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ILLUSTRATED
First iras in Irate,
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\THOLIC rilBLICATIOX SOCIETY,
No. 9 WARREN STREET.
Cfe c^- (
IN MEMORIAM
FLOR1AN CAJORI
THE
YOUNG CATHOLIC'S
I !
ILLTJ8TEATED
TABLE BOOK
AND
FIRST LESSONS m NUMBERS.
N EW YORK :
THE CATHOLIC PUBLICATION SOCIETY,
9 WARREN STREET.
Boston : P. DONAHOE. Louisville : C. A. ROGERS.
Baltimore : J. MURPHY & Co. San Francisco : M. FLOOD.
St. Louis: P. Fox. San Jos6, Cal. : A. WALDTEUFEL.
Newark ; J. J. O'CONNOR & Co. Portland, Or.: S. J. McCor.MicK.
Entered, according to Act of Congress, in the year 1875, by
LAWRENCE KEHOE,
In the Office of the Librarian of Congress, at Washington, D. C,
u/
FIRST LESSONS IN NUMBERS.
COUNTING.
LESSON I.
i. A single thing is culled a Unit, or One.
2. A Number is
one, or more than
one.
3. Figures are
Marks used to ex-
press n umbers.
4. Counting is ex-
pressing numbers
by words.
5. How many dogs
has the girl in the
picture ? One.
6. How many eyes
have ou ? Two,
6
FIRST LESSORS AY I
7. Two cents are how many more than one
cent ?
8. If you had two cents and spent them, how
many would you hare left ?
9. How many are two pictures and one pic-
ture ? Three.
10. Three cents are how many more than two
cents ?
11. If you had three cents and spent them,
how many would you have left ?
12. How many are three pencils and one
pencil ? Four.
13. Count the fingers of your left hand : how
many have you ?
14. Four cents are how
many more than three
cents ?
15. Count from one to
four.
1 6. Count from four back-
to naught.
17. Hold up four fingers.
18. Copy and read the
figures denoting naught,
one, two, three, and four.
Printed form, 01234
Xame. naught, one, two, three, four.
Slate form,. 1 % > 1
19. Which figure expresses the greatest number 'i
LESSORS IN NUMBERS.
LESSON II.
1. Calling the thumb a finger, how many
fingers have you on your righc hand ? Five.
2. Five cents are how many more
than four cents ?
3. Count from one to five.
4. Name five objects or things in
the room.
5. How many are five boys and one boy ? Six,
6. Six is how many more than five ?
7. Count from one to six.
8. From six back to naught.
9. Draw six straight lines on the black-board.
10. Draw one more : how many are six lines
and one line ? Seven,
1 1. Name seven boys or girls,
12. Count from one to seven.
13. From seven back to naught.
14. Place seven pencils on the table : if you
place one more with
them, how many will
there be ? Eight.
15. How many are
seven chickens and one
chicken ?
1 6. Eight is how
many more than seven?
17. Eight is how many more than one ?
8 FIRST LESSORS ix X UMBERS.
1 8. Count from one to eight
19. From eight back to naught.
20. How many are eight oranges and one
orange ? Nine.
21. What comes next before nine ? Before
eight ?
22. Count from three to nine. From live to
nine.
23. Copy and read the figures denoting five,
six, seven, eight, and nine.
Printed form. 56 7 8*9
Xame, five, nx, seven, eight, nine.
Slate form, J r 3 9
24. Which iigure expresses the smallest number?
25. Which iigure expresses the greatest number?
LKSSOX III.
1. How many lingers and thumbs have you on
both hands ? Ten,
2. Count from one to
ten. f-fr
3. From ten back to
one.
4. Ten is one more than what number ?
5. Count by twos from t\vo : as, two, four, etc.
6. Count by twos- from one : as, one. three, etc,
FIRST LESSUSS IN S~I*MBERS.
7. Count the balls on the upper wire of the
Numeral Frame, as they are moved from left to
right.
8. How many will one ball on the next wire
make counted with the ten on the upper wire ?
Eleven.
9. Two balls on the next wire counted with
the ten on the upper wire will make how many ?
Twelve.
10. Three balls on the next wire counted with
the ten, will make how many ? Thirteen,
10 FIUST LESXONS IN NCMBERS.
11. Four balls on the next wire counted with
the ten, will make how many ? Fourteen.
12. Five balls with the ten, how many ?
Fifteen.
13. Six balls with the ten, how many ?
Sixteen.
