pupil
that all numbers are composed of single units, and
that the words one, two, three, ec., always express the
same number of units, respectively; which should be
indelibly impressed on the mind, and retained in the
memory, of young children.




~6 ~      NOTATION AND NUMIERATION.
LESSON  I.
NOTATION is writing numbers; Numeration is reading
them.  Numbers are written or expressed by words, by figures, and by capital letters.
The Arabic method of expressing numbers by figures is
used in all arithmetical computations.  Ten figures are
used, viz., the figure one (1), the figure two (2), the
figure three (3), the figure four (4), the figLure five
(5), the figure six  (6), the figure seven  (7), the
figure eight (8), the figure nine (9), and the cipher
(0); each of which expresses as many units as its name
indicates.  These ten figures are called the arithmetical
alphabet.
The Roman method of expressing numbers by letters
is used in numbering  the chapters of books, sections,
&c. Seven letters are used, viz., I, V, X, C,,    D,
and M.  The letter I expresses one; V, five; X, ten;
L1, fifty; C, one hundred; D, five hundred; and M, one
thousand.
All numbers can be expressed by these ten figures, or
seven letters, by combining and repeating them, which will
be shown to some extent in the following lessons:-~
LESSON  II.
One                1                                   I.
Two                2                2                 II.
Three              3               3                 III.
Four               4               4                 IV.
Five               5                5                  V.
Six'               6                6                VI.
Seven              7                7               VII.
Eight              8                               VIII.
Nine               9                9                IX.
Ten              10               10                  X.
Eleven           11               //                 XI.
Twelve           12               12                XTI.




NOTATION AND NUMERATION.              7
LESSON  III.
Thirteen            13                         XIII.
Fourteen            14             -           XIV.
Fifteen             15             15           XV.
Sixteen             16            16           XVI.
Seventeen           17            17          XVII.
Eighteen            18            1d         XVIII.
Nineeteen           19            /9           XIX.
Twenty              20            20            XX.
Twenty-one          21            2            XXI.
Twenty-two          22            22          XXII.
Twenty-three        23            23         XXIII.
Twenty-four         24            24         XXIV.
LESSON  IV.
Twenty-five         25            25          XXV.
Twenty-six          26            26         XXVI.
Twenty-seven        27            27        XXVII.
Twenty-eight        28            2   XXVIII.
Twenty-nine         29            29         XXIX.
Thirty              30            30          XXX.
Thirty-one          31            3J         XXXI.
Thirty-two          32            32        XXXII.
Thirty-three        33            33       XXXIII.
Thirty-four         34            34       XXXIV.
Thirty-five         35            35        XXXV.
Thirty-six          36            36       XXXVI.




8            INOTATION AND NUMERATION.
LESSON  V.
Thirty-seven         37            37       XXXVII.
Thirty-eight         38         3o          XXXVIII.
Thirty-nine          39            39        XXXIX.
Forty                40;0             XL.
Forty-one            41             4/            XLI.
Forty-two            42            -2            XLII.
Forty-three          43             J3          XLIII.
Forty-four           44           44            XLIV.
Forty-five           4             45            XLV.
Forty-six            46            46           XLVI.
Forty-seven          47            47          XLVII.
Forty-eight          48            4          XLVIII.
LESSON  VI.
Forty-nine           49            49           XLIX.
Fifty                50            50                L.
Fifty-one            51             5/              LI.
Fifty-two            52            52              LII.
Fifty-three          53            53             LII.
Fifty-four           54            54             LIV.
Fifty-five           55            55              LV.
Fifty-six             56            56            LVI.
Fifty-seven          57             57           LVII
Fifty-eight          58            5o           LVIII.
Fifty-nine           59             59            LIX.
Sixty                60             60             LX.




NOTATION AND NUMERIAT[ON.               9
LESSON  VII.
Sixty-one            61             61            LXI.
Sixty-two            62             62           LXII.
Sixty-three          63             63          LXIII.
Sixty-four           64            64           LXIV.
Sixty-five           65             65           LXV.
Sixty-six            66             66          LXVI.
Sixty-seven          67             67         LXVII.
Sixty-eight          68             6 o    LXVIII.
Sixty-nine           69             69          LXIX.
Seventy              70            70            LXX.
Seventy-one          71             7/          LXXI.
Seventy-two          72             72         LXXII.
LESSON  VIII.
Seventy-three        73            73         LXXIII.
Seventy-four         74            74,        LXXIV.
Seventy-five         75            75          LXXV.
Seventy-six          76             76        LXXVI.
Seventy-seven        77             77       LXXVII.
Seventy-eight        78             7Y      LXXVIII.
Seventy-nine         79             79        LXXIX.
Eighty               80            gO          LXXX.
Eighty-one           81              Jf       LXXXI.
Eighty-two           82             &2       LXXXII.
Eighty-three         83             J3    LXXXIII.
Eighty-four          84,4;    LXXXIV.




10           NOTATION AND NUMERATION.
LESSON IX.
Eighty-five              85         95       LXXXV.
Eighty-six               86?6     LXXXVI.
E-ighty-seven            87         &7   LXXXVII.
Eighty-eight              88        ^    LXXXVIII.
Eighty-nine               89          9     LXXIX.
Ninety                    90          0            XC.
Ninety-one                91        9/            XCI.
Ninety-two                92       92            XCII.
Ninety-three              93         3         XCIII.
Ninlty-four               94       9/a          XCTIY,
Ninety-five                         95           XCV.
Ninety-six                96        9 6         XCVI.
LESSON X.
Ninety-seven              97        97         XCVII.
Ninety-eight              98        9         XCVIII.
Ninety-nine               99        99          XCIX.
One hundred             100      /00                 C.
One hundred and one    101       /0/                CI.
One hundred and two    102,02              CII.
One hundred and three  103        j03            CIII.
One hundred and four   104       /   4            CIV.
One hundred and five   105       /05               CV.
One hundred and six    106       / 0              CVI.
One hundred and seven  107       /J7             CVII.
One hundred and eight  108                      CVIII.
/O<s




NOTATION AND NUMERATION.              11
LESSON  XI.
One hundred and nine         109  109           CIX.
One hundred and ten          110   //0           CX.
One hundred and eleven       111   1f1          CXI.
One hundred and twelve       112   /12         CXII.
One hundred and thirteen     113  //3         CXIII.
One hundred and fourteen    114  /f/          CXIV.
One hundred and fifteen      115   f/5         CXV.
One hundred and sixteen      116   116        CXVI.
One hundred and seventeen   117   /17        CXVII.
One hundred and eighteen    118    //       CXVIII.
One hundred and nineteen    119   ff9         CXIX.
One hundred and twenty       120,20         CXX.
LESSON  XII.
One hundred and twenty-one  121   121         CXXI.
One hundred and twenty-two  122   122        CXXII.
One hundred and twenty-three 123  123    CXXIII.
One hundred and twenty-four 124  1,2.       CXXIV.
One hundred and twenty-five  125   J25       CXXV.
One hundred and twenty-six  126   12 6    CXXVI.
One hundred and twenty-seven 127   J27   CXXVII.
One hundred and twenty-eight 128   129  CXXVIII.
One hundred and twenty-nine 129  129    CXXIX.
One hundred and thirty       130  130        CXXX.
One hundred and thirty-one   131   13/      CXXXI.
One hundred and thirty-two   132  132   CXXXII




12           NO'OTATION AND NUIMERATlION.
LESSON  XIII.
One hundred and thirty-three 133  J33     CXXXIII.
One hundred and thirty-four 134  /34       CXXXIV.
One hundred and thirty-five 135  135        CXXXV.
One hundred and thirty-six  136  136       CXXXVI.
One hundred and thirty-seven 137  /37    CXXXVII.
One hundred and thirty-eight 138  /,Y    CXXXVIII.
One hundred and thirty-nine 139  /,9       CXXXIX.
One hundred and forty      140    40O           CXL.
One hundred and forty-one  141  1j4            CXLI.
One hundred and forty-two  142  142           CXLII.
One hundred and forty-three 143 143          CXLIII.
One hundred and forty-four 144 /,4           CXLIV.
LESSON  XIV.
One hundred and sixty    160  /60               CLX.
One hundred and seventy  170  170             CLXX.
One hundred and eighty   180  1/0           CLXXX.
One hundred and ninety   190    9 0             CXC.
Two hundred and ten      210  2/0               CCX.
Three hundred and twenty  320  320          CCCXX.
Four hundred and thirty   430  4830    CCCCXXX.
Five hundred and forty    540  540              DXL.
Six hundred and fifty    650  650               DCL.
Seven hundred and sixty  760  760           DCCLX.
Eight hundred and seventy 870  S70       DCCCLXX.
Nine hundred and eighty  980  9O 6   CCCCLXXX.




LESSON XV.
NOTATION AND NUMERATION TABLE.
The figure 1 in the first place on the right expresses only its
simple number one, and is called a unit of the first:'order; 1 in
p.rio. ist period.  the second place expresses ten, or ten times one,
T'iehusa.tnds. Ullits.  and is called a unit of the second order; 1 in
1 1 111 1  I the third place expresses one hundred, or ten
~ +    ~. ~ 1   times ten, and is called a unit of the third oro         o  der; I in the fourth place expresses one thosand,
r_ I P' 4  and is a unit of the fourth order; 1 in the fifth
s JE  ~   ~ ^  place expresses ten thousand, and is a unit of
c! W.c  the fifth order, and 1 in the sixth place exn g B.- r^ g. presses one hundred thousand, and is a unit of
0 ) S'  ~ W  the sixth order.  The number expressed by this. * F  line of figures is one hundred eleven thousand
one hundred and eleven..~ m "     6  Six,
6 5  Sixty-five
6 5 4  Six hundred fifty-four.
6 5 4 3  Six thousand five hundred forty-three.
6 6 5 4 3 2  Sixty-five thousand four hundred thirty-two.
6 5 4 3 2 1  Six hundred fifty-four thousand three hundred
twenty-one.
LESSON XVI.
Pupils should be required to read the following numbers:150.       211.       1,234.       76,543.        123,456.
161.       321.       2,345.       87,654.        234,567.
172.       432.       3,456.        98,765.       345,678.
183.       543.       4,567.        89,567.       406,504.
194.       654.       5,678.        78,456.       805,402.
200.       765.       6,789.        67,034.       999,999.
Learners should be required to express the following numbers
by figures.
1. Two thousand five hundred and forty-three.
2. Five thousand seven hundred and eighty-five.
3. Ten thousand nine hundred and ninety-six.
4. Thirty-five thousand four hundred and twenty-five.
5. Seventy-eight thousand six hundred and fifty-seven.
6. Ninety-nine thousand nine hundred and ninety-nine.
7. Five hundred and five thousand four hundred and i'orty.
8. Nine hundred and eight thousand seven hundred and sixty.
2C)




.14           ADDITION AND SUBTRhACTIONo
LESSON  XVII.
I and  I are  2      1 fiom  2 leaves 1
I and  2 are  3      1 from  3 leaves 2
1 and  3 are  4      1 from  4 leaves  3
I and  4 are  5      1 from   5 leaves  4
1 and  5 are  6      1 from  6 leaves  5
1 and  6 are  7      1 from  7 leaves  6
1 and  7 are  8      1 from  8 leaves  7
1 and  8 are  9      1 from  9 leaves  8
1 and  9 are 10      1 from 10 leaves  9
1 and 10 are 11      1 from 11 leaves 10
I and 11 are 12      1 from 12 leaves 11
I and 12 are 13      1 from 13 leaves 12
LESSON  XVIII.
I and 1 are how many?   I from  2 leaves how many?
2 and I are how many?   2 from  3 leaves how many?
3 and 1 are how many?   3 from  4 leaves how many?
4 and 1 are how many?   4 from   5 leaves how many?
5 and I are how many?   5 from  6 leaves how many?
6 and 1 are how many?   6 from  7 leaves how many?
7 and I are how many?   7 from  8 leaves how many?
8 and 1 are how many?   8 from  9 leaves how many?
9 and 1 are how many?   9 from 10 leaves how manyy?
10 and I are how many?  10 from 11 leaves how many?
11 and 1 are how many?  11 from 12 leaves how many?
12 and 1 are how many?  12 from 13 leaves how many?
LESSON XIX.
EXERCISES TO BE PERFORMED ON THE SLATE.
c /  /   3   /   5   /
c7G6X3 2   A   6   8   o0  i2
%f^       I    /   /   I    y   I




ADDITION AND SUBTRACTION.              15
LESSON  XX.
1. William has 1 marble; if his brother should give him
1 more, how many would he then have?
2. I-enry had 2 cents, and lost 1 of them; how many
had he left?
3. Lucy found 1 pin, and her sister gave her 2 more;
how many pins had Lucy?
4. Sarah had 3 needles, and has lost 1 of them; how
many has she left?
5. Charles has I orange, and Henry has 3; how many
have both of them?
6. Thomas had 4 apples, and has given away 1 of them;
how many has he left?
7. Susan had I pear given her, and she bought 4 more;
how many pears had Susan then?
S. Jane bought 5 peaches, and has eaten 1 of them;
how many has she left?
9. If you should buy 1 book to-day, and 5 more to
morrow, how many books would you have?
10. If you have 6 cents, and should lose one of them,
how many would you have left?
11. James gave 1 cent for a marble, and 6 cents for a
ball; how many cents did he give for both?
12. If you have 7 birds in a cage, and one of them should
die, how many would be left alive?
13. If you place 1 chair by the side of 7 chairs, how many
chairs will theie be?
14. Catharine had 8 pinks, and has given 1 of them  to
Lucy; how many has she left?
15. Emily has 8 roses, and her little sister has I; how
nmany roses have both of them?
16. John bought 9 nuts, and has lost 1 of them; how
m-any l as h left?
I7.  Francis paid 9 cents for a slate, and 1 cent for a
pencil; how many cents did both cost him?
r8. Sarah had  0 choerries, and gave her sister I of them;
how manlly 1as she left?
19. Villiam paid 12 cents for a book, and 1 cent for a
pen; how many cents did he pay a.way?




10            ADDITION AND SUBT ACTION.
LESSON XXI.
2 and  1 are  3      2 from   3 leaves  1
2 and  2 are  4      2 from  4 leaves  2
2 and  3 are  5      2 from   5 leaves  3
2 and  4 are  6      2 from  6 leaves 4
2 and  5 are  7      2 from   7 leaves  5
2 and  6 are  8      2 from   8 leaves  6
2 and  7 are  9      2 from   9 leaves  7
2 and  8 are 10      2 from 10 leaves  8
2 and  9 are 11      2 from 11 leaves  9
2 and 10 are 12      2 from 12 leaves 10
2 and 11 are 13      2 from 13 leaves 11
2 and 12 are 14      2 from 14 leaves 12
LESSON XXII.
1 and 2 are how many?   I from   3 leaves how many?
2 and 2 are how many?   2 from  4 leaves how many?
3 and 2 are how many?   3 from   5 leaves how many?
4 and 2 are how many?   4 from   6 leaves how many?
5 and 2 are how many?   5 from  7 leaves how many?
6 and 2 are how many?   6 from  8 leaves how many?
7 and 2 are how many?   7 from  9 leaves how many?
8 and 2 are how many?   8 from 10 leaves how many?
9 and 2 are how many?   9 from 11 leaves how many?
10 and 2 are how many?  10 from 12 leaves how many?
11 and 2 are how many?  11 from 13 leaves how many?
12 and 2 are how many?  12 from 14 leaves how many'?
LESSON  XXIII.
EXERCISES TO BE PERFORMED ON THE SLATE.
&n-/ 2   3   2   8   22 1                             2
a.-.   2    2    AX    2   J0    /
Yo,. 5    /                       1 //  12  /4
aIe 2    2    2    2    2    2




ADDITION AND SUrB'TRACTI fON.          17
LESSON XXIV.
1. Richard bought 2 marbles, and found 2 more; how
many marbles had he then?
2. Samuel has 4 cents; if he should lose 2 of them, how
many would he have left?
3. There re  2 lamps on the maitel-piece, and 3 on the
table; how many are there in the room?
4. Henry had 5 cents, and lhas lost 2 of them; how
many hai hhe left?
5. 6) litle girls  ere on a visiit, and 4 of them went
home; how nmany remained?
6. James has 5 nuts, and John has 2; how many have
both of them?
7. If a man have 7 children, and 2 of them should die,
how many would he have living?
8. A farmer paid 6 dollars for four, and 2 dollars for
sugar; how many dollars did he pay away?
9. Augustus had 8 cents, and paid away 2 of them for
an orange; how many had ie left?
i0. A laay paid 7 dollars for a bonnet, and 2 dollars for
a cap; how many dollars did she pay for both?
II. Julia had 9 plums, and gave 2 of them to her sister;
how many had she left?
12. Mary gave 8 roses to her teacher, and 2 to her sister;
how many roses did she give away?
13. If you have 10 pens, and should give 2 of them to
your sister, how many would you have left?
14. Albert solved 9 questions in arithmetic, and Alfred
2; how many did they both solve?
15. A farmer having II barrels of apples, sold 2 of them;
how many had lie left 
16. A boy sold 10 peaches, and had 2 remaining; how
many had he at first?
17. Mary bought 12 needles, and has broken 2 of them;
how many has she left?
18. A farmer had 12 cows, and purchased 2 more; how
many cows did he then lave?
19. Susan is 14 years old, and Jane is 12; how many
years older is Susan than Jane?
f ^'"




18            ADDITION AND SUBTRAPtCTION,.
LESSON XXV.
3 and  I are  4      3 from  4 leaves  I
3 and  2 are  5      3 from   5 leaves  2
3 and  3 are  6      3 from   6 leaves  O
3 and  4 are  7      3 from   7 leaves  4
3 and  5 are  8      3 fiom   8 leaves  5
3 and  6 are  9      3 from   9 leaves  6
3 and  7 are 10      3 from 10 leaves  7
3 and  8 are 11      3 from 11 leaves  8
3 and  9 are 12      3 from 12 leaves  9
3 and 10 are 13      3 from 13 leaves 10
3 and 1I  are 14     3 from 14 leaves II
3 and 12 are 15      3 from 15 leaves 12
LESSON XXVI.
I and 3 are how many?    1 from   4 leaves how many?
2 and 3 are how many?   2 from   5 leaves how many?
3 and 3 are how many?   3 from   6 leaves how many?
4 and 3 are how many?   4 fiom  7 leaves how many?
5 and 3 are how many?    5 from   8 leaves how many?
6 and 3 are how many?    6 from   9 leaves how many?
7 and 3 are how many?   7 from 10 leaves how many?
8 and 3 are how many?   8 from 11 leaves how many?
9 and 3 are how many?   9 from 12 leaves how manay?
10 and 3 are how many?  10 from 13 leaves how many?
11 and 3 are how many?  11 from 14 leaves how many?
12 and 3 are how many?  12 from 15 leaves how many?
LESSON XXVII.
EXERCISES TO BE PERFORMED  ON THE SLATE.
eA/ 3   5   3   7   3  /2
ai d              3    6    3    //    3
97 /6                    10   12   1               I 15
".2^1    3    3    3    3    3    3




ADDITION AND SUBTRACTION.             19
LESSON  XXVIII.
1. A poor widow has 3 sons and 4 daughters; how many
children has the poor widow?
2. A man has 7 children; 4 of them are boys.  Hov
many of them are girls?
3. If you pay 5 cents for an orange, and 3 cents for a
lemon, how many cents do you pay for both?
4. Ralph bought a ball for 5 cents, and sold it for 8
cents; how many cents did he gain by trading?
5. Eliza has 6 roses on one bush, and 3 on another;
how many roses are there on both?
6. Eliza had 9 roses, and she gave 3 of them  to her
sister; how many had she left?
7. There are 3 birds on one tree and 7 on another; how
many are there on both trees?
8. There were 10 birds in a cage, but a boy has taken
3 of them out; how many are left in the cage?
9. A little girl bought 8 cherries, and her brother gave
her 3 more; how many had she then?
10. Julia bought 11 plums, and she has eaten 3 of them;
how many has she left?
11. George gave 3 cents for a pencil, and 9 cents for a
book; how many cents did he give for both of
them?
12. Frank had 12 chickens, but 3 of them have been killed
by the hawkss; how many has he left?
13. A farmer purchased 10 cows of one man, and 3 of
another; how many cows did he purchase?
14. Joseph paid 13 cents for a knife, and sold it for 10
cents; how many cents did he lose?
15. Margaret is 11 years old, and Eliza is 3 years
older than Margaret; how old is Eliza?
16. A cooper made 14 barrels, and has sold 11 of them;
how many ha h    e remaining unsold?
17. A farmer sold a firkin of butter for 12 dollars, and a
cheese for 3 dollars; how many dollars did he receive?
18. A grocer purchased 15 firkins of butter, and has sold
3 of them; how many has he remaining unsold?




20            ADDITION AND SUJBTRAC TION.
LESSON XXIX.
4 and  1 are  5      4 from   5 leaves  1
4 and  2 are  6      4 from  6 leaves  2
4 and  3 are  7      4 from  7 leaves  3
4 and  4 are  8      4 from   8 leaves  4
4 and  5 are  9      4 from   9 leaves  5
4 and  6 are 10      4 from 10 leaves  6
4 and  7 are 11      4 from 11 leaves  7
4 and  8 are 12      4 from 12 leaves  8
4 and  9 are 13      4 from 13 leaves  9
4 and 10 are 14      4 from 14 leaves 10
4 and 11 are 15      4 from 15 leaves 1 
4 and 12 are 16      4 from 16 leaves 12
LESSON XXX.
I anc 4 are how many?    1 from   5 leaves how many?
2 and 4 are how many?   2 from  6 leaves how many?
3 and 4 are how many?   3 from   7 leaves how many?
4 and 4 are how many?   4 from   8 leaves how many?
5 and 4 are how many?   5 from   9 leaves how many?
6 and 4 are how many?    6 from 10 leaves how many?
7 and 4 are how many?    7 from 11 leaves how many?
8 and 4 are how many?    8 from 12 leaves how many?
9 and 4 are how many?    9 from 13 leaves how many?
10 and 4 are how many?  10 from 14 leaves how many?
11 and 4 are how many?  11 from 15 leaves how many?
12 and 4 are how many?  12 from 16 leaves how many?
LESSON XXXI.
EXERCISES TO BE PERFORMED ON THE SLATE.'-//                      /   1 A  0         A    2 
and  6   A   9   A  -/   A
7I v 0 11  13  /135   6
^5.               7              2 4 11 4




ADDITION AND SUBTRACTION.             21
LESSON XXXII.
1. A boy found 4 eggs in one bird's nest, and 3 in another; how many eggs did he find in both nests?
2. If you have 7 pigeons, and 3 of them should die, how
many would remain alive?
3. Frances paid 4 cents for a thimble, and 5 cents for
some needles; how many cents did she pay away?
4. A truant boy robbed some birds' nests of 9 eggs, and
broke 4 of them; how many remained unbroken?
5. There are 6 girls in one class, and 4 in another; how
many are there in both classes?
6. 10 boys were called out to recite; 4 of them, not having learned the lesson, were sent back.  How many
recited?
7. A boy lived in Dedham  till he was 7 years old, and
then moved to Boston, where he has lived 4 years.
How old is he?
8. Rebecca is now 11 years old, and has attended school
the last 7 years.  How old was Rebecca when she
began to attend school?
9. There are 8 houses on one side of a street, and 4 on
the other; how many houses are there on both sides?
10. If a man who owns 12 horses should sell 4 of them,
how many horses would he have left?
11. If a skein of silk is worth 4 cents, and a yard of ribbon 9 cents. how many cents are both of them
worth?
12. Sarah paid 13 cents for a paper of pins and a yard
of tape.  The price of the pins was 9 cents; what
was the price of the tape?
13. If a boy perform 10 questions in arithmetic in the
forenoon, and 4 more in the afternoon, how many
questions will he have performed during the day?
14. If a girl have 14 questions in arithmetic given her for
a lesson, and she perform but 10 of them, how
many remain to be performed?
15. In a recitation there were 12 questions answered correctly, and 4 answered incorrectly; how  many
questions were asked?




22           ADDITION AND SUBTRACTION,
LESSON  XXXIII.
5 and  1 are  6      5 from  6 leaves  1
5 and  2 are  7      5 from  7 leaves  2
5 and  3 are  8      5 from  8 leaves  3
5 and  4 are  9      5 from  9 leaves  4,
5 and  5 are 10      5 from 10 leaves 5
5 and  6 are 11      5 from 11 leaves 6
5 and  7 are 12      5 from 12 leaves  7
5 and  8 are 13      5 from 13 leaves  8
5 and  9 are 14      5 from 14 leaves 9
5 and 10 are 15      5 from 15 leaves 10
5 and II are 16      5 from 16 leaves 11
5 and 12 are 17      5 from 17 leaves 12
LESSON XXXIY.
1 and 5 are how many?   1 from  6 leaves how many?
2 and 5 are how many?   2 from  7 leaves how many?
3 and 5 are how many?   3 from  8 leaves how many?
4 and 5 are how many?   4 from  9 leaves how many?
5 and 5 are how many?   5 from 10 leaves how many?
6 and 5 are how many?   6 from 11 leaves how many?
7 and 5 are how many?   7 from 12 leaves how many?
8 and 5 are how many?   8 from 13 leaves how many?
9 and 5 are how many?   9 from 14 leaves how many?
10 and 5 are how nmany?  10 from 15 leaves how many?
11 and 5 are how many?  11 from 16 leaves how many?
12 and 5 are how many?  12 from 17 leaves how many?
LESSON XXXV.
EXERCISES TO BE PERFORMED ON THE SLATE.
KI 5   8   55  /0   5   2
(9C/!     6                        5                2 5
a%  //  /3  /4  /5   /6  /7
9, 6   5 Y                         5 sf             5




ADDITION AND SUBTRACTION.             23
LESSON XXXVI.
1. A hen has 5 black chickens and 4 white ones; how
many chickens are there of both colors?
2. A  farmer has 9 cows; 5 of them  are red, and the
others are brown.  How many are brown?
3. How many cents will it take to purchase 2 picturebooks, if one of them cost 6 cents and the other 5
cents?
4. A drover had 11 lambs, but he has sold 5 of them;
how many lambs has he left?
5. Robert has 5 cherries, and Julia has 7.  If Robert
gives his to Julia, how many will she then have?
6. Julia had 12 cherries, but she has eaten 5 of them;
how many has she left?
7. There are 8 birds in one cage, and 5 in another; how
many birds are there in both cages?
8. If a man own 13 horses, and should sell 5 of them,
how many would he have left?
9. If a man have 5 pigs in one pen, and 9 in another,
how many pigs are there in both pens?
10. If a butcher have 14 fat pigs, and should kill 5 of
them, how many would he have left alive?
11. A farmer has 10 cows in one pasture, and 5 in another; how many cows has he in both pastures?
12. If a man who owns 15 cows should sell 5 of them,
how many would he have left?
13. A farmer collected 5 bushels of apples from one tree,
and 11 bushels from another; how many bushels
did he collect from both trees?
14. Thomas paid 16 dollars for a watch, and sold it for
11 dollars; how  many dollars did he lose by
trading?
15. A flour-merchant sold 12 barrels of flour on Monday,
and 5 barrels on Tuesday; how many barrels did
he sell in the two days?
16. In a pasture there are 17 sheep; 5 of them are black,
and the others are white.  How many of them are
white?




21~4      ADDITION AND 8UBTHACTION.
LESSON XXXVII.
6 and  1 are  7       6 from  7 leaves  1
6 and  2 are  8       6 from   8 leaves  2
6 and  3 are  9       6 from  9 leaves  3
6 and  4 are 10       6 from 10 leaves  4
6 and  5 are 11       6 from 11 leaves  5
6 and  6 are 12       6 from 12 leaves 6
6 and  7 are 13       6 fiom 13 leaves  7
6 and  8 are 14       6 from 14 leaves  8
6 and  9 are 15       6 from 15 leaves  9
6 and 10 are 16       6 fiom 16 leaves 10
6 and 11 are 17       6 from 17 leaves 11
6 and 12 are 18       6 from 18 leaves 12
LESSON XXXVIII.
I and 6 are how many?    1 from  7 leaves how many?
2 and 6 are how many?   2 from   8 leaves how many?
3 and 6 are how many?    3 from   9 leaves how many?
4  iand 6 are how many?   4 from 10 leaves how many?
5 and 6 are how many?   5 from 11 leaves how many?
6 and 6 are how many?   6 from 12 leaves how many?
7 and 6 are how many?   7 from 13 leaves how many?
8 and 6 are how many?   8 from 14 leaves how many?
9 and. 6 are how many?   9 from 15 leaves how many?
10 and 6 are how many?  10 from 16 leaves how many?
11 and 6 are how many?  11 from 17 leaves how many?
12 and 6 are how many?  12 from 18 leaves how many?
LESSON XXXIX.
EXERCISES TO BE PERFORMED ON THE SLATE.../.. 6  6 0o  6 2
c4 6  6  69  6 o                                      6
^ga242/  BX    B/         @s    40         at' 




ADDITION AND SUBT'lACTION.             25
LESSON XL.
1. There are 6 boys in one division of a class, and 4
boys in another; how many boys are there in both
divisions?
2. There are 10 girls in a class at school; 6 of them are
studying, and the others are idle.  How many of
them are idle?
3. Thomas owns 6 doves; if he should buy 5 more, how
many doves would he then own'?
4. If you have 11 pigeons, and should kill 6 of them,
how many would be left alive?
5. There are 7 apple-trees and 6 pear-trees in a garden;
how many trees are there in the garden?
6. There are 13 fruit-trees in a garden; 6 of them are
peach-trees, and the others are cherry-trees.  How
many of them are cherry-trees?
7. Henry paid 6 cents for a writing-book, and 8 cents
for pens; how many cents did the book and pens
cost him?
8. Lucy paid 14 cents for a skein of silk and a paper of
pins; the price of the silk was 6 cents.  What
was the price of the pins?
9. If you pick 9 quarts of strawberries to-day, and 6
quarts to-morrow, how many quarts will you have
picked in the two days?
10. George gave 15 peaches to his sister, and 9 to his
brother; how many more did he give to his sister
than he gave to his brother?
11. A tailor sold a coat for 10 dollars, and a pair of pants
for 6 dollars; how many dollars did he receive for
both garments?
12. Stephen rode 16 miles in the cars, and 6 miles in a
chaise; how many more miles did he ride in the
cars than in the chaise?
13. A grocer sold 6 pounds of sugar at one time, and 11
pounds at another time; how many pounds of sugar
did the grocer sell?
14. Sarah is 17 years old, and James is 12; what is the
difference of their ages?




26            ADDITION AND SUBTRACTION.
LESSON XLI.
7 and  1 are  8      7 from   8 leaves  1
7 and  2 are  9      7 from   9 leaves  2
7 and  3 are 10      7 from 10 leaves  3
7 and  4 are 11      7 from 11 leaves  4
7 and  5 are 12      7 from 12 leaves  5
7 and  6 are 13      7 from 13 leaves  6
7 and  7 are 14      7 from 14 leaves  7
7 and  8 are 15      7 from 15 leaves  8
7 and  9 are 16      7 from 16 leaves  9
7 and 10 are 17      7 from 17 leaves 10
7 and II are 18      7 from 18 leaves 11
7 and 12 are 19      7 from 19 leaves 12
LESSON XLII.
I and 7 are how many?    I from   8 leaves how many?
2 and 7 are how many?   2 from  9 leaves how many?
3 and 7 are how many?   3 from 10 leaves how many?
4 and 7 are how many?   4 from 11 leaves how many?
5 and 7 are how many?   5 from 12 leaves how many?
6 and 7 are how many?   6 from 13 leaves how many?
7 and 7 are how many?   7 from 14 leaves how many?
8 and 7 are how many?    8 from 15 leaves how many?.9 and 7 are how many?   9 from 16 leaves how many?
10 and 7 are how many?  10 from 17 leaves how many?
11 and 7 are how many?  11 from 18 leaves how many?
12 and 7 are how many?  12 from 19 leaves how many?
LESSON  XLIII.
EXERCISES TO BE PERFORMED ON THE SLATE.
dc Ka              7 6              1 0   7   72
cazz    / 3   6 //   /7  /1
^^k    5  7  9  0o   7  /2




ADDITION AND SUBTRACTION.            27
LESSON XLIV.
1. If you spend 7 cents to-day, and 5 more to-morrow,
how many cents will you have spent in both days?
2. If a market-man have 12 chickens, and should sell 5
of them, how many would he have left?
3. If there are 6 children in one family and 7 in another,
how many children are there in the two families?
4. There are 13 children in two families; in one of them
there are 7 children.  How many are there in the
other?
5. A little boy had 7 apples in a basket, and his sister
put in 7 more; how many apples are there in the
basket?
6. If you have 14 pears in a basket, and should sell 7
of them, how many would you have remaining?
7. A farmer paid 8 dollars for a plough, and 7 dollars
for a harrow; how many dollars did he pay for
both of them?
8. A market-woman had 15 oranges, and sold 7 of them;
how many has she remaining unsold?
9. How many cents would be required to pay for two
picture-books, if the price of one of them is 7 cents,
and the price of the other 9 cents?
10. A boy paid 16 cents for a ball and humming-top;
the price of the humming-top was 9 cents.  What
was the price of the ball?
II. A  girl paid 10 cents for a doll, and 7 cents for
ribbon; how many cents did she pay away?
12. A boy has 17 cents; if he should spend 7 of them,
how many would he have left?
13. There are two pieces of cloth; one of them contains 7
yards, and the other 11 yards.  How many yards
are there in the two pieces?
14. A  trader had a piece of silk which measured 18
yards; he sold 11 yards of it to a lady for a dress.
How many yards were left?
15. Julia and Mary went into the garden to gather
flowers; Mary gathered 12 roses, and Julia 7.
How many roses did they both gather?




28           ADDITION AND SUBTRACTION.
LESSON XLV.
8 and  I are  9     8 from  9 leaves  1
8 and  2 are 10     8 from 10 leaves 2
8 and  3 are 11     8 from 11 leaves  3
8 and' 4 are 12     8 from 12 leaves 4
8 and  5 are 13     8 from 13 leaves 5
8 and  6 are 14     8 from 14 leaves 6
8 and  7 are 15     8 from 15 leaves 7
8 and  8 are 16     8 from 16 leaves  8
8 and  9 are 17     8 from 17 leaves  9
8 and 10 are 18     8 from 18 leaves 10
8 and 11 are 19     8 from 19 leaves 11
8 and 12 are 20     8 from 20 leaves 12
LESSON XLVI.
1 and 8 are how many?   1 from  9 leaves how many?
2 and 8 are how many?   2 from 10 leaves how many?
3 and 8 are how many?   3 from 11 leaves how many?
4 and 8 are how many?   4 from 12 leaves how many?
5 and 8 are.how many?   5 from 13 leaves how many?
6 and 8 are how many?   6 from 14 leaves how many?
7 and 8 are how many?   7 from 15 leaves how many?
8 and 8 are how many?   8 from 16 leaves how many?
9 and 8 are how. many?   9 from 17 leaves how many?
10 and 8 are how many?  10 from 18 leaves how many?
11 and 8 are how many?  11 from 19 leaves how many?
12 and 8 are how many?  12 from 20 leaves how many?
LESSON  XLVII.
EXERCISES TO BE PERFORMED ON THE SLATE.
ard   8   B                         8  80         2
/ 5  /6 /7  /$ /?  20
e^1^  27                            8  //   8




ADDITION AND SUBTRACTION.              29
LESSON  XLVIII.
1. If a writing-book cost 8 cents, and a lead-pencil
5 cents, how many cents do they both cost?
2. A boy having 13 cents, paid away 8 of them for a
slate; what number of cents had he left?
3. If one boy should catch 6 perch, and another 8, how
many would they both catch?
4. A boy caught 14 trout, and sold 6 of them; how many
had he left?
5. 8 boys are playing in one street, and 7 in another;
how many are playing in both streets?
6. 15 little girls were on a visit; at nine o'clock, 7 of
them went home.  How many remained?
7. There are 9 boys in one sleigh, and 8 in another;
how many boys are there in both sleighs?
8. There are 17 girls in a class; 9 of them are ciphering,
and the others are writing.  How many are writing.?
9. There are 8 boys in the first division of a class, and
10 in the second; how many boys are there in the
class?
10. Two places are 18 miles apart; if a boy start from
one place, and travel 10 miles towards the other,
how many miles is he from the other place?
11. If you should buy 11 apples of one kind, and 8 of
another kind, how many apples would you have
of both kinds?
12. A boy purchased 19 pears, and has sold 8 of them;
how many has he left unsold?
13. Eliza has 12 flower-pots, and Jane has 8; how many
flower-pots have both of them?
14. Emma counted 20 roses on her rose-bush this morning; afterwards she picked off 8 of them.  How
many remained on the rose-bush?
15. Catharine's book has 8 pictures in it, and Mary's
has 12; how many pictures do both books contain?
16. In the arithmetic class there are 20 pupils; 12 of
them recited their lesson correctly.  How many of
them failed?
3^




30            ADDITION AND SUBTRACTION.
LESSON XLIX.
9 and  1 are 10      9 from 10 leaves  1
9 and  2 are 11      9 from 11 leaves  2
9 and  3 are 12      9 from 12 leaves  3
9 and  4 are 13      9 from 13 leaves  4
9 and  5 are 14      9 from 14 leaves  5
9 and  6 are 15      9 from 15 leaves  6
9 and  7 are 16      9 from 16 leaves  7
9 and  8 are 17      9 from 17 leaves  8
9 and  9 are 18      9 from 18 leaves  9
9 and 10 are 19      9 from 19 leaves 10
9 and 11 are 20      9 from 20 leaves 11
9 and 12 are 21      9 from 21 leaves 12
LESSON L.
1 and 9 are how many?    1 from 10 leaves how many?
2 and 9 are how many?   2 from 11 leaves how many?
3 and 9 are how many?    3 from 12 leaves how many?
4 and 9 are.how many?   4 from 13 leaves how many?
5 and 9 are how many?   5 from 14 leaves how many?
6 and 9 are how many?   6 from 15 leaves how many?
7 and 9 are how many?    7 from 16 leaves how many?
8 and 9 are how many?    8 from 17 leaves how many?
9 and 9 are how many?    9 from 18 leaves how many?
10 and 9 are -how many?  10 from 19 leaves how many?
11 and 9 are how many?  11 from 20 leaves how many?
12 and 9 are how many?  12 from 21 leaves how many?
LESSON LI.
EXERCISES TO BE PERFORMED ON THE SLATE.
(ad   5   6$                       $   f/    $ 2
y7mZ 10 15  17  $  20  21
7ae  5   $   8   $  11  12




ADDITION AND SUBTiACTION.'1
LESSON  LIi.
i. A boy was born in Milton, and lived there until he
was 9 years old; he then moved to Boston, and
has lived in'Boston 5 years.  How old is he?
2. A girl is 14 years old; she lived in the country lintl
she was 9 years old, and has since lived in Boston.
How many years has she lived in Boston 
3. There are 9. chairs in one room, and 6 in anrit!er 
how many chairs are there in the two rooms?
4. If there are 15 plates upon a table, and 6 of them
should be taken off, how many would remain upon
the'table?
5. If one hen has 9 chickens, and another hen has 7,
how many chickens have both hens?
6. If you have 16 young turkeys, and 7 cf them should
die, how many would be left alive?
7. If there are 8 sheep in one pasture, and 9 in another,
how many sheep are there in the two pastures?
8. If a drover have 17 fat sheep, and should sell 8 of
them, how many would he have remaining unsold?
9. There are 9 windows on the front side of a house, and
9 on the back side; how many windows are there
on the two sides?
10. If there are 18 panes of glass in a window, and 9 of
them should be broken by a storm, how many would
remain whole?
II. Julia has recited 1 0 lesso.ns to her Sab!bath-school
teacher, and her sister Hiarriet has recite. 9.  How
many lessons have they both recited?
12. There are 19 scholars in the first class of a Sabbathschool; ten of them  are boys, and the others are
girls.  How many of them are girls?
13. A man paid 11 dollars for three hats, and 9 dollars
for two pairs of boots; how many dollars did he
pay for the whole?
14. A gentleman purchased 20 pounds of flour, and after
using a part of it, found that he had 1II pounds
left; how many pounds had he used?