14. Seven balls with the ten, how many ?
Seventeen.
15. Eight balls with the ten, how many ?
Eighteen.
1 6. Nine balls with the ten, how many ?
Nineteen.
17. Ten balls with the ten, how many ?
Twenty.
LESSON IV.
1. Ten roses and one rose are how many ?
2. Eleven is how many more than ten ?
3. How do you express eleven ?
Ans. By writing the figure i with a figure i on
the right.
4. Ill expressing eleven, how many figures are
used ?
5. Eleven peaches and one peach are how
many ?
6. Count from one to twelve.
FIRST LESSONS ix NUMBERS. 11
7. How do you express twelve ?
Ans. By writing the figure i with a figure 2 on
the right.
8. Count from twelve back to naught.
9. Count by threes to twelve.
10. Twelve is how many more than ten ?
11. Show by the numeral frame that twelve is
two more than ten.
12. Twelve pears and one pear are how many ?
13. Thirteen is how many more than ten ?
14. Show it by the numeral frame.
15. How do you express thirteen?
1 6. Thirteen oranges and one orange 'are how
many ?
17. Fourteen is how many more than ten ?
1 8. Show it by the numeral frame.
19. How do you express fourteen ?
20. Count from one to fourteen.
21. From fourteen back to one.
22. Copy and read the figures denoting ten,
eleven, twelve, thirteen, and fourteen.
io ii 12 13 14
ten, eleven, twelve, thirteen, fourteen.
10 11 12 13 14
1-' /V//.ST Lvssoxs i\ J
LHSSOX V.
1. What is the moaning of the word thirteen ?
Three and Ten,
2. What is the meaning of the word fourteen?
Four and Ten.
3. Count by twos to fourteen.
4. Fourteen plums and one plum are how
many ?
5. Fifteen is how many more than ten ?
6. Show it by the numeral frame.
7. How do you express fifteen ?
8. Count from ten to fifteen.
9. How many cents are fifteen cents and one
cent ?
10. Sixteen is how many more than ten ?
11. Show it by the numeral frame.
12. How do you express sixteen ?
13. Count from ten to fifteen.
14. What is the meaning of the word sixteen ?
15. What is the meaning of the word fifteen ?
Five and Ten.
1 6. How many dollars are sixteen dollars and
one dollar ?
17. Seventeen is how many more than ten ?
1 8. Show it by the numeral frame.
19. Count from ten to seventeen.
20. How do you express seventeen ?
2j. What is the meaning of the word seven-
teen ?
FIRST LESSORS /.v NUMBEUS. 13
LESSON VI.
1. How many men arc seventeen men and
one man ?
2. Show by marks on the black-board that ten
and eight are eighteen.
3. How do you express eighteen ?
. 4. What number comes next after eighteen ?
5. Count from ten to nineteen.
6. How do you express nineteen ?
7. What is the meaning of the word nineteen?
8. What number comes next after nineteen ?
9. Twenty is how many more ihan ten ?
14 FIRST LESSOXS ix
10. Copy and read the figures denoting fifteen,
sixteen, seventeen, eighteen, nineteen.
1~> 10 i: 18 19
11. Copy and compare the following :
*10
1 11 Eleven is 10 more than i.
2 12 Twelve is 10 and 2.
3 13 Thirteen is 10 more than 3.
4 14 Fourteen is 10 more than 4.
5 15 Fifteen is 10 more than 5.
6 JO Sixteen is 6 more than 10.
7 77 Seventeen is 7 more than 10.
8 18 Eighteen is 8 and 10.
9 J$ Nineteen is 9 more than TO.
Test the pupil's knowledge of the above groups by allow-
ing him to read them in order, down and up, and out of order.
LESSON VII.
1. What is the meaning of the word twenty :
Two Tens.
2. How do you express twenty '?
3. In expressing twenty, how many figures
are used ?
4. What is the figure <n the right called r
Naught.
5. What figure is in the second place ? Two.
FIRST LESSONS IN NUMBERS. 15
6. Draw ten marks on the black-board.
7. Draw ten more, and count how many there
are in both rows.
8. If you draw one more, how many ?
Twenty-one.
9. If you draw one more, how many ?
Twenty-two.
10. Another, how many ? (Continue to 29.)
Twenty-three.
n. Twenty-nine is how many more than
twenty ?
12. How do you express twenty-one, etc,?
13. Count from twenty to twenty-nine.
14. Copy and read the figures denoting twenty,
twenty-one, etc.