82           ADDITION AND S-UBTRACTION1.
LESSON  LIII.
10 and  I are 11     10 from 11 leaves I
10 and  2 are 12     10 from 12 leaves 2
10 and  3 are 13     10 from 13 leaves 3
10 and  4 are 14     10 from 14 leaves 4
10 and  5 are 15     10 from 15 leaves 5
10 and  6 are 16     10 from 16 leaves  6
10 and  7 are 17     10 from 17 leaves 7
10 and  8 are 18     10 from 18 leaves 8
10 and  9 are 19     10 from 19 leaves 9
10 and 10 are 20     10 from 20 leaves 10
10 and 11 are 21     10 from 21 leaves 11
10 and 12 are 22     10 from 22 leaves 12
LESSON LIV.
1 and 10 are how many?  I from 11 leaves how many?
2 and 10 are how many?  2 from 12 leaves how many?
3 and 10 are how many?  3 from 13 leaves how many?
4 and 10 are how many?  4 from 14 leaves how many?
5 and 10 are how many?  5 from 15 leaves how many?
6 and 10 are how many?  6 from 16 leaves how many?
7 and 10 are how many?  7 from 17 leaves how many?
8 and 10 are how many?  8 from 18 leaves how many?
9 and 10 are how many?  9 from 19 leaves how manyy?
10 and 10 are how many? 10 from 20 leaves how many?
11 and 10 are how many? 11 from 21 leaves how many?
12 and 10 are how many? 12 from 22 leaves how many?
LESSON LV.
EXERCISES TO BE PERFORMED ON THE SLATE.
~I d4o   6  /o    2  //  to
ccd'  5   /0    7  /0   /0 2                        2
a;oI5  i6 t5 7  /?  2/  22
57^D_ j               tO   7               t  tO  0




ADDITION AND SUBTRACTION.               83
LESSON LVY
1. A little boy is 10 years old, and his sister is 4 years
older than he is; how old is his sister?
2. Amelia is 14- years old, and her brother Marcellus
is 4 years younger; how old is Miarcellus?
3. The American gold eagle is valued at 10 dollars, the
half eagle at 5 dollars; what is the value of both
of them?
4. Caroline has 15 credit-marks, and Jane has 10; how
many more has Caroline than Jane?
5. A lady paid 6 dollars for a cap, and 10 dollars for a
bonnet; how m1any dollars did she pay for both?
6. A man gave 16 dollars for a vest and coat.  The
price of the coat was 10 dollars; what was the
price of the vest?
7. Henry paid 10 cents for a writing-book, and 7 cents
for pens; how many cents did the writing-book and
pens cost him?
S. Albert is 17 years old, and his sister is 10; how many
years older is Albert than his sister?
9. Annie is 8 years old, and Emily is 10; what is the
sum of both their ages?
10. William purchased 18 pears, and gave 10 of them to
his sister; how many has he left?
].1. If I pay 10 cents for a pound of raisins, and 9 cents
for a pounnd of figs, how many cents do they cost
me?
12. A farmer has 19 lambs; if he should sell 10 of them,
how many would he have left?
13. Jane has 10 pears and 10 peaches in her fruit-basket;
how many of both kinds of fruit has she in her
basket?
14. Charles bought 20 nuts, and gave 10 of them to Edward; how many had he left?
15. There are 11 girls in the first section of a class, and
10 in the second; how many girls are there in the
class?
16. In a private school there are 21 scholars, and 10 of
them are boys; how many of them are girls?




34            ADDITION AND SUBTRACTION.
LESSON  LVII.
11 and  I are 12      11 from 12 leaves  1
11 and  2 are 13      11 from 13 leaves  2
11 and  3 are 14      11 from 14 leaves  3
11 and  4 are 15      11 from 15 leaves  4
11 and  5 are 16      11 from 16 leaves  5
11 and  6 are 17      11 from 17 leaves  6
11 and  7 are 18      11 from 18 leaves  7
11 and  8 are 19      11 from 19 leaves  8
11 and  9 are 20      11 from 20 leaves  9
11 and 10 are 21      11 from 21 leaves 10
11 and 11 are 22      11 from 22 leaves 11
11 and 12 are 23      11 from 23 leaves 12
LESSON  LVIII.
I and 11 are how many?  I from 12 leaves how many?
2 and 11 are how many?  2 from 13 leaves how many?
3 and 11 are how many?  3 from 14 leaves how many?
4 and 11 are how many?  4 from 15 leaves how many?
5 and 11 are how many?  5 from 16 leaves how many?
6 and 11 are how many?  6 from 17 leaves how many?
7 and 11 are how many?  7 from 18 leaves how many?
8 and 11 are how many?  8 from 19 leaves how many?
9 and 11 are how many?  9 from 20 leaves how many?
10 and 11 are how many? 10 from 21 leaves how many?
11 alnd 11 are how many? 11 from 22 leaves how many?
12 and 11 are how many? 12 from 23 leaves how many?
LESSON LIX.
EXERCISES TO BE PERFORMED ON THE SLATE.
211^ //            6   //   /0   //  -
c/'  5/ //  //  //  /
^cg ^6  17  20  21/  22  23
cahe 5  /1/  //   0  //  12




ADDITION AND IUBTIRACTION.            35
LESSON LX.
1. One man gives a poor girl 11 cents, and another
gives her 4; lhow many cents does the poor girl
get?
2. A poor boy has 15 cents; if he should pay away 4
of them for bread, how many cents would he have
left?
3. William has 11 apples, and Henry has 4; how many
apples have both. of them?
4. A market-woman having 16 eggs, sold 11 of them;
how many had she remaining unsold?
5. Robert caught 11 fish, and Henry caught 6; how
many did they both catch?
6. William is 17 years old, and Jane is 11; what is the
difference of their ages?
7. A farmer sold 11 barrels of apples to one man, and 7
barrels to another; how many did he sell to both
of them?
8. William sold a knife for 18 cents, which was 7 cents
more than it cost him; what did he pay for the
knife?
9. Samuel sold some pears for 11 cents, and some peaches
for 8 cents; how many cents did he receive for his
pears and peaches?
10. Henry carried 19 boxes of strawberries to market, and
sold 8 boxes of them; how many boxes has he
remaining unsold?
11. A farmer has two fields of wheat; one contains 9
acres and the other 11 acres.  How many acres
are there in the two fields?
12. A grocer purchased 20 boxes of figs, and has sold 9
of them; how many boxes has he remaining unsold?
13. Elizabeth purchased 11 yards of silk, and Jane purchased 10 yards; how many yards did they both
purchase?
14. A  merchant had a piece of muslin containing 21
yards, and sold 11 yards of it to a lady; how many
yards are there left?




36            ADDITION AND SUBTRACTION.
LESSON LXI.
12 and  I are 13      12 from 13 leaves  1
12 and  2 are 14      12 from 14 leaves  2
12 and  3 are 15      12 from 15 leaves  3
12 and  4 are 16      12 from 16 leaves 4
12 and  5 are 17      12 from 17 leaves  5
12 and  6 are 18      12 from 18 leaves  6
12 and  7 are 19      12 from 19 leaves  7
12 and  8 are 20      12 from 20 leaves  8
12 and  9 are 21      12 from 21 leaves  9
12 and 10 are 22       2 12 from 22 leaves 10
12 and 11 are 23      12 from 23 leaves 11
12 and 12 are 24      12 from 24 leaves 12
LESSON  LXII.
I and 12 are how many? 12 from 13 leaves how many?
2 and 12 are how many? 12 from 14 leaves how many?
3 and 12 are how many? 12 from 15 leaves how many?
4 and 12 are how many? 12 from 16 leaves how many?
5 and 12 are how many? 12 from 17 leaves how many?
6 and 12 are how many? 12 from 18 leaves how many?
7 and 12 are how many? 12 from 19 leaves how many?
8 and 12 are how many? 12 from 20 leaves how many?
9 and 12 are how many? 12 from 21 leaves how many?
10 and 12 are how many? 12 firom 22 leaves how many?
11 and 12 are how many? 12 from 23 leaves how many?
12 and 12 are how many? 12 from 24 leaves how many?
LESSON  LXIII.
EXERCISES TO BE PERFORMED ON THE SLATE.
Aidd /5  6   2   2  /d  /2
er/7  /2  22  2/  23  2A
A 5 5 2  -    /2  //  /2




ADDITION AND SUBTRACTION.             37
LESSON  LXIV.
1. A mechanic paid 12 dollars for a firkin of butter, and
5 dollars for a barrel of flour; how many dollars
did the two articles cost him?
2. A  man purchased 17 bushels of oats, and has used
5 bushels in feeding his horses; how many bushels
has he reimaining?
A. A boy purchased a box for 12 cents, and paid 6 cents
for painting it; how many cents did the box cost
him?
4. A man borrowed 18 dollars, and has paid 12 dollars
of it; how many dollars remain unpaid?
5. Thomas paid 8 cents for a musk-melon, and 12 cents
for a water-melon; how many cents did the two
melons cost him?
6. Catharine had a present of 20 oranges, and gave 8
of them to her playmates; how many has she left?
7. A truckmana paid 12 dollars for a load of hay, and 9
dollars for twenty bushels of oats; how many dollars did he pay away?
8. A man paid 21 dollars for a cow, and 9 dollars for four
bundles of hay; how much more did he pay for the
cow than for the hay?
9. A drover purchased five sheep for 12 dollars, and two
calves for 10 dollars; how many dollars did he
pay for the whole?
10. Caroline has performed 22 questions in arithmetic,
and Frances has performed 12 questions; how many
more questions has Caroline performed than Frances?
11. There are two pieces of cloth; one of them measures
12 yards, and the other measures 11 yards.  How
many yards are there in the two pieces?
12. A farmer picked 23 bushels of quinces, and has sold
8 bushels of them to one man, and 4 to another;
how many bushels has lie remaining unsold?
13. Harriet wrote 12 lines in her wwrting-book in the
morning, aid 12 lines more in the afternoon; how
many lines did she write during the day?
4




38            ADDITION ANJD S!uBl'TACTION,
LESSON  LXV.
I and  2 and  3 less I are how0 many?,
2 and  3 and  4 less  2 are how many?.
3 and  4 and  5 less 3 are how many?
4 and  5 and  6 less 4 are how many 
5 and  6 and  7 less 5 are how many.'
6 and  5 and  4 less 6 are how many?
7 and  4 antd  3 less 2 are how many
8 and  3 and  2 less 4 are how many 
9 and  6 and.    3 less 5 are how many'
10 and  5 and  4 less 6 are how many?
11 and  4 and  3 less 7 are how many?
12 and  6 and  4 less 8 are how many?
13 and  3 and  2 less 9 are how many?
14 and  4 and  5 less 10 are how many?
15 arid  5 and  6 less 1  are how many?
16 and  6 and  7 less 12 are how many?
17 and  7 and  I less 2 are how many?
18 and  8 and  2 less 3 are how many?
LESSON  LX'VL.
19 and  9.and  3 less 4 are how lmany?
20 and 10 and  4 less 5 are how many?
21 and 11 and  5 less 6 are how many?
22 and 12 and  6 less 7 are how many?
23 and  2 and  3 less  8 are how manyv?
24 and  3 and  4 less 9 are how many?
25 and  5 and  6 less 10 are how many?
26 and  6 and  4 less 11 are how many?
27 and  7 and  5 less 12 are how many?
28 and  8 and  6 less 4 are how many?
29 and  9 and 10 less 5 are how many?
30 and 10 and  5 less 6 are how many?
10 and 20 and 30 less 40 are how many?
20 and 20 and 30 less 50 are how many?
30 and 30and20 less 60 are how many?
40 and 40 and 10 less 70 are how many?
50 and 50 and 20 less 80 are how many?
00 and 60 and 10 less 90 are htow many?




ADDITION AN]) SUBT'RCTION.               }'9
LESSON LXVII.
1. A grocer purchased 10 barrels of four of A, 5 of B,
and 3 of C, -and has sold 6 barrels' of it; how many
barrels has he remaining unsold?i
2. A farmer having 20 barrels of apples, sold 10 barrels
to C, and 5 barrels to D; how lmany barrels had
he left?
3. William  purchased 24 peaches, and gave 8 of them
to his sister, and 6 of them  to his brother; how
many had he left?
4. A trader borrowed 100 dollars, and paid 50 dollars
at one time, and 30 dollars at another time; how
many dollars remain unpaid?
5. A man bought a wagon for 45 dollars, and paid 5
dollars for painting it; he then sold it for 55 dollars. How many dollars did he gain by trading?
4. Mary bought a pair of gloves for 50 cents, a comb
for 15 cents, and a paper of pins for 10 cents.
She, handed the clerk a dollar; how much change
ought she to receive?
7. A jeweller bought a watch for 30 dollars, a chain for
15 dollars, and a key for 5 dollars, and sold them
all for 60 dollars; how many dollars did he gain
by trading?
8. A  -merchant, who had GO barrels of flour, sold 20
barrels to one man, and 15 barrels to another;
how many barrels had he leTf, 
). Jane had 20 cets, her father gave h-rs 15 cents, and
her mother gmve her 10 cents.  She ithen bought a
book for 25 cents; how many cents had she left?
10. A farmer sold a cow for 20 dollars, a calf foGt 5 dollars,
and a sleep ifr 3 dollars           a and in payment received a sleigh worth 18 I ]dolla.  How many dollars remain unpaid?
II. A market-man paid 12 dollars for a firkin of butter,
10 dollars for five barrels of apples, and 3 dollars for
a b.arrel of cranberries, and sold them  all for 28
dollars  how much was gained?




40      ADDITIO-N AND SUJBTRACTIONT
LESSON LXVIII.
EXERCISES TO BE PERFORMED ON THE SLAT.AJd    A, fJ 0   3   8  //
5   3  1  4             7  1o
amnc    6   7    2   5   6 
o   15  211 33  12  29  36
9,a /   / 3  22   /  13  2f
C/ 6   9?12   7   0 o
axnd    7?      J $  // 
a P~    7 1      1o 1f 15  2, 15
cd    3      8 63? 90
ac    2   9   7   2   0
d41   i0  6'0  70  50  60  90
aE'W1  20  50  s0  40  70  30
an.30   0     30 0         20




ADI)TION AND SUBiTItA.CT[ON.             4i
LESSON LXIX.
1. A  man bought eighteen  oranges for 54 cents, six
lemons for 12 cents, and a melon for 10 cents;
how many cents dlidc he pay for all of them?
2. There is a rnas', 5 feet of which is in the mudc, 10
feet in the water,  and 15 feet above the water; how
long is the mast?
8. In a school 15 girls learn to write, 12 learn arithmetic, 10 learn grammar, 8 learn geography, and
6 learn history; how many girls are there in the
school?
4. There is an orchard in which there are 50 apple-trees,
25 peach-trees, 15 pear-trees, and 10 pluml-trees;
how many trees are there in the orchard?
5. There is a school in which there are four classes.  In
the first class there are 15 boys, in the second 10,
in the third 9, and in the fourth 8; how  many
boys are there in the school?
6. If you have 20 cents, and spenc 8 or them for raisins and. 6 for oranges, how many cents will you
have left?
7. A man borrowed 30 dollars; at one time he paid I5
dollars, at another 10 dollars.  How many dollars
remain unpaid?
8. A man bought a horse for 60 dollars, and paid 5 dollars for keepin'  hLim, a.nd sold him for  5 dollars;
what numbedr of     dollars did he gin?
9. A man sold a horse for 120 dollars, which was 30
dollars more than he gave for him; what  idl he
give for the horse?
10. A drover purchased 25 shlopn of one man, 15 of another, 12 of another, and 10 of anotler; he has
since sold 12 of them.  How many has he left.?
11. A  boy bought a book for 50 cents, a slate for 2
cents, and a dozen pencils for 5 cents; he paid for
them with a one dollar bank bill, which is equal to
100 cents.  How  many cents ought he to receive
back in change?
4*




42          MiULTIPLICATION AND DIYISTOi>
LESSON LXX.
2 times  1 are  2     2 in  2  1 times
2 times  2 are  4     2 in  4  2 times-.
2 times  3 are  6     2 in  6  3 times.
2 times  4 are  8     2 in  8  4 times.
2 times  5 are 10     2 in 10  5 times.
2 times  6 are 12     2 in 12  6 times.
2 times  7 are 14     2 in 14  7 times.
2 times  8 are 16     2 in 16  8 times,
2 times  9 are 18     2 in 18  9 times.
2 times 10 are 20     2 in 20 10 times.
2 times 11 are 22     2 in 22 11 times.
2 times 12 are 24     2 in 24 12 times.
LESSON LXXI.
I time 2 are how many?        What is 1 half of 2? ~
2 times 2 are how many?       What is 1 half of 4?
3 times 2 are how many?       What is I half of 6?
4 times 2 are how many?       What is 1 half of 8?
5 times 2 are hor many?       What is I half of 10?
6 times 2 are how many?       What is 1 half of 12?
7 times 2 are how many?       What is 1 half of 14?
8 times 2 are how many?       What is 1 half of 16?
9 times 2 are how many?       What is I half of 18?
10 times 2 are how many?       What is 1 half of 20?
11 times 2 are how many?       What is 1 half of 22?
12 times 2 are how many?       What is 1 half of 24?
LESSON LXXII.
EXERCISES TO BE PERFORMED ON THE SLATE.
Cw/0           /    X             10   11/            2
222  2  2  2
iw v eA 2  I6   2                                   2 ^^
* When any number is divided into two equal parts, each part
is called one half of the number,




MULTIPLICATION AND DIVISION.            4S
LESSON  LXXIII.
1. If you pay one cent for an apple, how many cents must
you pay for 2 apples?
2. If 2 peaches cost 2 cents, what will one peach cost?
3. A little girl has 2 hands; how many hands have 2
little girls?
4. 2 little girls have 4 eyes; how many eyes has one
little girl?
5. Mary has 3 picture-books, and Jane has 2 times as
many; how many picture-books has Jane?
6. Jane has 6 pears, and Mary has only one half as
many; how many pears has Mary?
7. If one yard of ribbon cost 4 cents, how many cents
will 2 yards cost?
8. If 2 oranges cost 8 cents, how many cents will one
orange cost? t},
9. If a quart of milk is worth 5 cents, how many cents
are 2 quarts worth?
10. If 2 quarts of milk are worth 10 cents, how many
cents is one quart worth?
11. If a loaf of bread is worth 6 cents, how many cents
are 2 loaves worth?
12. If you have 12 cents, how many loaves of bread can
you buy with them at 6 cents each?
13. What will 2 yards of cloth cost, at 7 dollars a yard?
14. If 2 yards of cloth cost 14 dollars, what is one yard
of it worth?
15. Henry has 8 marbles, and James has 2 times as
many; how many marbles has James?
16. William has 16 nuts, and Albert has only one half
as many; how many nuts has Albert?
17. If a stage run 9 miles in an hour, how many miles
will it run in 2 hours?
18. How many hours will it take a man to travel 18
miles, if he travel 9 miles an hour?
19. There are 10 dollars in a gold eagle; how many dollars are there in 2 eagles?
20. In 20 dollars, how many eagles are there of 10 dollars each?




44          MULTIPLICATION AND DIVISION.
LESSON LXXIV.
3 times  I are  3     3 in  3  1 time.
3 times 2 are  6      3 in  6  2 times.
3 times  3 are  9     3 in  9  3 times.
3 times  4 are 12     3 in 12  4 times.
3 times  5 are 15     3 in 15" 5 times.
3 times 6 are 18      3 in 18  6 times.
3 times  T are 21     3 in 21  7 times.
3 times  8 are 24     3 in 24  8 times.
3 times 9 are 27      3 in 27  9 times.
3 times 10 are 30     3 in 30 10 times.
3 times 11 are 33     3 in 33 11 times.
3 times 12 are 36     3 in 36 12 times.
LESSON LXXV.
I time 3 are how many?        What is 1 third of 3? 
2 times 3 are how many?       What is 1 third of 6?
3 times 3 are how many?       What is 1 third of 9?
4 times 3 are how many?       What is 1 third of 12?
5 times 3 are how many?       What is 1 third of 15?
6 times 3 are how many?       What is I third of 18?
7 times 3 are how many?       What is 1 third of 21?
8 times 3 are how many?       What is 1 third of 24?
9 times 3 are how many?       What is 1 third of 27?
10 times 3 are how many?       What is I third of 30?
II times 3 are how many?        Whhat is 1 third of 33?
12 times 3 are how many?        What is 1 third of 36?
LESSON LXXVI.
EXERCISES TO BE PERFORMED ON THE SLATE.
7  3  9 8                             // /8   8
3  3 33   3   3   3
Qfz{w   2   y 3  2 70 3   36? 6
* When any number is divided into three equal parts, each
of the parts is called one third of the number.




MIULTIPLICATION AND DIVISION.            45
LESSON LXXVII.
1. Sophia has one rose, and Maria has 3 times as many;
how many roses has Maria?
2. Maria has 3 pinks, Sophia has only one third as
many; how many pinks has Sophia'?
3. In one quart there are 2 pints; how many pints are
there in 3 quarts?
4. There are 2 pints m one quart; how many quarts are
there in 6 pints?
5. There are 3 feet in one yard; how many feet are
there in 3 yards?
6. In one yard tlere are 3 feet; how many yards are
there in 9 feet?
7. There are 4 farthings in one penny; how many farthings are there in 3 pence 
8. In one penny there are 4 farthings; how many pence
are there in 12 farthings?
9. If you recite 5 lessons each day, how many lessons
will you recite in 3 days?
10. Charles recited  15 lessons in 3 days; how  many
lessons did he recite each day?
11. There are 6 shillings in one dollar; how many shillings are there in 3 dollars?
12. In one dollar there are 6 shillings; how many dollars are there in 18 shillings?
13. If one yard of broadcloth cost 7 dollars, what will
3 yards cost?
14. If 3 yards of broadcloth are worth 21 dollars, what is
the value of one yard?
15. If a quart of cherries be worth 8 cents, what are 3
quarts worth?
16. If 3 quarts of cherries are worth 24 cents, how many
cents is one quart worth?
17. If a pound of raisins cost 9 cents, how many cents
will 3 pounds cost?
18. If 3 pounds of raisins are worth 27' cents, what is the
value of one pound?
19. If a writing-book cost 10 cents, how many cents will
3 writing-books cost?




46          MULTIPLICATION AND 1IYISION.
LESSON LXXVIII
4 times 1 are  4     4 in  4  1 time.
4 times 2 are  8    4 in  8  2 times.
4 times 3 are 12     4 in 12  3 times.
4 times 4 are 16    4 in'16  4 times.
4 times  5 are 20    4 in 20  5 times.
4 times 6 are 24     4 in 24  6 times.
4 times 7 are 28     4 in 28  7 times.
4 times 8 are 32     4 in 32  8 times.
4 times 9 are 36    4 in 36  9 times.
4 times 10 are 40    4 in 40 10 times.
4 times 11 are 44    4 in 44 11 times.
4 times 12 are 48    4 in 48 12 times.
LESSON LXXIX.
I time 4 are how many?      What is 1 fourth of 4? 
2 times 4 are how many?    What is 1 fourth of 8?
3 times 4 are how many?     What is 1 fourth of 12?
4 times 4 are how many?    What is 1 fourth of 16?
5 times 4 are how many?    What is 1 fourth of 20?
6 times 4 are how many?    What is 1 fourth of 24?
7 times 4 are how many?    What is 1 fourth of 28?
8 times 4 are how many?    What is I fourth of 32?
9 times 4 are how many?    VWVhat is 1 fourth of 36?
10 times 4 are how many?    What is 1 fourth of 40?
11 times 4 are how many?    What is 1 fourth of 44?
12 times 4 are how many?    What is 1 fourth of 48?
LESSON LXXX.
EXERCISES TO BE PERFORMED ON THE SLATE.
^^   /r   8  9  /0  1/  /2
we2. 
l When any number is divided into four equal parts, each
of the parts is called onefourth of the number.




3iMULTIPLIC(AT2ION AND DIVISION.         47
LESSON LXXXI.
1. Caroline writes one page of her writing-book in a day;
how many pages does she write in 4 days?
2. Caroline has written 4 pages of her writing-book in 4
days; how many pages has she written each day?
3. A  bird has 2 wings; how many wings have 4
birds?
4. How many pears, at 2 cents a-piece, can you buy
with 8 cents?
5. How  many cents will 4 oranges cost, at 3 cents
a-piece?
6. If 4 oranges cost 12 cents, how many cents does one
orange cost?
7. There are 4 quarts in one gallon; how many quarts are
there in 4 gallons?
8. 4 quarts are equal to one gallon; how many gallons
are there in 16 quarts?
9. There are 5 quarters in an English ell; how many
quarters are there in 4 ells?
10. In an English ell there are 5 quarters; how many ells
are there in 20 quarters?
11. There are 6 feet in one fathom; how many feet are
there in 4 fathoms?
12. In one fathom  there are 6 feet; how many fathoims
are there in 24 feet?
13. If one barrel of four is worth 7 dollars, how many
dollars are 4 barrels worth?
14. How many barrels of flour can you buy with 28 dollars, at 7 dollars a barrel?
15. What will 4 pounds of sugar come to, at 8 cents a
pound?
16. How many pounds of beef can you purchase with 32
cents, at 8 cents a pound?
17. Thomas has 9 cents, and John has 4 times as many;
how many cents has John?
18. John has 36 nuts; Thomas has only one fourth as
many.  How many nuts has Thomas?
19. If a pound of cheese is worth 10 cents, what is the
value of 4 pounds?




48          rMULTIPLICATION AND DIVISION,
LESSON LXXXII.
5 times  I are  5      5 in  5  1 time.
5 times  2 are 10      5 in 10  2 times.
5 times  3 are 15      5 in 15  3 times.
5 times  4 are 20      5 in 20  4 times.
5 times  5 are 25      5 in 25  5 times.
5 times  6 are 30      5 in 30  6 times.
5 times  7 are 35      5 in 35  7 times.
5 times  8 are 40      5 in 40  8 times.
5 times  9 are 45      5 in 45  9 times.
5 times 10 are 50      5 in 50 10 times.
5 times 11 are 55      5 in 55 11 times.
5 times 12 are 60      5 in 60 12 times.
LESSON LXXXIII.
1 time  5 are how many?        What is 1 fifth of 5? *
2 times 5 are how nmany?       What is 1 fifth of 10?
3 times 5 are how many?        What is 1 fifth of 15?
4 times 5 are how many?        What is I fifth of 20?
5 times 5 are how many?        What is 1 fifth of 25?
6 times 5 are how many?        What is 1 fifth of 30?
7 times 5 are how many?        What is I fifth of 35?
8 times 5 are how many?       What is 1 fifth of 40?
9 times 5 are how many?        What is I fifth of 45?
10 times 5 are how many?         What is 1 fifth of 50?
11 times 5 are how many?        What is 1 fifth of 55?
12 times 5 are how many?        What is 1 fifth of 60?
LESSON LXXXIV.
EXERCISES TO BE PERFORMED ON THE SLATE.
^^  / 8 f /o // /9
<,5   5 5    5   5   5
ae35 355                      O y 5  55 y 5
When any number is divided into five equal parts, each
of the parts is called one fifth of the number.




MULTIPLICATION AND DIVISION.             49
LESSON LXXXV.
1. If Maria walks one mile each morning, how many miles
will she have walked in 5 mornings?
2. Maria has walked  5 miles in  5 mornings; how
many miles did she walk each morning?
3. A cow has 2 horns; how many horns have 5 cows?
4. William  has 10 apples; Henry has only one fifth as
many.  How many apples has Henry?
5. If the postage on a letter is 3 cents, what will be the
postage on 5 letters?
6. In one yard there are 3 feet; how many yards are
there in 15 feet?
7. There are 4 quarters in one yard; how many quarters are there in 5 yards?
8. There are 4 quarts in one gallon; how many gallons
are there in 20 quarts?
9. If a skein of silk is worth 5 cents, what is the value
of 5 skeins?
10. How many skeins of silk can you purchase with 25
cents, at 5 cents a skein?
11. If a barrel of flour cost 6 dollars, how many dollars
will 5 barrels cost?
12. If 5 yards of broadcloth are worth 30 dollars, how
many dollars is one yard worth?
13. There are 7 days in a week; how many days are
there in 5 weeks?
14. In one week there are 7 days; how many weeks are
there in 35 days?
15. There are 8 gills in one quart; how many gills are
there in 5 quarts?
16. In one quart there are 8 gills; how many quarts are
there in 40 gills?
17. If one apple-tree bears 9 bushels of apples, how many
bushels will 5 trees bear?
18. A  farmer picked  45  bushels of apples  from  5
trees; how many bushels were picked from  each
tree?
19. If a girl perform  10 questions in arithmetic in one
day, how many will she perform in 5 ldays?
5




50          MULTIPLICATION AN]D DIVISION.
LESSON LXXXVI.
6 times  1 are  6     6 in  6  1 time.
6 times  2 are 12     6 in 12  2 times.
6 times  3 are 18     6 in 18  3 times.
6 times  4 are 24     6 in 24  4 times.
6 times  5 are 30     6 in 30  5 times.
6 times  6 are 36     6 in 36  6 times.
6 times  7 are 42     6 in 42  7 times.
6 times  8 are 48     6 in 48  8 times.
6 times  9 are 54     6 in 54  9 times.
6 times 10 are 60     6 in 60 10 times.
6 times 11 are 66     6 in 66 11 times.
6 times 12 are 72     6 in 72 12 times.
LESSON LXXXVII.
I time 6 are how many?        What is I sixth of 6? -
2 times 6 are how many?       What is 1 sixth of 12?
3 times 6 are how many?        What is 1 sixth of 18?
4 times 6 are how many?        What is I sixth of 24?
5 times 6 are how many?       What is 1 sixth of 30?
6 times 6 are how many?       What is 1 sixth of 36?
7 times 6 are how many?       What is 1 sixth of 42?
8 times 6 are how many?       What is I sixth of 48?
9 times 6 are how many?       What is 1 sixth of 54?
10 times 6 are how many?        What is 1 sixth of 60?
11 times 6 are how many?        What is 1 sixth of 66?
12 times 6 are how many?        What is 1 sixth of 72?
LESSON LXXXVIII.
EXERCISES TO BE PERFORMED ON THE SLATE.
^i37   8                   Y 9 0   //  /2
6  6  6   6   6   6
^m^cg ^Add6  6,6  6  7   6
* When any nullber is divided into six equal parts, each of
the parts is called one sixth of the number.




MIULTIPLICATION AND DIVISION.           51
LESSON LXXXIX.
1. If a tailoress can make one vest in a day, how many
can she make in 6 days?
2. If a tailoress can make 6 vests in 6 days, how many
can she make in one day?
3. If Mary writes 2 copies each day, how many will she
write in 6 days?
4. Julia has written 12 pages in 6 days; how many
pages has she written each day?
5. If you give 6 girls 3 apples each, how many apples
do you give away?
6. If 18 peaches be equally divided among 6 boys, how
many will each boy have?
7. If you should buy 6 oranges, and pay 4 cents a-piece
for them, how many cents would the oranges cost?
8. If you pay 24 cents for 6 yards of tape, how many
cents is one yard of it worth?
9. William has 5 cents, and James has 6 times as many;
how many cents has James?
10. If 30 cents be put into 6 equal piles, how many cents
will there be in each pile?
11. What will 6 lead-pencils cost, at 6 cents a-piece?
12. If one yard of cloth is worth 6 dollars, how many
yards can you purchase with 36 dollars?
13. If a girl can make 7 palm-leaf hats in a week, how
many can she make in 6 weeks?
14. A cabinet-maker sold 7 tables for 42 dollars; how
many dollars did he get for each of them?
15. There are 8 pints in one gallon; how many pints are
there in 6 gallons?
16. In one gallon there are 8 pints; how many gallons
are there in 48 pints?
17. If a yard of cloth is worth 9 cents, what are 6 yards
of it worth?
18. A girl paid 54 cents for 6 yards of calico; how many
cents did she pay for each yard?
19. If one pound of beef is worth 12 cents, what is the
value of 6 pounds?




52         IMULTIPLICATION AND DIVISION.
LESSON  XC.
7 times 1 are  7      7 in  7  1 time.
7 times  2 are 14     7 in 14  2 times.
7 times  3 are 21     7 in 21  3 times.
7 times 4 are 28      7 in 28  4 times.
7 times  5 are 35     7 in 35  5 times.
7 times  6 are 42     7 in 42  6 times.
7 times 7 are 49      7 in 49  7 times.
7 times  8 are 56     7 in 56  8 times.
7 times  9 are 63     7 in 63  9 times.
7 times 10 are 70     7 in 70 10 times.
7 times 11 are 77     7 in 77 11 times.
7 times 12 are 84     7 in 84 12 times.
LESSON XCI.
I time 7 are how many?   What is I seventh of 7? 
2 times 7 are how many?   What is 1 seventh of 14?
3 times 7 are how many?   What is 1 seventh of 21?
4 times 7 are how many?   What is 1 seventh of 28?
5 times 7 are how many?   What is 1 seventh of 35?
6 times 7 are how many?   What is 1 seventh of 42?
7 times 7 are how many?   What is 1 seventh of 49?
8 times 7 are how many?   What is 1 seventh of 56?
9 times 7 are how many?   What is 1 seventh of 63?
10 times 7 are how many?   What is 1 seventh of 70?
11 times 7 are how many?   What is 1 seventh of 77?
12 times 7 are how many?   What is 1 seventh of 84?
LESSON  XCII.
EXERCISES TO BE PERFOiRMED ON THE SLATE.
J^^/2    8 g   ^0o  /   A2
~/.7   7   7                     7        7,7(          3             77e l7 63?
~ When any number is divided into seven equal parts, each of
the parts is called one seventh of the number.