20 21 22 23
twenty, twenty-one, twenty-two, twenty-three,
24 25 26 27
twenty-four, twenty-five, twenty-six, twenty-seven,
28 29
twenty-eight, twenty-nine.
1 5. Copy and compare the following :
10 20
1 11 21
2 12 22
3 13 23
4 14 24
Etc.
9 19 29
1G FixsT LESSONS IN NUMBERS.
LESSON VIII.
1. What, is the meaning of the word thirty ?
Three Tens.
2. In expressing thirty how many figures are
used ?
3. What is the figure on the right called ?
4. What figure is in the second place ?
5. Count from thirty to thirty-nine.
6. Thirty is how many more than twenty ?
7. How many more than twenty-nine ?
8. Write the figures denoting thirty, thirty-
one, thirty-two, etc.
9. How do you express thirty-two ?
10. How do you express twenty-three ?
11. Copy and compare the following :
10 20 30
1 11 21 31
I 1.2 23 32
Etc.
9 10 29 39
12. What number comes next after thirty-
nine ? Forty.
13. What is the meaning of the word forty ?
Four Tens.
14. In expressing forty, what figure occupies
the second place ?
15. Count from forty to forty-nine.
FIRST LESSONS IN NUMBERS. 17
1 6. Write the figures denoting forty, forty-
one, forty-two, etc.
17. Copy and compare the following:
10
20
30
40
1
11
21
31
41
2
12
22
32
&
8
13
23
33
43
Etc.
9
'19
29
39
49
LESSON IX.
1. Count from one to one hundred.
2. Count by twos to one hundred.
3. In one hundred, what is the figure on the
right called ?
4. What figure is in the second place ?
5. What figure is in the third place ?
6. If a man had a hundred dollars and earned
a hundred more, how many dollars would he
have? Two hundred.
7. In expressing two hundred, how many
figures are used ?
8. What figure is in the first place ? Second ?
Third ?
9. Two hundred and one hundred are how
many ?
18 FIRST LESSORS nv NUMBERS.
10. How is three hundred expressed ?
By writing three in the third place, naught in
the second place, and naught in the first place.
11. How is four hundred expressed ?
12. Five hundred ? 13. Six hundred ?
14. Seven hundred ? 15. Eight hundred ?
1 5. Nine hundred ?
Ans. By writing the figure 9 with two naughts on
the right.
17. Count by hundreds from one hundred to
nine hundred.
1 8. Copy and read :
100 200 300 400 500 600 700 800 900
19. Copy and compare the following :
10 100
2 20 200
3 30 300
Etc.
9 00 000
LESSON X.
1. A man spent $100 for a horse and one dollar
for a whip ; how many dollars did he spend ?
One hundred and one dollars.
2. How is one hundred and one expressed ?
By writing one in the third place, naught in the
second place, and one in the first place.
FIRST LESSONS IN NUMBERS. 19
3. Count from one hundred to one hundred
and nine.
4. Copy and read the following :
100 101 102 103 104 105 106 107 108 109
5. What number comes next after 109 ?
One hundred and ten.
6. Count from no to 119.
7. Copy and read the figures denoting one hun-
dred and ten, etc., to one hundred and nineteen.
8. Copy and compare :
100 110
101 111
102 112
Etc.
109 119
9. What number comes next after 119 ?
10. Count from 120 to 129.
n. Copy and read :
120 121 122 123 124 125 126 127 128 129
12. Compare:
100 110 120
101 111 121
102 112 122
Etc.
109 119 129
13. One hundred and nineteen is how many
more than one hundred and nine ?
14. One hundred and twenty-nine is how many
more than one hundred and nine ?
20 FIRST LESSONS IN
LESSON XL
1. Notation is the art of writing numbers.
2. Numbers are written or expressed by words,
letters, or figures.
3. The method of writing or expressing num-
bers by letters is called the Roman Method,
4. The method of writing or expressing num-
bers by figures is called the Arabic Method.
5. The Roman Method of Notation employs
seven capital letters to express numbers.
6. The letter I, denotes one ; V, five ; X, ten ;
L, fifty ; C, one hundred ; D, five hundred ; and
M, one thousand.
7. Other numbers are expressed by repeating
and combining these capitals.
8. Repeating a letter repeats its value ; as,
XXX, thirty.
9. If a letter is placed before one of greater
value, the value of the less is taken from the
greater ; as, XL, forty.