MULTIPLICATION AND DIVISION.             53
LESSON  XCIII.
1. If one gallon of wine cost 2 dollars, what will 7 gallons cost?
2. A man paid 14 dollars for 7 sheep; how many dollars did each sheep cost him?
3. If one biscuit cost 3 cents, what will 7 biscuits cost?
4. At 3 cents a-piece, how many biscuits can you purchase with 21 cents?
5. There are 4 weeks in one month; how many weeks
are there in 7 months?
6. In one month there are 4 weeks; how many months
are there in 28 weeks?
7. If a man earn 5 dollars in one day, how many dollars
can he earn in 7 days?
8. If a man's expenses be 35 dollars a week, how much
is that a day?
9. There are 7 boys, and each boy has 6 cents; how
many cents have all of them?
10. If you divide 42 nuts equally among 7 boys, how
many nuts will each boy receive?
11. If a boy earn 7 dollars in one month, how many dollars can he earn in 7 months?
12. A boy received 49 dollars for 7 months' labor; how
many dollars did le receive for each month's labor?
13. There are 8 quarts in one peck; how many quarts
are there in 7 pecks?
14. In one peck there are 8 quarts; how many peeks
are there in 56 quarts?
15. William has 9 cents, and Henry has 7 times as many;
how many cents has Henry?
16. Henry has 63 cents, and William has only one seventh
as many; how many cents has William?
17. If you can learn 10 questions in an hour, how many
questions can you learn in 7 hours?
18. If you are required to learn 70 questions in arithnmetic, and wish to learn them all in 7 hours, how
many of them must you learn each hour?
19. In one shilling there are'12 pence; how many pence
are there in 7 shillings?
5,




54          MULTIPLICATION AND DIVISION.
LESSON  LXACIV.
8 times  1 are  8     8 in  8  1 time.
8 times  2 are 16     8 in 16  2 times.
8 times  3 are 24     8 in 24  3 times
8 times 4 are 32      8 in 32  4 times.
8 times  5 are 40     8 in 40  5 times.
8 times  6 are 48     8 in 48  6 times.
8 times 7 are 56      8 in 56  7 times.
8 times  8 are 64     8 in 64  8 times.
8 times  9 are 72     8 in 72  9 times.
8 times 10 are 80     8 in 80 10 times.
8 times 11 are 88     8 in 88 11 times.
8 times 12 are 96     8 in 96 12 times.
LESSON XCV.
1 time 8 are how many?   Wrhat is I eighth of 8?
2 times 8 are how many?   What is 1 eighth of 16?
3 times 8 are how many?   What is 1 eighth of 24?
4 times 8 are how many?   What is 1 eighth of 32?
5 times 8 are how many?   What is 1 eighth of 40?
6 times 8 are how many?   What is 1 eighth of 48?
7 times 8 are how many?   What is I eighth of 56?
8 times 8 are how many?   What is 1 eighth of 64?
9 times 8 are how many?   What is I eighth of 72?
10 times 8 are how many?   What is 1 eighth of 80?
11 times 8 are how many?   What is I eighth of 88?
12 times 8 are how many?   What is 1 eighth of 96?
LESSON  XCVI.
EXERCISES TO BE PERFORMED ON THE SLATE.
W;;Z   17  882 16    1   12
* When any number is divided into eight equal parts, each
of the parts is called one eighth of the number.




MULTIPLICATION AND DIVISION.             55
LESSON XCVII.
1. A man purchased 8 barrels of apples, at 2 dollars a
barrel; how manay dollars did the 8 barrels cost him?
2. How many pears can you buy with 16 cents, at 2
cents a-piece r
3. What will 8 barrels of cider cost, at 3 dollars a barrel?
4. How many oranges can you buy with 24 cents, at 3
cents a-piece:?
5. Francis has 4 mlarbles, and John has 8 times as
many; how many marbles has John?
6. If 32 marbles be equally divided among 8 boys, how
many marbles will each boy receive?
7. What will 8 weeks' board come to, at 5 dollars a
week?
8. HIow many yards of cloth can you purchase with 40
dollars, at 5 dollars a yard?
9. A man has 8 children, and gives 6 dollars to each of
them; how many dollars does he give away?
10. A  mother distributed 48 peaches equally among
her 8 children; how many did she give them
a-piece?
11. In one week there are 7 days; how many days are
there in 8 weeks?
12. There are 7 days in one week; how many weeks are
there in 56 days?
13. If a man can earn 8 dollars in one week, how many
dollars can he earn in 8 weeks?
14. If 64 boys be divided into classes, containing  8
boys each, how many classes would there be?
15  If a vessel sail 9 miles in an hour, how many miles
will she sail in 8 hours?
16. How many hours will it take a man to travel 72
miles, if he travels 9 miles in an hour?
17. There are 10 cents in one dime; how many cents
are there in 8 dimes?
18. In one dime there are 10 cents; how many dimes
are there in 80 cents?
19. If one ton of hay is worth 11 dollars, what are 8 tons
worth?




56          MULTIPLICATION AND DIVISION.
LESSON XCVIII.
9 times  1 are   9      9 in   9  1 time.
9 times 2 are  18       9 in  18  2 times.
9 times  3 are  27      9 in  27  3 times.
9 times 4 are  36       9 in  36  4 times.
9 times  5 are  45      9 in  45  5 times.
9 times  6 are  54      9 in  54  6 times.
9 times  7 are  63      9 in  63  7 times.
9 times  8 are  72      9 in  72  8 times.
9 times  9 are  81      9 in  81  9 times.
9 times 10 are  90      9 in  9010 times.
9 times 11 are  99      9 in  9911 times.
9 times 12 are 108      9 in 108 12 times.
LESSON XCIX.
1 time 9 are how many?    What is 1 ninth of   9?
2 times 9 are how many?    What is 1 ninth of 18?
3 times 9 are how many?    What is 1 ninth of 27?
4 times 9 are how many?    What is I ninth of 36?
5 times 9 are how many?    What is I ninth of 45?
6 times 9 are how many?    What is I ninth of 54?
7 times 9 are how many?    What is 1 ninth of 63?
8 times 9 are how many?    What is 1 ninth of 72?
9 times 9 are how many?    What is 1 ninth of 81?
10 times 9 are how many?    What is 1 ninth of 90?
11 times 9 are how many?    What is I ninth of 99?
12 times 9 are how many?    What is 1 ninth of 108?
LESSON C.
EXERCISES TO BE PERFORMED ON THE SLATE.
1./    8 7                   0  / /   12
7 2            _f 9           9     2  9
~ When any number is divided into nine equal parts, each
of the parts is called one ninth of the number.




MIULTIPLICATION AND DIVISION.           57
LESSON  CI.
1. What will 9 yards of cloth cost, at 2 dollars a yard?
2. How many barrels of apples can you buy with 18
dollars, at 2 dollars a barrel?
3. There are 3 miles in one league; how many miles are
there in 9 leagues?
4. In one league there are 3 miles; how many leagues
are there in 27 miles?
5. In one yard there are 4 quarters; how many quarters
are there in 9 yards?
6. How many yards are there in 36 quarters of a yard?
7. If a quart of milk cost 5 cents, how many cents will
9 quarts cost?
8. How many quarts of milk can you buy with 45 cents,
at 5 cents a quart?
9. If one book cost 6 cents, what will 9 books cost?
10. If you pay 54 cents for 9 books, how many cents do
you pay for each book?
11. How much will 9 yards of ribbon cost, at 7 cents a
yard?
12. If a stage runs 63 miles in 9 hours, how many miles
does it run each hour?
13. If a man earn 8 dollars in one week, how many dollars can he earn in 9 weeks?
14. A man received 72 dollars for 9 weeks' work; how
many dollars did he receive for each week's work?
15. What will 9 pounds of sugar come to, at 9 cents a
pound?
16. If 1S cents be equally divided among 9 boys, how
many cents will each boy receive?
17. If one pound of coffee cost 10 cents, how many cents
will 9 pounds cost?
18. How many writing-books, at 10 cents each, can you
buy with 90 cents?
19. If 11 men can do a piece of work in 9 days, how
many men will be required to do the same work in
one day?
20. If 99 nuts be equally distributed among 9 boys, how
many nuts will each boy receive.?




58          MULTIPLICATION AND DIVISION.
LESSON CIT.
10 times 1 are  10      10 in  10  1 time.
10 times 2 are  20      10 in  20  2 times.
10 times  3 are  30     10 in  30  3 times.
10 times 4 are  40      10 in  40  4 times.
10 times 5 are  50      10 in  50  5 times.
10 times 6 are  60      10 in  60  6 times.
10 times 7 are  70      10 in  70  7 times.
10 times  8 are  80     10 in  80  8 times.
10 times 9 are  90      10 in  90  9 times.
10 times 10 are 100     10 in 100 10 times.
10 times 11 are 110     10 in 110 11 times.
10 times 12 are 120     10 in 120 12 times.
LESSON  CIII.
1 time 10 are how many?      What is 1 tenth of 10? 
2 times 10 are how many?      What is 1 tenth of 20?
3 times 10 are how many?    What is 1 tenth of 30?
4 times 10 are how many?      What is 1 tenth of 40?
5 times 10 are how many?    What is 1 tenth of 50?
6 times 10 are how many?    What is 1 tenth of 60?
7 times 10 are how mahy?      What is I tenth of 70?
8 times 10 are how many?     What is 1 tenth of 80?
9 times 10 are how many?     What is 1 tenth of 90?
10 times 10 are how many?     What is 1 tenth of 100?
1 times 10 are how many?      What is 1 tenth of 110?
12 times 10 are how many?      What is 1 tenth of 120?
LESSON  CIV.
EXERCISES TO BE PERFORMED ON THE SLATE.
^0: /10 /0 /0 /0 /0,    y vofo  fno  O o o o
* When any number is divided into ten equal parts, each
of the parts is called one tenth of the number.




MULTIPLICATION AND DIVISION.            59
LESSON CV.
1. If one lemon is worth 2 cents, what are 10 lemons
worth?
2. How many peaches can you buy with 20 cents, at 2
cents a-piece?
3. If you give 10 boys 3 apples each, how many apples
will you give to all of them?
4. If 30 roses be equally divided among 10 girls, how
many roses will each girl receive?
5. Susan is 4 years old, which is one tenth the age of
her mother; how old is her mother?
6. Mrs. Williams is 40 years old; her daughter Susan
is only one tenth the age of her mother.  How old
is Susan?
7. If one lead-pencil is worth 5 cents, what are 10 pencils
worth?
8. How many yards of broadcloth can you purchase with
50 dollars, at 5 dollars a yard?
9. If you pay 6 cents for riding one mile, how many
cents must you pay for riding 10 miles?
10. AMary paid 60 cents for 10 yards of ribbon; how
many cents did she pay for each yard?
11. What will 10 pounds of figs come to, at 7 cents a
pound?
12. Bought 10 pounds of sugar for 70 cents; what is one
pound of it worth?
13. There are 8 pints in one gallon; how many pints are
there in 10 gallons?
14. 8 pints are equal to one gallon; 80 pints are equal
to how many gallons?
15. If a man earn 9 dollars in one week, how many dollars can he earn in 10 weeks?
16. If 90 dollars be equally divided among 10 men, how
many dollars will each man receive?
17. In al school there are 10 classes; in each class there are
10 girls.  How many girls are there in the school?
18. In a school of 100 boys there are 10 divisions; each
division contains the same number of boys.  How
many boys alre there in each division?




60          BIULTIPLICATION AND DIVISION.
LESSON  CVI.
11 times 1 are  II      11 in  11   time.
11 times 2 are  22      11 in  22  2 times.
I1 times 3 are  33      11 in  33  3 times.
11 times 4 are  44      11 in  44  4 times.
11 times  5 are  55     11 in  55  5 times.
11 times  6 are  66     11 in  66  6 times.
11 times 7 are  77      11 in  77  7 times.
11 times  8 are  88     11 in  88  8 times.
11 times 9 are  99      11 in  99  9 times.
11 times 10 are 110     11 in 110 10 times.
11 times 11 are 121     11 in 121 11 times.
11 times 12 are 132     11 in 132 12 times.
LESSON  C VII.
I time 11 are how many?  What is 1 eleventh of 11?
2 times 11 are how many?  What is 1 eleventh of 22?
3 times 11 are how many?  What is 1 eleventh of 33?
4 times 11 are how many?  What is 1 eleventh of 44?
5 times 11 are how many?  What is 1 eleventh of 55?
6 times 11 are how many?  What is I eleventh of 66?
7 times 11 are how many?  What is 1 eleventh of 77?
8 times 11 are how many?  What is 1 eleventh of 88?
9 times 11 are how many?  What is 1 eleventh of 99?
10 times ll are how many?  What is I eleventh of 110?
11 times 11 are how many?  What is 1 eleventh of 121?
12 times 11 are how many?  What is I eleventh of 132?
LESSON CVTII.
EXERCISES TO BE PERFORMED ON THE SLATE.
5H^  /  8 7                   9o - Y    /  / 
//  // // // //  //
* When any number is dividedl into eleven equal parts, each of
the parts-is called one elevclldh of the luilber.




MULTIPLICATION AND DIVISION.            61
LESSON CIX.
1. Lucy bought 2 yards of ribbon, at 11 cents a yard;
how many cents did she pay for it?
2. If 2 barrels of beef cost 22 dollars, what is one barrel of it worth?
3. There are 1f half-yards in one rod; how many halfyards are there in 3 rods?
4. Emily paid 33 cents for 3 yards of silk braid; how
many cents did it cost per yard?
5. If one book cost 11 cents, how many cents would 4
books cost?
6. If 4 loads of hay can be purchased for 44 dollars,
what would one load of it cost?
7. What will 5 pounds of cheese come to, at 11 cents a
pound?
8. If 55 nuts be equally divided among 3 boys and 2
girls, how many nuts will each of them receive?
9. There are 6 shillings in one dollar; how many shillings are there in 11 dollars?
10. A lady paid 66 shillings for a piece of silk measuring
11 yards; what did each yard of it cost?
11. In one week there are 7 days; how many days are
there in 11 weeks?
12. If 77 acres of land should be divided into 11 equal
parts, how many acres would each part contain 
13. If one ounce of nutmegs cost 11 cents, what will S
ounces cost?
14. A  farmer purchased 11 pounds of sugar, for which
he paid 88 cents; what did it cost him per pound?
15. If 11 men can perform  a piece of work in 9 days,
how many men would be required to perform the
same in one day?
16. If 99 men can perform a piece of work in one day,
how many men would be required to perform  the
same in 11'days?
17. There are 10 cents in one dime; how many cents are
there in 11 dimes?
18. How many pounds of coffee can you purchase with
110 cents, at 11 cents a pound?
6




62           MULTIPLICATION AND DIVISION.
LESSON CX.
12 times  1 are  12      12 in  12  1 time.
12 times  2 are  24      12 in  24  2 times.
12 times  3 are  36      12 in  36  3 times.
12 times 4 are  48       12 in  48  4 times.
12 times  5 are  60      12 in  60  5 times.
12 times  6 are  72      12 in  72  6 times.
12 times  7 are  84.    12 in  84  7 times.
12 times  8 are  96      12 in  96  8 times.
12 times  9 are 108      12 in 108  9 times.
12 times 10 are 120      12 in 120 10 times.
12 times 11 are 132      12 in 13'2 11 times.
12 times 12 are 144      12 in 144 12 times.
LESSON CXI.
I time 12 are how many?    What is 1 twelfth of 12?
2 times 12-are how many?    What is 1 twelfth of 24?
3 times 12 are how many?    What is 1 twelfth of 36?
4 times 12 are how many?    What is I twelfth of 48?
5 times 12 are how many?    What is I twelfth of 60?
6 times 12 are how many?-   What is 1 twelfth of 72?
7 times 12 are how many?    What is I twrelth of 84?
8 times 12 are how many?    What is I twelfth of 96?
9 times 12 are how lmany?   aWhat is I twelfth of 108?
10 times 12 are how many?    What is 1 twelfth of 120?
11 times 12 are how many?    What is 1 twelfth of 132?
12 times 12 are how many?    What is I twelfth of 144?
LESSON  CXII.
EXERCISES TO BE PERFORMED ON THE SLATE.
ce we    7' /    8 2           y 0  //  /2
62/1   /2  /1  12 12 12
S>m^e SAy2 96 dy2 Xz/^y 
* When any number is divided into twelve equal parts, each
of the parts is called one twelfth of the number.




MUrLTIPLICATION AND DIVISION.           63
LESSON  CXIII.
1. If one pair of shoes are worth 2 dollars, what are 12
pairs worth?
2. Bought 12 pairs of shoes, for which I paid 24 dollars;
how much did the shoes cost per pair?
3. One yard is equal to 3 feet; how many feet are there
in 12 yards?
4. A grocer sold 3 pounds of raisins for 36 cents; what
was the price per pound?
5. A half-dime is ecual to 5 cents; 12 half-dimes are
equal to how many cents?
6. 5 dollars are equal to one half-eagle; 60 dollars are
equal to how many half-eagles?
7. There are 6 shillings in one dollar; how many shillings are there in 12 dollars?
8. A boy placed 72 cents in 6 equal piles; how many
cents did he place in each pile?
9. Henry has 7 cents, and Samuel has 12 times as
many; how many has Samuel?
10. A drover purchased 12 sheep, for which he paid 84
dollars; what did each sheep cost?
11. What will 12 cords of wood come to, at 8 dollars a
cord?
12. In one year there are 12 months; how many years
are there in 96 months?
13. When sugar is worth 9 cents a pound, what must be
paid for 12 pounds?
14. There are 12 pence in one shilling; how many shillings are there in 108 pence?
15. When eggs are worth 12 cents per dozen, what must
be paid for 10 dozen?
16. 12 eggs are called a dozen; 120 eggs are equal to
how many dozen?
17.. A lady purchased 12 yards of cambric, for which she
paid 11 cents a yard; what did she pay for the 12
yards?
18. A man purchased 12 tons of coal, for which he paid
132 dollars; what did it cost him per ton?




64          MULTIPLICATION AND DIVISION.
LESSON CXIV.
MULTIPLICATION AND DIVISION COMBINED.
1.  3 times 4 are how many times 2?
Solution. -  3 times 4 are 12; and 2 is contained in 12
6 times.  Therefore, 3 times 4 are 6 times 2.
2.   3 times  8 are how many times  4?   6?
3.   3 times 10 are how many times  5?   6?
4.   3 times 12 are how many times  6?   9?
5.   4 times  6 are how many times  8?   3?
6.   4 times  5 are how many times 10?   2?
7.   4 times 10 are how many times  3?   8?
8.   4 times  9 are how many times 12?   6?
9.   5 times  6 are how many times 10?   3?
10.   5 times  8 are how many times  4?  10?
11.   6 times  3 are how many times  9?   2?
12.   6 times  6 are how many times  4?   9?
13.   6 times  8 are how many times 12?   4?
14.   7 times 10 are how many times  5?  10?
15.   8 times  3 are how many times  6?  12?
16.   8 times  9 are how many times 12?   6?
17.   8 times 10 are how many times  5?  10?
18.   8 times 12 are how many times  6?  12?
19.   9 times  2 are how many times  6?   3?
20.   9 times  8 are how many times 12?   6?
21.   9 times 10 are how many times  59  10?
22.   9 times 12 are how many times  6?  12?
23.  10 times  2 are how many times  4?   5?
24.  10 times  3 are how many times  5?  10?
25.  10 times  4 are how many times  8?   5?
26.  10 times  6 are how many times 12?   6?
27.  10 times  9 are how many times  6?   9?
28.  11 times  6 are how many times  3?   6?
29.  11 times  8 are how many times  4?   8?
30.  11 times 10 are how many times  5?  10?
31.  11 times 12 are how many times  6?  12?
32.  12 times  3 are how many times  4?   9?
33.  12 times  4 are how many times  8?   4?
34.  12 times  6 are how many times  9?   8?




MTULTTIPLICATION AND DIVISION.           Go5
LESSON CXV.
PRACTICAL QUESTIONS COMBINING  MULTIPLICATION
AND DIVISION.
1. If 2 oranges cost 4 cents, what will 3 oranges cost?
Solution. -If 2 oranges cost 4 cents, 1 orange will cost
one half of 4 cents, which is 2 cents.  If 1 orange
cost 2 cents, 3 oranges will cost three times 2 cents,
which are 6 cents; therefore, 3 oranges will cost 6
cents.
2. If 3 melons cost 24 cents, how many cents will 4
melons cost?
3. If 4 peaches cost 8 cents, what will 6 peaches
cost?
4. If 5 pine-apples cost 60 cents, how many cents will 8
pine-apples cost?
5. If 6 pears cost 18 cents, what will 10 pears cost?
6. If 7 slates cost 70 cents, how many cents will 12
slates cost?
7. If 8 quarts of milk cost 40 cents, what will 12 quarts
cost?
8. If 9 quarts of strawberries cost 108 cents, how many
cents will 12 quarts, cost?
9. If 10 dozen eggs cost 120 cents, what will 12 dozen
eggs cost?
10. If 4 sheep cost 12 dollars, how many dollars will
9 sheep cost?
11. If 5 calves cost 30 dollars, how many dollars will 8
calves cost?
12. If 6 men cut 18 cords of wood in one day, how many
cords will 10 men cut in the same time?
13. If 6 men can do a piece of work in 5 days, in how
many days can 5 men do the same work?
14. How many men will it take to do as much work in
6 days as 4 men can do in 12 days?, 
15. How  many days will it take 5 men to accomplish
what it takes 6 men 10 days to perform?
16. In how many days can 12 men earn as much as 9
men can earn in 8 days?
(is p z 




6G           MULTIPLICATION AND DIVISION.
LESSON CXVI.
1. If 2 barrels of flour cost 10 dollars, what will 5 barrels cost?
2. 10 is 2 fifths of what number?
3. If 4 yards of cloth cost 40 cents, what will 9 yards cost?
4. 90 is 9 times I fourth of what number?
5. If 5 books cost 60 cents, what will 12 books cost?
6. 60 is 5 twelfths of what number?
7. 144 is 12 times 1 fifth of what number.?
8. If 6 lead-pencils cost 36 cents, what will 11 leadpencils cost?
9. 36 is 6 elevenths of what number?
10. 66 is 11 times 1 sixth of what'number 
11. If 7 cuarts of cherries are worth 56 cents, what are
10 cuarts worth?
12. 56 is 7 tenths of what number?
13. 80 is 10 times I eighth of what number?
14. If 8 boxes of strawberries are worth 160 cents, what
are 12 boxes worth?
15. 160 is 8 twelfths of what number?
16. 240 is 12 times 1 eighth of what number?
17. If 9 pears are worth 27 cents, what are 5 of them
worth?
18. 27 is 9 times I fifth of what number?
19. 15 is 5 ninths of what number?
20. If a turkey weighing 10 pounds cost 120 cents, what
will a turkey weighing 7 pounds cost?
21. 120 is 10 times I seventh of what number?
22. 84 is 7 tenths of what number?
23. William says to Henry, who is 10 years old, your age
is 1 eighth of 4 times my age; how old is Williai?
24. 10 is 1 eighth of 4 times what number?
25. 80 is 8 times 1 fourth of what number?
26. A  lady being asked her age, answered, that her
youngest daughter was 12 years old, which was 1
twelfth of 3 times her own age; what was the lady's
age?
27. 144 is 12 times I fourth of what number?
28. 48 is 1 third of twelve times what number?




LESSON  CXVII,
ADDITION.
ADDITION'iS the method of fincldg te total number of
units contained in two or more numbers, and expressing
them in one number, called the amount, or sum.
Illustration. -  A man has three bags of money.  No.
1 contains 950 dollars; No. 2 contains 875 dollars; No.
3 contains 764 dollars.  What is the total amount or sum
of money in the three bags?
We begin at the bottom of the colu s  mn of units, and add all the figures
in that column, and find the sum of
950        them  to be 9 units, which we write
875        under the column of units.  We then
764        add all the figures in the column of
Ans. 2,589 dolls.  tens, and find the sum of them to be 18
tens, or 1 hundred, and 8 tens; we
write the 8 (tens) under the column of tens, and then add
the 1 (hundred) with the figures in the column of hundreds, and find the sum of them to be 25 hundred, or 2
thousand, and 5 hundred; we write the 5 (hundred)
under the column of hundreds, and the 2 (thousand) at the
left of the 5 hundred; and find the whole amount or sum
of money in the three bags to be 2,589 dollars.
From the above illustration, we obtain the following
RXTLE. - Write the numbers, placing units under units,
ten.s under tens, hundreds under hundreds, and draw a
line under them.
Beyin at the bottom of the column of units, and add
all tie fig/ures in that column in succession: if the
amount does not exceed nine, write it under the column;
if the amount exceeds nine, write the right-hand figure
of it under the column, and add the left-hand zfiure, or
fgures,with the igures in the next column.
Add the figures in each succeeding column in the same
manner, and write down the whole amount of the last
co 7lumn.




68 8                 ADD:TION.
LESSON  CXVIIX.
EXERCISES TO BE PERFORMED ON THE SLATE.
(1.)       (2.)       (3.)        (4.)
123        567         222         666
234        678         333         777
355        789         444         888
466        912         555         999
(5.)       (6.)        (7.)       (8.)
1,234      2,345       3,456       4,444
5,678      5,432       4,444       5,555
9,123      3,456       5,656       6,666
4,567      6,543       6,767       7,777
8.934      4,567       7,878       8,888
(9.)       (10.)      (11.)       (12.)
11,111     23,232      22,333      34,435
22,222     34,343      33,444      45,546
33,333     45,454      44,555      56.654
44,444     56,565      55,666      67,765
55,555     67,676      66,777      78,786
66,666     78,787      77,888      89,987
Two short parallel lines (   ) indicate equality: thus,
I dollar =  100 cents; which is read, 1 dollar is equal
to 100 cents.
This cross (   ) indicates addition:. thus, 5 + 7 = 12;
which is read, 5 plus 7 equal 12, or 5 and 7 equal 12.
13. What is the sum  of 5,665 + 6,545 + 7,546 +
8,564?
14. What is the sum of 23,456 +  34,567 + 45,678 ---
56,789?
15. What is the sum of 40,405 + 50,604 -- 60,708 +
70,910?
16. What is the sum of 75,704 +  85,406 - 95,115 +
48,412?
17. What is the sum of 48,444 + 57,555 + 66,333 +
99,999?




ADPfITION.                      69
LESSON CXIX.
1. In a school 25 girls learn to write, 20 learn arithmetic, 18 learn grammar, 15 learn geography, and
12 learn history; what number of girls are there in
the school?
2. There is an orchard in which there are 75 apple-trees,
25 peach-trees, 15 pear-trees, and 12 plum-trees;
what is the whole number of trees in the orchard?
3. There is a school in which there are 4 classes; in the
first class there are 125 girls, in the second 120, in
the third 124, and in the fourth 175.  What is the
whole number of girls in the school?
4. A gardener has in his nursery 525 apple-trees, 375
peach-trees, 275 cherry-trees, 250 plum-trees, 175
pear-trees, and 750 other trees of various kinds;
how many trees are there in the nursery?
5. In a certain farm there are 124 acres under cultivation, 75 acres for mowing, 140 acres of pasture,
and 175 acres of wood-land; what number of acres
are there in the farm?
6. A man purchased a farm  for which he paid 5,750
dollars; he afterwards paid 375 dollars for clearing
and fencing, and 325 dollars for barns and sheds.
How many dollars did the farm cost him?
7. A"mechanic owns five houses.  No. I is worth 7,525
dollars; No. 2, 6,475 dollars; No. 3, 5,845 dollars;
No. 4, 5,425 dollars; No. 5, 5,300 dollars.  What
number of dollars are the five houses worth?
S. A teacher wished to know  how many questions had
been performed by the first class in arithmetic during
the last 5 weeks; and on inquiry, he found that the
class had performed 75 questions during the first
week, 85 during the second week, 95 during the
third, 105 during the fourth, and 125 during the
fifth week.  H-ow.many questions had they performed during the last five weeks?
9. Three trains of cars started fro1m  Boston on the same
day; the first train carried 525 passengers, the
second 675, and the third 750.  How many passengers were tbere in the three trains?




LESSON CXX,
SUBTRACTION.
SuBrlBACTiloN is the method of taking a less number
from a greater, to find the remaincler, or dilferenee.
The less number is called the subtrakenzd, and the
greater, the minuend.
The number found by taling a less number from  a
greater is called the remainder, or difference, and it
shows how many the greater number exceeds the less.
Subtraction is performed, when each figure of the less
number -is smaller than the corresponding figure of the
greater, by taking each figure of the less number from the
corresponding figure of the greater, and writing the reremainder underneath; the several remainders will express
the whlole difference.
Illustration. -  A  merchant purchased 765 yards of
cloth, and has since sold 523 yards of it; what number
of yards has h e h  remaining unsold?
We first write down the
765 No. of yards purchased.  greater number; then we
523 No. of yards sold.        write the less number under
242 No. of yards unsold.      the greater, placing units
under units, tens under
tens, and hundreds under hundreds.  We then take 3
tunits from  5 units, and 2 units remain, which we write
directly under the units.  Then 2 tens fiom 6 tens, and
4 tcos remain, which we write under the tens.  Lastly,
5 hundred from  7 hundred, and  2 hundred remain,
which we write under the hundreds.  The whole remainder
or dicfference is 242.
When any figure of the less number is larger than the
corresponding figure of the greater number, the following
question and its illustration will show the method of performing the operation: -
A man borrowed 94 dollars, and has paid 46 dollars;
how many dollars remain unpaid?
We cannot take 6 units from
Borrowaed  94 dollars.
Paicld    4  dolla.    4 units; and as 10 units of any
doas.   lower order  are equal to 1 unit
UTnpaid   48 dollars.   of the next higher ordoer, we




SUBTACT ION.                    71
acdd 10 units to 4 units, and the sum  is 14 units; and 6
units from 14 units leave 8 units.  We now add I (ten)
to the 4 tens, and the sumt is 5 tens, and 5 tens from 9
tens leave 4 tens; therefore 48 dollars remain unpaid.
The reason of this method of performing subtraction depends upon a self-evident truth, viz., that if two unequal
numbers be equally increased, their diference remains
the same.
From the above examples and illustrations, we derive
the following
RULE. -  Write down the greater number; then write
the less number under it, placing units under units, tens
under tens, hundreds under hundreds, and draw a line
underneath..Begin with the units, and subtract each figure of the
less number in succession from  the jigure over it, and
write the remainder underneath.
Whenever a figure of the less number is greater than
the figure over it, add ten to the upper figure, subtract the lower figure from the amount, then add one to
the next lower figure before it is subtracted,
Subtraction is indicated by a short horizontal line, thus,
12-  8  = 4; which is read, 12 minus 8 equals 4. or 12
less 8 equals 4.
LESSON CXXI.
EXERCISES TO BE PERFORMED ON THE SLATE.
(1.)         (2.)        (3.)         (4.).
345          678         954          560
123         456          463          344
(5.)        (6.)         (7.)         (8.)
9,876       4,325        5,015        6,305
1,234       1,416        4,144        4,117
(9.)        (Ioc)        (11.)        (12.)
54,321       98,765      50,000       75,015
12,345      40,876      43,221       46,346




t72                  SUJIBTACTION.
LESSON  CXXII.
1. A  merchant borrowed 1,275 dollars, and has paid
750 dollars; how many dollars remain unpaid?
2. A trader purchased 2,500 yards of cloth, and has
sold 1,745 yards of it; how many yards has he
remaining unsold?
3. If a farm and the buildings on it be valued at 12,000
dollars, and the buildings be valued at 4,575 dollars, what is the value of the land?
4. A man purchased an estate, for which he paid 13,750
dollars, and has sold it for 15,225 dollars; what
number of dollars did he gain by trading?
5. The Rocky Mountains are 12,500  feet above the
level of the ocean, and the Andes are 21,440 feet;
how many feet higher are the Andes than the Rocky
Mountains?
6. A merchant purchased a quantity of goods for which
he paid 2,750 dollars; the goods being damaged,
he sold them for 395 dollars less than cost.  What
did he get for the goods?
7. A farmer raised 1,275 bushels of wheat, and has sold
786 bushels of it; what number of bushels has he
remaining unsold?
8. A farmer sold a load of cheese for 195 dollars, and
took goods in payment to the amount of 49 dollars, and the balance in money; how much money
did he receive?
9. A man paid 125 dollars for a horse, and 75 dollars
for a wagon; how much did the cost of the horse
exceed the cost of the wagon?'
10. A tree 95 feet in height was broken off by the wind;
the top part which fell was 39 feet in length.  hHow
high was the part which was left?
11. A merchant purchased a piece of broadcloth, for which
he paid 240 dollars; but being damaged, he sold it
for 185 dollars.  Iow many dollars did he lose?
12. A cargo of fruit cost 1,075 dollars, but it was so much
damaged by a storm that the owner sold it for 890
dollars; what number of dollars did he lose?




ADDITIOIN AND SUBTI'iA'tION.             38
LESSON  CXXIII.
1. A gentleman purchased a gold watcsh: O' 65 dollars,
a chain for 12 dollars, and a key:fr 5 dollars; he
afterwards sold the whole for 100 dollars.  Did he
gain or lose, and lhow lrlmc?
2. Charles had 175 marbles; to0w- l-tan-y o  a;t he 1-'ft
after giving 25 to William, 19 to C-eorgle 38 to
Samuel, 49 to Edward, -41 to Johna, and losing' 2?
3. Purchased a farm  for 2,125 dollars, paid for buildings and stock 1,250 dollars; for how' much must
I sell the whole to gain 500 dollars?
4. A tracer sold from a piece of silk contaninng 45 yards,
at one time 15 yards, at another time 10 yards,
and at another time 12 yards;  how many yards
were loft in the piece?
5. " A boy bought a sled for 28 cents, and gave 14 cents
to have it repaired; he sold it for 40 cents.  Did
he gain or lose by the bargain, and how much? "
6. A. man owing 350 dollars, paid at one time 47 dollars;
at another time 84 dollars, -at another tim e 35 dollars, and a.t another' time 120 dollars; how much
did he then owe?
7. A  lady gave 6,000 dollars to humane institutions;
viz., 1,500 dollars to the Orphan Asylum, 2,500
dollars to the Institution for the Blind, and the
remainder for the education of the Deaf and Dumb.
What was the sum- given to the last-named institution?
S. A  market-man having 575 pounds of butter, sold
125 pounds to one man, 95 pounds to another, and
45 pounds to another; how many pounds had he
remaining unsold?
9. 915 +  624++  450 +  375 -  1,125: how many?
10. 15,475 +  25,750 +  145,725 -  85,000  -   how
many?
11. 75,425 +  84,676 -  95,500 -  150,000 =   how
many?
12. 94,645 +  15,106 +  44,350 -  105,666     what
number?
7




LESSON CXXIV.
MULTIPLICATION.
MULTrIPLICATIONl is the method of taking or repeating
o-e of two given numbers as many times as there are units
itl the other.  Mutiplication is also a short method of perfo>ning addition, when all the numbers to be added are
alike.
One of tho two'given numbers is called the multiplicand l, and is the numrbler to be multiplied.
The other is called the multiplier, and it is the number
to multiply by, and shows the number of times the multiplicand is to be taken or repeated.
The  nunber produced by miltiplying one of the two
given numbers by the other is called the product, and it
contains either of the two given numbers as many times as
there are units in the other.
The multiplicnand and multiplier are called faictors of
the product.
The sign of multiplication is an inclined cross; thus,
8 X 5-  40, which is read, 8 multiplied by 5 is equal to 40.
Illustrateon  First. -  Suppose we wish to find the cost
of 3 yards of cloth, at 12 cents a yard.  It is plain that 3
yards will cost three times as nmany cents as one yard.
First Method.                  Second MJethod.
AMultiplicand, 12 cents, the price of I yd.        12 cents.
Miultiplier,    3, the number of yards.            12 cents.
12 cents.
Product,      38 cents, the cost of 3 yds.            
The cost of 3 yards, 36 cents.
We may write down 12 cents, the price of one yard,
and multiply them by 3, the number of yards, as is done
in the first method; or, we may write down 12 cents, the
price of one yard, 3 times, and add them, as is done in tie
second method: the result is the same in each of the
methods.
Illustration Second. -  If an acre of land is worth 125
dollars, how many dollars are 9 acres worth?
If one acre is worth 125 dollars, 9 acres are worth 9




MULTIPLICATION.                   75
times 125 dollars: and nine times 125 dollars can be
found by multiplying 125 by 9, in the following manner:
Ve write down the multi-'ill 6.'~   plicand, 125; and write the
M icr            125 d o-ls.  multiplier, 9, under the units
3Iult;iphicand,  125 dcols.'  
ultip ie,               of the multiplicand.  We then'  ____.      say, 9 times 5 units are 45
Product,       1.125 dol s.  units, or 4 tens and 5 units;
we write down the 5 units,
and reserve the 4 tens: then, 9 times 2 tens are 18 tens, and
4 tens which we reserved are 22 tens, or 2 hundred, and
2 tens; we write down the 2 tens, and reserve the 2 hundred: then, 9 times 1 hundred are 9 hundred, and 2 hundred which we reserved are 11 hundred, or 1 thousand,
and 1 hundred; both of which we write down, and the
whole product is 1,125, the number of dollars that 9 acres
are worth.
From  the preceding questions and illustrations, we derive the following rule for multiplication, when the nmultiplier does not exceed 12.
RULE. - Trite down the multiplicand; then write the
multiplier under the multiplicand, placing units under
units, tens under tens, and draw a line underneath.
AMultiply each figure of the multiplicand, beginning
with units, by the multiplier: when the product of any
figure does not exceed nine, write it under- the figure
zmultiplied; when  the product exceeds  nine, write
down, the right-hand figure of it, and add the leftt-hand
figure. or figures, to the product of the next figure, and
writ.e down the whole product of the last figure.
LE SSON CXXV.
(1.).  )       ()         (3.)        (4.)
lMultiply      432          543           654          765
by          5            6            7            8
(5.)         (6.)         (7.)         (s.)
Multiply    20,406       46,075       56,708       76,543
by          9           10           11           12




7                     MULT'I3PTLICA.T:0'y.
9. What is the value of 9 acres of land, at 125 ldoHlia'nl acre?
10. Tlher-e ae,760 yards in one mile; how many yards:
are ther-e in 10 miles?
11. in one year there are 3'65 days; how many days are
there in II years?
12. There are  2,240  pounds in  one ton; how  many
pounds are there in 12 tonms 
LESSON CXXVIo
What will be the product of 7,654 mu ltiplied by 543 9
]llustrati'on of     7,654 multiplicand.
the process.          543 multiplier.
22962 =        3 times the multiplicand.
306.6  -    40 times the multiplicand.
38270          500 times the multiplicand.
Product, 4,156,12 2 =  543 times the multiplicand.
When the multiplier consists of several figures, we first
multiply the multiplicanid by the units of the multiplier,
as directed in the  preceding rule.  We next multiply the
msul'tipicand. byt t   tenos of the multiplier, and' write the
first figure of lte product in the place of tens, because
units muitiplied  by tens prodlce tens.  Then we multiPTlv the multi'pliocmd by the hundreds of the multiplier,
and write the first figure of the product in the place of
hundreds, because units multiplied by hundreds produce
l.undreds.  Finally, we add the several products, and the
total product thus obtained is 4,156,122.
1 roen the preceding illustration we deduce the following:'ide for mulitipication, when. the multiplier consists of several figrees  -~
t, uJLE. -  Wite coWn the mdtolic te    ti an d; t/he  write the
multipvlier under the multiplicancld, placing units under
untits, tens unclder tens, and hcundreds under hundreds.
Mltaiihply the inlltiplibcand b7y each, si?,gnificant,fiTgre'




MULTJ PIICATION.                  7 
qo the multiplier, in succession, beginning with units,
and write the first fiure of each product directly under
the figure by which you are multi3plying.
Ficnd thee zm of the several products; their sumt  will
be the total product required.
LESSON CXXVII.
1. What will be the product, of 325 multiplied by  23?
2. Wha-t will be the product of 436 multiplied by  45?
3. What will be the product of 578 multiplied by  67?
4. What will be the product of 908 multiplied by  98?
5. What will be the product of 315 multiplied by 234?
6. What will be the product of 435 multiplied by 506?
7. What will be the product of 508 multiplied by 805?
8. What will be the product of 645 multiplied by 744?
9. What will be the product of 719 multiplied by 912?
10. What will be the product of 915 mu-ltiilied by 814?
11. If a ship sail uniformly 175 miles each dav, what
number of miles will she sail in 25 days?
12. A man purchased a wood-lot, containing 45 acres, at
35 dollars an acre; what did it cost him?
13. If an acre of land produce 32 bushels of wheat, how
many bushels will 64 acres produce?
14. If a bale of sheeting contain 36 pieces, and each
piece measures 32 yards, what number of yards
does the bale contain?
15. If an acre of land produce 225 bushels of potatoes,
what number of bushels will 25 acres produce?
16. If an acre of land is worth 225 dollars, what is the
value of a farm containing 175 acres?
17. A merchant imported 350 boxes of oranges.   What
number of oranges did he import, supposing each
box to contain 180 oranges?
18. In an orchard there are 120 apple-trees.  Supposing
each tree to bear 10 bushels of apples, and each
bushel to contain 240 apples, and each apple to contain 12 seeds, what number of seeds are there iI
the whole number of apples?
7*




LESSON CXXVIIT.
DIVISION.
D-Vx'ISI:ON is the milethod of  uinding how many timles, or
whatt part of a tine, one of two given numbers is containedl
in the other  or, it is the process of finding any required
part of any given number.  Division is also a short method
of performling  several subtractions of the same number.
Oie of the two given numbers is called the diviclend,
and is the nu mber to be divided.
The other is called the divisor, ancd is the number to
divide by, and indicates w hat part of the dividend is
required.
The number found by the operation is called the quotient, and it shows the number of times, or part of a. time,
~it;at the divisor is contained in the dividend.  It expresses
ailso:  number1 of  nits. or npabt of, pat  nit,, in the required'iart of the c. iclenid.
Thle si),   ot dvlision is a short line betwTeen two points,
thus,  e ancd is read, Cdvilded tbi.  W hen placed between
two pnumltaers, it s how  ihat the nlu.tmbner before it is to be
divided  by  the  nu-mbelr after it; thus, 20 -  5-=  4,
which is read, 20 divided by 5 equals 4.
DSivision is also denoted by writing the divisor undey
itie  dividend,'with  a -short line between  them; thus,
I, w hich iy be read, 12-divided by 6, 3 divided by 4.
jllustration  7i'irst. -- Suppose  we   ish  to  find  how
many yards of cloth can be purchased with 36 cents, at 12
cents a yard.  It is plain that as many tines as 12 cents
are containedi in 38 cents, so many yards can be purchased.
In the first method,
Ist mcethodl.              we  write  36,  the
The divisor 12) 36  the dividend.  number of cents, for
3  the quotient.   le   dividend,  and
then  write  12, the
number of cents in the price   of a yard, at the left of the
dividend, for the divisor; we find that 12 is contained in
38, 3 times; hence 3 is the number of yards that can be
purchased with 38  cents, at 12 cents a yard.




ITYJISION. 7,
2d nethod.       In the second method, we write cown 36
36 cents.   cents, and subtract 12 cents from  36 cents,
12 cents.   and 24 cents remain; we next subtract 12
4 cents    cents from  24 cents, and 12 cents remain;
12 cents   finally, we subtract 12 cents from  12 cents,
and nothing remains.  NWe here see that 12
12 cents.   cents has been s-ubtracted ftom  36 cents 3
12 cents.   times; hence 3 is the number of yards that
can be purchased with 36 cents, at 12 cents
a yard.  We have rfus found t'hat the same number of
yards can be purchased with 36 cents, by each of the
methods.
Illustration Second. -- How many tnmes is 9 contained
in 675?  We write down the dividend and draw a curve
line on'each side of it, and thenl write- the divisor at the
left of the dividend.
We next find the number of times that the'II' 1 divisor, 9, is con-tained in 67 tens, which is
)    (E-S   i7 (tens) times; we write he'7 (tens) at the
9)675 (75
6 3        riright of the dividend for the first figure in the
-    quotient, and multiply the divisor by the 7
45       (tens); the product is 63  tens, which we
45      write'under the 67 tens: we then subtract 63
tens from  67 tens; the remainder is 4 tens.
We then place the 5 units of the dividend at the right of
the remainder, and we have the number 45.  The divisor,
9, is contained 5 times in 45; we write the 5 units at the
right of the 7 tens in the quotient, and multiply the divisor
by the 5 units; the product is 45, which we write under the
45.  There being no remainder, the operation is completed,
and we have found that 9 is contained 75 times in 675.
Jllust. 3d. -If 10,624
1ivisor. Dividentl. QLotin At    dollars be equally divided
15) 10624 ( 708-  1 Ans.
1 05                      among 15 men, what num_______                   ber of dollars will each man
124                    receive?   We first write
120                    down  the  dividend, and
I- rem a r,    then write the divisor at its
4 -remnajindler.
left, as before. We perceive
tha.t the divisor, 15, is contsained in. 106 (hund.red) 7 (hun



80                     DIVISION.
dred) times; we write 7 (hundred) in the quotient, and mul.
tiply the divisor by it; the product is 105 hundred, which
we write under 106 hundred; we then subtract; and the
remainder is I hundred: we then place the 2 (tens) of the
dividend at the right of the remainder, and the number is
12 tens, which being less than the divisor, we write a cipher
in the place of tens in the quotient, and then place the 4
units of the dividend at the right of the 12 tens, and the
nulmber is 124: we find that 15 is contained in 124,8
times; we write 8 in the quotient, and multiply the divisor
by i-t; the product is 120, which we subtract from 124, and
the remainder is 4.  This remainder, 4, will contain 15
4 fifteenths of one time, which we write in a fractional
form at the right of the quotient figures before found, and
we have the complete quotient, 708 —w, which is the number
of dollars that each man will receive.
From the preceding questions and illustrations we derive
the following gyenel cd rule for division: -
IIULE. -Write down the dividend; draw a curve line
on each side of it, and write the divisor at its left.
ake so maniy of the highest orders of figures of the
dividend as will contain the divisor; find the number of
times the divisor is contained in them; write a figure
expressing the n2umber at the right of the dividend, for
the first figure of the quotient; then multiply the divisor
by this quotient figure, and write the product under those
figures of the dividend taken.
Szubtract this product f'romi those figures, and place
the next undivided figure of the dividend at the right of
the remainder; then divide these orders of figures as
before, and thus proceed until all the figures of the dividezd are divided.
If there be a final remainder, write it over a short line
at the right of the quotient figures already found, and
place the divisor under it, which will express what part
of a time the remainder contains the divisor, and completes the quotient.
Whenever a figure of the dividend has been annexed
to the remainder, if this partial dividend is less than the




DIVISION.                     81
divisor, write a cipher in the quotient, and annex another
figure.
LESSON CX IX.
1. How many times is 13 contained in 4,056?
2. I-low many times is 15 contained in 5,475'?
3. How many times is 16 contained in 6,804?
4. How many times is 18 contained in 9,221?
5. How many times is 21 contained in 8,757?
6. What is I thirty-fifth of 75,445?  Of 150,890?
7. What number of times is 125 contained in 46,875?
8. WYhat number of times is 276 contained in 89,700?
9. What nunber of times is 365 contained in 147,825?
10. If a man's income be 5,110 dollars a year, what is
that a day, allowing the year to contain 365 days?
11. There are 144 square inches in 1 square foot; how
many square feet are there in 10,800 square inches?
12. In one acre there are 160 square rods; how many
acres are there in 28,000 square rods?
13. A  man purchased a farm  containing 275 acres for
6,875 dollars; how many dollars did he pay for
each acre?
14. The circumference of the earth is about 25,000 miles;
if a railroad car travel at the rate of 480 miles a
day, in how many days would it travel round the
earth?
LESSON  CXXX.
TWhen the divisor does not exceed 12, the operation
may be shortened by performing the operation mentally,
and writing only the quotient.
Illustration. -  If 109,025 acres of land be ecually
divided among 12 men, what number of acres will each
man have?
12) 109,025                The two highest orders of figAns.    9.085.-  acres.  ures being less than the divisor,




82                      DIVIStON.
we take the three highest, 109 (thousand), and find that 12
is contained in 109 (thousand) 9 (thoursand) times; we
write the 9 under the order of thousands in the dividend,
and, mentally, multiply the divisor by it; the product is
108 (thousand), which we subtract from 109 (thousand);
the remainder is 1 (thousand); this remainder and next
figure of the dividend, 10 (hundred), being less than the
divisor, we write a cipher in the place of hundreds in the
quotient: we then find that the divisor is contained in the
remainder andc two next figures of the dividend, 102
(tens), 8 times; we write 8 in the quotient, in the place
of tens, and multiply the divisor by it; the product is 96
(tens), which we subtract from 102 (tens); the remainder is 6 (tens): we then find that the divisor is contained
in this remainder and last figure of the dividend, 65, 5
times; we write 5 in the quotient, in the place of units;
we then multiply the divisor by it, and the product is 60,
which we subtract from  65; the remainder is 5: this
remainder will contain the divisor 5 twelfths of 1 time,
which we place at the right of the quotient figures before
found, and the complete quotient is 9,085-2-, the number
of acres which each man will have.
1. Divide each of the following numbers by 2 and 4.
446; 682; 506; 874; 916; 1,276; 2,548.
2. Divide each of the following numbers by 4 and 6.
448; 816; 564; 728; 824; 936; 1,272.
3. Divide each of the following numbers by 6 and 8.
324; 648; 786; 672; 846; 936; 1,236.
4. Divide each of the following numbers by 8 and 9
848; 728; 928; 1,688; 1,806; 1,248; 1,848.
5. Divide each of the following numbers by 9 and 10.
819; 729; 1,242; 1,539; 1,863; 2,745.
6. Divide each of the following numbers by 10 and I1.
540; 624; 850; 1,260; 1,580; 2,460.
7. Divide each of the following numbers by 11 and 12.
372; 612; 720; 840; 1,80.0; 1,728.
8. If 1,296 dollars be equally divided among 9 men,
what number of dollars will each man receive?
9. If 12 bales.of cotton, each of the same size, weigh
6,912 pounds, what is the weight of each bale?




FR AC TI 0N S.
INTRODUCTORY   LESSON.
Dejin'itions and Illustrations.
WHEN any whole thing or number is divided into any
number of equalparts, the parts are called fractions of
the thing or number.
If an orange be divided into two equal parts, the parts
are called halves.  If it be divided into three equal parts,
the parts are called thirds.  If it be divided into four
equal parts, the parts are called fourths.  If it be divided
into five equal parts, the parts are called fifths.  If it
be divided into six equal parts, the parts are called sixths.
If it be divided into seven equal parts, the parts are called
sevenths.  If it be divided into eight equal parts, the parts
are called eighths.  If it be divided into nine equal parts,
the parts are called ninths.  If it be divided into ten
equal parts, the parts are called tenths.   If it be divided
into eleven equal parts, the parts are called elevenths.  If
it be divided into twelve equal parts, the parts are called.
twelfths.  The number of equal parts into which  any
whole thing or number is divided  always indicates the
name of the parts.
Fractions are usually expressed by two numbers written
one above the other, with a short line between them;
t.us. I one  2 two  S3 three  4 frl   5 five  (  six    7 eevei.    -lhalf,   3 thirds,     fourths,   5 filths,     sixths,   7 sevenths,
8 eightl  9  nine  10  ten     1 eleven
ninths, TO tenths, TTelevenths, T  twelfths.
The number below the line expresses the number of
equal parts into which  the whole  thing  or number is
supposed to be divided; and it is called the denominator,
because it indicates the name of the parts, as. thirds,
Jourths, fifths, &c.
The number above the line is called  the numerator,
because it shows the number of equal parts expressed by
the fraction..




84   MULTIPLICATION AND DIVISION OF FBRACTIONS.
LESSON  I.
1. In a unit, or 1, there'ae 2 halves.  How  many
halves are there in 2?   In 21-   In 4?  In 41 
In 6..:In   In6?- In 8   In 8     n 10?  In 10?I
T'le 2 Ialtves of cany whole ting or unit are equal to
the whole thing or unit; hence, in any number of halves,
there must be 1 half as many whole ones or units as
there are halves.
2. Hlow many whole ones are there in 4 halves?  In 5
halves'e In 8 halves?-!I1n 9 halves?  In 12 halves?
In 13 halves?  In 16 halves?  In 17 halves?  In
20 halves  - In 21 halves?, In 24 halves?
3. In a unit, or 1, there are 3 thirds.  Iow many thirds
are there in 2?  In 21?  In 4?  In 4?  In  6?
6            ~             - i~,;
Since the 3 thirds of any whole th'ing or unit are
equal to the vwhole thing or unit, there must be 1 third
as many whole ones or units as there are thirds.
4. HI-ow many whole ones are there in 6 thirds?  In 7
thirds?   I I12 thirds?   In 14 thirds?   In 18
thirds?   In 19 thirds?   In 24 thirds?:
5. in-  a unit, or 1, there are 4 fourths.  -How  manvy
fortcths  arte t  in 3?  In 5        n?  In  9-?
Since 4 /fourtlts are ctqual to a whole one, there must
bIe 1 fon.th as many -whole ones as there e afourths.
6. How many whole ones in 12 fourths?  In 21 fourths?
In 28 fourthis?  In 38 fourths?
7. In a unit, or., thre are 5 fifths.  How many fifths
are there in 2  In 3:?  In 4?  In 5?  In 6?
ASince 5  qffths are equal to a whole one, there must
be I fifth as mnany whole ones as there are fifths.
8. I1-ow many whole'ones are there in 10 fifths?  In 16
fit      In 20 f iths?i: In  02 f ifths?      hs In 30 fifths?
9. In a unit, or 1, there are 6 sixths. How many sixths
are there in 3  In 4-9.In 5?: In 6-1?'In 7?
Since 6 sixths are equal to a whole one, there must
be   sifxth as many whole ones as there are sixths.
10. How many whole ones are there in 18 sixths?  In 25'sixAh? In 30 si  s? In 38 sixths? In 42 sixths?':x:.Gs In  0 rx.t]~s,




MULTIPLICATION AND DIVISION Of' I'FRCTIONS.  85
LESSON  II.
1. In a unit, or 1, there are 7 sevenths.  How imany
sevenths are there in 4    In 5-. In 6?  In 7-?
In 8?. I.n9-?  Inl0.   In   2?
Since 7 sevenths are equal to a whole one, there must
be 1 seventh as many whole ones as there are sevenths.
2. How many whole ones are there in 28 sevenths?
In  36  sevenths?  In  42  sevenths?- In  51
sevenths?   In 56 sevenths?   In  66 sevenths?
In 84 sevenths?
3. In a unit, or 1, there are 8 eighths?  How many
eighths are there in 5?  In 6-'?  In 7?  In 8?
In99.  In 10-1?  i1 ll?  In 12?
Since 8 eighths are equal to a whole one, there must
be 1 eighth as many whole ones as there are eighths.
4. How many whole ones are there in 40 eighths?  In
51 eighths?  In 56 eighths?  In 69 eightihs?  In
72 eighths?  In 86 eighths?  In 88 eighths? In
96 eighths?
5. In a unit, or 1, there are 9 ninths. How many ninths
are there in 6?  In 7?  In? I     n 9?   In n 10?
In 1O-    In?     nl?   n 12?
Since 9 ninths are equal to a whole one, there must
be I ninth as many whole ones as there are ninths.
6. How many whole ones are there in 54 ninths?  In
64 ninths?.'In 72 ninths? In 84 ninths?: In 90
ninths?  In 95 ninths?  1n 99 ninths?  In 108
ninths?
7. In a unit, or 1, there are 10 tenths.  How many
tenths are there in 5? In?a 6-   n?   8?In 9 —?
In  10?  In 11%?  iln  2?
Since 10 tenths are equal to a whole one, there must
be 1 tenth as many whole ones as there are tenths.
8. I-low many whole ones are there in 50 tenths?  In
63 tenths?  In 80 tenths?  In 96 tentlhs?  In
100 tenths?       In 119 tenths?  In 120 tenths?
H




86   MULTIPLICATION AND DIVISION  OF FRACTIONS.
LESSON  III.
1. If 1 hclf of a yard of cloth cost 5 cents, what will 2
halves, or a whole yard, cost?
2. If I third of a yard of cloth cost 4 cents, what will 2
thirds of a yard cost,?  What will 3 thirds, or a
whole yard, cost?
3. If 1 fourth of a gallon of milk is worth 5 cents, what
are 2 fourths of a gallon worth?- 3 fourths?  What
is a gallon worth?
4. If 1 fifth of a bushel of apples is worth 10 cents,
what are 2 fifths of a bushel worth?  3 fifths?  4
fifths?  What is a bushel worth?
5. If 1 sixth of a bushel of wheat is worth 12 cents,
what are 2 sixths of a bushel worth?  3 sixths?  4
sixths?  5 sixths?  What is a bushel worth?
6. If 1 seventh of a yard of silk cost 10 cents, what
will 2 sevenths of a yard cost?  3 sevenths?  4
sevenths?  5 sevenths?  6 sevenths?   What will
a yard cost?
7. If 1 eighth of a pound of tea cost 7 cents, what will
2 eighths of a pound cost?  3 eighths    4 eighths?
5 eighths?  6 eighths?  7 eighths?  What will a
pound cost?
8. If 1 nzint  of an acre of land is worth 12 dollars,
whatt a e 2 ninths of an acre worth?  3 ninths?  4
ninths'   5 ninths?   6 ninths?   7  ninths?   8
ninths?  W.hat is an acre worth?
9. If 1 tenth of a bushel of apples cost 10 cents, what,
will 2 tenths of a bushel cost?  3 tenths?  4 tenths?
5 tenths?  6 tenths?   7 tenths?  8 tenths?   9
tenths?  What will a bushel cost?
10. If 1 twelfth of a pound of gold dust is worth 16 dollars, what are 2 twelfthls of a pound worth?  3
twelfths?  4 twelfthii?  5 twelfths?  6 twelfths?
7 twelfths?  8 twelths 0   9 twelfthsl?  10 twelfths?
11 twelfths?'What is a pound worth?
11. If a yard of silk is worth 80 cents, what are  1a  yards
worth?  What are 121- yards worth?




.MU:LTIPlICATION AlND DIVISION  OF FI.ACTIONS.  87
LESSON IV.
1. When corn is worth 3 fourths of a dollar a bushel,
how many dollars will 8 bushels cost?   How many
dollars will 12 bushels cost?
2  If a boy can earn 3 fifths of a dollar in a day, how
many dollars can he earn in 5 dasiY   -ow many
dollars can he earn in 10 days?
3. A man worked 10 days for 6 fifths of a dollar a day;
how many dollars did he earn in the 10 days?
4. William paid 3 eighths of a dollar for a pair of gloves,
and 8 times as much for a hat; how many dollars
did he pay for his hat?
5. A lady paid 7 eighths of a dollar for a pair of shoes,
and 8 times as much for a bonnet; how many dollars did she pay for her bonnet?
6. A man paid 5 eighths of a dollar for a bushel of corn;
how many dollars must he pay for 8 bushels?
7. Mary is 10 years old, and her age is just 2 thirds the
age of Susan; how old is Susan?
8. A boy paid 10 cents for 5 sixths of a pound of raisins; what would a pound cost, at the same rate?
9. A trader purchased a quantity of oats and corn; he
paid 35 cents per bushel for the oats, which was 7
tenths as much as he paid per bushel for the corn.
What was the price of the corn per bushel?
10. A  farmer paid 27 dollars for a cow, which was 3
eighths of what he paid for a horse; how many
dollars did he pay for his horse?
11. A trader sold a gold watch for 96 dollars, which was
8 sevenths of what the watch cost him; what was
the cost of the watch?
12. Mary is 12 years old, and 5 sixths of Mary's age is 2
thirds of Caroline's age; how old is Caroline?
13. A piece of cloth containing 12 yards was sold for 60
dollars, which was 5 fourths of what it cost; what
did it cost?: What was the gain on each yard?
14. A  man sold a horse for 63 dollars, which was 7
eighths of what the horse cost him; what was the
cost of the horse?  How much did ho ]os?




88    ADDITION AND SUBTR ACTION OF.FR-ACTIONS.
LESSON V.
Fracttions (or fractional parts of the samet thing o?
number) having the same  name or denominator are
added and subtracted in the same manner as whole nucmbers are added and subtracted.
1. 1 half and 2 halves and 3 halves and 4 halves, less 6
halves, are how many halves?  How many whole
ones?
2. 2 thirds and 4 thirds and 5 thirds and 7 thirds, less
6 thirds, are how many thirds?  How many whole
ones?
3. 3 fourths and 5 fourths and 6 fourths and 10 fourths,
less 8 fourths, are how many fourths?  How many
whole ones?
4. 2 fifths and 3 fifths and 4 fifths and 6 fifths, less 10
fifths, are how many fifths?  How  many whole
ones 9?
5. 8 sixths and 7 sixths and 5 sixths and 4 sixths, less
1 2 sixths, are how many sixths?  I-ow many whole
ones?
6. 3 sevenths and 4  sevenths  and  5 sevenths and
9  sevenths, less  7  sevenths, are  how  many
sevenths?  How many whole ones?
7. 10 eighths and 9 eighths and 7 eighths and 4 eighths,
less 6 eighths, are how many eighths?' How many
whole ones?
8. 4 ninth-s and 5 ininths and 6 ninths and 7 ninths and
8 ninlh1s, less 3 ninths, are how  many ninths?
Ilow  many whole ones?
9. 9 tenills anc 8 tenths and 7 tenths and 6 tenths and
5 teenths and 3 tenth      s, lss 8 ten as, are how mainy
tenths? -:-How many whole ones?
10. 4 elevenths and 5 elevenths and 6 elevenths and 10
elevenths, less 3 elevenths, are how many elevenths?
Hlow many whole ones?
11. 10 twelfths and 9 twelttlhs and 8 twelfths and 7
twelftihs and. 6 twelfths, less 4 twelfths, are hrow
imany t welft:hs.?  How many whole ones?




ADDITION AND SUBTRACTION OF TERACTIONS.   89
LESSON  VI.
When fractions having dfferent names or denominators are to be added or subtracted, they must first be
changed to fractions having the same name or denominator. -This may be done by multiplying the numerator
and denomninator of one or both of the given fractions
by such number as will produce the same number for a
denominator of each fraction.
1. What is the sum of - and ~?  What the difference?
=  -, and i and c  =, their sum.   - less  -=,
their difference.
2. What is the sum of 2 and I?  What the difference?
i = g    and I _ = - A - 1 7 -                   15,
their sum.  -9  ~- -  =', their difference.
3. What is the sum of I and 2? What the difference?
4. What is the sum of a and  -? What the difference?
5. What is the sum of ~ and -? What the difference?
8. What is the sum of I and I? What the difference?
9. What is the sum of - and -? What the difference?
9. What is the sum of 3 and-? What the difference?
10. What is the sum of 2 and 5? What the difference?
11. Harriet purchased X of a yard of cloth at one store,
and 2 of a yard at another.  How many fourths of
a yard did she purchase? how many yards?
12. Augusta paid I of all her money for a shawl, and i
of it for a bonnet; what part of her money had she
remainino?
13. Henry purchased a pine-apple, and gave ~ of it to his
sister, and ~ of it to his brother; what part of it
had he left?
14. A man having undertaken to perform a job of work,
did 1 of it the first day, ~ of it the second day, and
the remainder of it the third day; what part of it
did he do the third day?
15. A market-woman sold 5 of all her apples to one man,
and i of them to another; what part of them  had
she remaining unsold?
_..




90     TABLES OF MONEY, WEIGH{T, AND  iEASUR.J.
F DERAL i MONEY 
Federal money is the national currency of the United
States.  The denominations of Federal money are, the
eagle, E.; the dollar, $,; the dime, d..; the cent, c.; and
the mill, m.
The gold coins are, the eagle, the double-eagle, the
half-eagle, the quarter-eagle, and the dollar.  The silver
coins are, the dollar, the half-dollar, the quarter-dollar,
the dime, the half-dime, acnd the three-cent piece.  The
copper coins are, the cent and the half-cent.
1 eagle  =   10 dollars. $.   1 dollar i=  T  of 1 eagle.
1 dollar =  10 dimes. d.   1 dime =-  - of 1 dollar.
I dime        10 cents.  c.   1 cent   = -   of I dime.
I cent  =  10 mills.   m.   1 mill  =-1-  of I cent.
The following table exhibits the value of the fractional
parts of one dollar, expressed in cents, which are in common l ue.,o of a dollar =    5  cts.   I of a dollar  = 25  cts.
I of a dollar =    6' cts.  I- of a dollar =  331 cts.
-  of a dollar =   81 cts.   - of a dollar -=  37  cts.
T1 of a dollar -  10  cts.   I of a dollar 5=    0  cts.
8 of a dollar =  121 Cts.   g of a dollar    621 cts.
*- of a dollar - 163 cts.        of a dollar -  75  cts.
I f a dollar   20  et.   7 of a dollar 8=  8 c7 ta.
In New York, and some other states, the denomlinations of money in common use are dollars, shillings, and
pence; the dollar being equal to 8 shillings or 100 cents,
the shilling 121 cents, and the penny 1 cent.
1 shilling, or -L of a dollar, =  121 cents.
2 shillings, or ~ of a dollar, =  25  cents.
3 shillings, or - of a dollar, =  371 cents.
4 shillings, or I of a dollar,       50  cents.
5 shillings, or A of a dollar, =  621 cents.
6 shillings, or I of a dollar, = 75  cents.
7 shillings, or - of a dollar, -   871 cents.
8 shillings, or 1 dollar,    =  100 cents.




TABLES OF MtONEY, WETO.UT, AND MEABUREi   91
EN GLIS S f MOE ll
The denominations of Eng'lish nioney are, the pound,
t.; the shilling, s.; tthe penny, d.; and the farthing, qr.
L poind  =  20 shillings.   I shilling  =- -, of I ~.
I shilling =  12 pence.      I penny  -=  L  of 1 s.
1 penny  =   4 farthings.  I farthing =   1 of 1 d.
T S 0 T  WEIGHT.
Troy weight is ulsed in weighing gold, silver, platina,
dianmonds, and other precious stones.  The denominations
of troy weight are, the pound, lb.; the ounce, oz.; the
pennyweight, pwt.; and the grain, gr.  The standard
troy pound of the United States is the weight of 22.794377 cubic inches of distilled water weighed in air.
1 pound      12 ounces.    1 ounce - =      - of I lb.
I ounce =  20 pwts.    1  pwt. -= -  of 1 oz.
I pwt.  =  24 grains.      1 grain =- 14 of 1 pwt.
AV OIR BU   P  VE s        I   IG  T a
&voirdupois weight is used in weighing most kinds of
merchandise, and all metals except silver ancl gold.  Its
denominations are, the ton, t.; the hundred-weight, cwt.;
tle quarter, qr.; the pound, lb.; the ounce, oz.; and the
dram, dr.
I ton      =  20 hund. wt. I cwt. = —           of 1 ton.
1 hund. wt. =   4 quarters.  1 qr. =   $ of I cwt.
1 quarter  -  28 pounds.  1 lb.  =          of I qr.
1 pound  -= 16 ounces.   I oz.  = — of  llb.
1 ounce  =-  16 drams.    1 dr. =  TU of 1 oz.




92    TABLES OF' MONILY, WVlGiGHT, ANiD  IEASUREo
APOTHIECARIES'   rEIGUHT.
This weight is used only by apothecaries and physicians
in compounding medicines.  Its denominations are, the
pound, lb.; the ounce,  t; the dram, 3; the scruple,  );
and the grain, gr.
I pound  = 12 ounces.    I ounce  2=  -  of 1 lb.
1 ounce  =    8 drams.      1 dram   =   -s of I ~.
1 dram   =    3 scruples.   I scruple-  ~ of 1 5.
I scruple    20 grains.     I grain  _=  ~ of 1 3.
LINEiAR MEASURE.
This measure is used in measuring distances, lengths,
breadths, heights, and depths.  Its denominations are, the
degree, deg.; the league, lea.; the mile, m.; the furlong,
fur.; the rod, rd.; the yard, yd.; the foot, ft..; and the
inch, in.
1 degree  =  60 G. miles.  1 G. mile =          of 1 deg.
1 degree     69j S. miles. 1 S. mile -= Ty  of 1 deg.
I league  =   3 miles.       I mile      -     of 1 lea.
I mile    =  8 furlongs.    1 furlong =    r of 1 m.
I furlong    40 rods.        I rod     — =      of 1 fur.
1 rod    --  5  yards.       1 yard            * _  Tr of 1 rd.
1 rod     =  16t feet.       1 foot      =       of I rd.
I yard     - 3 feet.         1 foot      = ~   of 1 yd.
1 foot    =  12 inches.      1 inch   -= Lk of 1 ft.
MISCELLANEOUS MEASURES.
12 single things  I dozen.   24 s. of paper   I1 quire.
12 dozen       -I gross.   20 quires        =    ream.
12 gross       =1 great gr.  2 reams        =  1 bundle.
144 dozen      == 1 greatgr. 20 single things =1 score.




TABLI3E  OF M.ONEY, IWEIHIT, AND M1iEAS1URE.    93
SUPERFICIAL OEo SQUARE IU EA SUiS'REo
Superficial or scquare measure is used  in measuring all
kinds of surfaces, such as land, paving, flooring, plastering, and everything which has length and breadth.  Its
denominattions are, the mile, m.; the acre, a.; the rood,
r.; tihe rod, rdl.; the yard, ydl.; the foot, ft.; and the
inch, in.
Gunter's chain, used by surveyors in measuring land,
also in  measuring distances, is 4 rods, or 66 feet, in
length, and is composeC of 100 links.
1 sq. mile == 640 sq. acres.  1 sq. a.  -, 4   of 1 sq. me
I sq. acre -4  sq. roods.        1 s.               of   sq.  a.
I sq. acre    160 sq. rods.   1 sq. rd.     - i-0 of I sq. a.
sq. rood    40  q  rds.    1 sq. rd.  - 4o- of 1 sq. r.
I sq. rod  -  30   sq. yards.  1 sq. yd.             o- I of 1 sq. rd.
1 sq. rodC  272                     sq. fee t. 1 s. ft.of 1 sq. rd.
I sq. yard= 9 sq. feet.          1 sq. ft. =  of 1 sq. yd.
1 sq. foot =  144 sq. inches. 1 sq. in. 1=  of I sq. ft.
CUBIC  rEv.EASU   E.
Cubic measure is used in measuring solids and capacities, or anything that has three dimensions, length, breadth,
and thickness.  Its denominations are, the cord, c.; the
ton, t.; the yard, yd.; the foot, ft.; and. the inch, in.
I cord'of wood -  128 c.f f    I          oot - -= f T     of 1 c.
of wood.
I foot of wood  16 e. ft.   I cubic foot =            - of I ft.
of wood.
I ton of timber =  40 c. ft.    I cubic foot -=  -         - of I ton
of timber.
I cubic yarrd  -  27 c. ft.   1 cubic foot =    -r of I c.
yard.
c eubic foot   = 1728 c. in. I cubic inch =- Ti-   of 1 c.
foot.




94A  TABLES OF BMONEY, WEIGHT, AND MEA1SUURE.
CLOTH  iMEA S UIE.
This measure is used for measuring cloth, and other
goods which are sold by the yard or ell.
Its denominaitions are, the English ell, E. ell; the
French ell, Fr. ell; the Flemish ell, Fl. ell; the yard,
yd.; the quarter, qr.; and the nail, na.
I English ell =- 5 quarters. I cr. -  of 1 E. ell.
I French ell     6 quarters. I qr.  -= --  of 1 Fr. ell.
1 Flemish ell =  3 quarters. 1 qr. =    of 1 Fl. ell.
I yard         - 4 quarters. 1 qr. =    of 1 yard.
I qu.rter    == 4 nails.      I nail =.  of 1 quarter.
DSRY MEASURE.
This measure is used in measuring grain, fruit, seeds,
roots, salt, sand, oysters, coal, &e. Its denominations are,
the chaldron, ch.; the bushel, bu.; the peek, pk.; the
quart, qt.; and the pint, pt.
1 clhaldron =  36 bushels.   I bushel = —, of 1 ch.
1 bushel  c=   4pecks.        I peck  =        of   bu.
1 peck    ==   8 quarts.    1 quart =-             of l pko
I quart         2 pints.       1 pint   =   ~ of   qt.
AiLE AID EIEEER MEASURE.
This measure is used in measuring porter, ale, beer,
milk, and water.  Its denominations are, the hogshead,
hhd.; the barrel, bbl.; the gallon, gal.; the quart, qt.
and the pint, pt.
The beer gallon measures 282 cubic inches.
I hogshead -  54 gallons.    1 gallon =; of 1 hhd.
1 barrel    =  36 gallons.   1 gallon =   g of  bbl.
1 gallon    =    4 quarts.      1 quart =   * ofl  gal.
1 quat    =    2 pints.    1   pint  =   g of 1 qt




'ABLES OF M'IONEY, WEIGUIT, AND MEASURE.    95
WINEr      MEASURE.
WNine measure is used in measuring wine, and all spirituous liquors, except porter, ale, and beer.  Its denominations are, the tun, t.; the pipe, p.; the hogshead, hhd.;
the barrel, bbl.; the gallon, gal.; the quart-. qt.; the
pint, pt; and the gill, gl.
The standard gallon of the United States is the wine
gallon, which measures 231 cubic inches, and contains
8.3388822 pounds avoirdupois of distilled water.
The British standard imperial gallon measures 277.274
cubic inches, and contains 10 pounds avoirdupois of distilled water.
I tun      =  2 pipes.       I pipe  -   of 1 tun.
1 pipe         2 hogsheads. I hhd.  =   - of 1 pipe.
1 hogshead =  63 gallons.   1 gallon =        of 1 Ihhd.
1 barrel    = 311 gallons. 1 gallon ='  of I bbl.
1 gallon    -- 4 quarts.     1 quart  -=     of 1 gal.
1 quart    =  2 pints.       1 pint  == _    of 1 qt.
I pint-,    = 4 gills.       1 gill   -   4 of I pt.
iES ASURE  OF  TIM  E,
Time is the measure of duration  or existence.  Its
denominations are, the century, c.; the year, yr.; the
month, mo.; the week, wk.; the day, d.; the hour, h.;
the minute, m.; and the second, s.
1 century     100 years.    1 yea'r  =-    - T     of I c.
1 year   =  12 cal. mo.    l c. mo.  =     of 1 yr.
I year   -  1.3y-  w. mo. 1 w. mo.  ---- r    of 1 yr.
o-~TAIY W  MO-                14
1 year  a-. 3654 days.    1 day   -=  T-1   of I yr.
1 month  =  4 weeks.         I week:=          of 1 io.
4
1 week   =7 days.            I day   -=         of I wk
1 day    =  24 hours.        I hour  --         of Id.
1 hour   -= 60 minutes.    I minute            O of  lh.
1 minute =  60 seconds.    1 second =       J -  of 1 m.




06    T'ABLES Ob MION- Y, WEIGHlFT, iND MEAStS URE.
The year is divided into 12 calendar months, as follows: 
January, 1st mo., has 31 days. July,     7th mo., has 31 days.
February, 2d  "    "28  "   August,  8th "   "C 31 
March,   3d  "   " 31  "'   September, 9th "   " 30         
April,   4th     "30"   October,  10th"   " 31 "
May,    5th "   " 31  "   November, 11th"   " 30 "
June,    6th "   " 30  "     December, 12th  "   31 ~
When any year can be divided by 4 without a remainder, it is called leap year, in which February has 29
days.
Circular measure is used in measuring circles, latitude
and longitude, and in computing the revolution of the
earth and other planets round the sun.  Its denominations are, the circle, c.; the sign, s.; the degree, 0; the
minute,'; and the second,"
1 circle  -  12 signs.       1  sign     =  -  of I c.
I circle  =  360 degrees.   I degree  — =   -   of 1 c.
I sign    =        30 degrees.    I degree = —         of 1 s.
1 degree =  60 minutes.    I minute -= -          of I deg.
1 minute  = 60 seconds.    1 second =:  -1  of 1 m.n
B O OKS.
A sheet folded in two leaves is called a folio.
A sheet folded in four leaves is called a quarto, 4to.
A sheet folded in eight leaves is called an octavo, or
8vo.
A  sheet folded in twelve leaves is called a duodecimo,
or 12mo.
A sheet folded in eighteen leaves is called an 18mo.
A  sheet folded in 24 leaves is called a 24mo.