10. If a letter is placed after one of greater
value, the value of the less is added to the
greater, as, LX, sixty.
n. The Roman Method of Notation is used in
numbering the chapters, lessons, etc., into which
books are divided, and in marking the hours on
clocks and watches.
* LESSONS /.v NUMBERS.
LESSON XII.
TABLE OF JIOMAST XOTATION.
I one.
XXV twenty-five.
II two.
XXVI twenty-six.
Ill three.
XXVII twenty-seven.
IV four.
XXVIII twenty-eight.
V five.
XXIX twenty-nine.
VI six.
XXX thirty.
VII seven.
XL forty.
VIII eight.
L fifty.
IX nine.
LIX fifty-nine.
X ten.
LX sixty.
XI eleven.
LXX seventy.
XII twelve.
LXXX eighty.
XIII thirteen.
XC ninety.
XIV fourteen.
C one hundred.
XV fifteen.
CO two hundred.
XVI sixteen.
COG three hundred.
XVII seventeen.
CD four hundred.
XVIII eighteen.
D five hundred.
XIX nineteen.
DC six hundred.
XX twenty.
DCC seven hundred.
XXI twenty-one.
DCCC eight hundred.
XXII twenty-two.
CM nine hundred.
XXIII twenty-three.
M one thousand.
XXIV twenty-four.
MM two thousand.
MDCCCLXXVI one
thousand ei^lit hundred
and seventy-six.
FIRST Licssoxs /.v
LESSON XIII.
1. Express 35 by letters. XXXV.
2. In XXXV, how often is X repeated ?
Three times.
3. Express 59 by letters. LIX.
4. Erom which letter is the value of I taken ?
5. Copy and read the following numbers :
III. XVI. XLV.
VI. XXIV. LXIX.
VIII. XXXVI. CIV.
6. The face of a clock is divided into twelve
equal parts, marked by the letters I, II, III,
IV, V, VI, VII, VIII, etc.
7. The short hand points
to the hours, and is called
the hour hand.
8. The long hand points
out the minutes, and is
called the minnte hand.
9. The hour hand moves
from one number to the
next in one hour.
10. If the hour hand is at
XII, what time is it when the minute hand
moves to I ? It is five minutes past twelve.
11. When the minute hand moves to II ?
Ten minutes past twelve.
12. When the minute hand moves to VI ?
Half-past twelve.
FIRST LESSONS IN NUMBERS. ;M
LESSON XIV.
ARABIC XOTATIOX.
1. The Arabic Method of Notation employs
ten figures to express numbers. These figures
were brought into Europe from Arabia.
0123456789
2. The figures from i to 9 are called signifi-
cant figures, because each has a value of its own.
3. They are also called digits, because the
ancients reckoned on their fingers (digitus, a
finger).
4. The first is called naught, because when
standing alone it has no value. It is also called
zero or cipher. Nine is the greatest number
expressed by a single figure.
5. The significant figures are called units,
or figures of the first order. Numbers greater
than ten form higher orders of units, called tens,
hundreds, thousands, etc.
6. Ten is expressed by writing i in the second
place, with a naught on the right : as, 10.
7. Figures standing in the second place are
called tens, or units of the second order.
8. A hundred is expressed by writing i in the
third place, with two naughts on the right.
9. Figures standing in the third place are
called hundreds, or figures of the third order.
10. Three figures form a period.
11. In every period the right-hand figure
represents units, the middle figure represents
tens, and the left-hand figure represents hun-
dreds.
12. What is the rule for expressing numbers of figures ?
Begin at the left, and write the figures of the
given orders in their places toward the right.
When intermediate orders are omitted, supply
their place with naughts.
LESSON XV. .
XUMERATIOX.
1. Numeration is the art of reading numbers.
2. In the French Method of Numeration three
orders form a period.
3. Numbers are read by naming the figures,
the places they occupy, and the period in which
they stand.
4. What is the rule for reading numbers?
Divide them into periods of three figures
each, beginning at the right.
Beginning at the left, read the periods in
succession, calling each by its proper name.
LESSONS ix NUMBERS.
NUMERATION TABLE.
34
Period. 2d
Period. ist
Period.
\
CO*
r~
CO
'2
O
c3
13
i
|
g
CO
g
H
1
w
2
3
to
rS
H
1 -s
CP
r2
0)
O
CO
Pi
H
O
f^
1
CO
5
1 l i
i
1
H
H
w
H
H W
H
P
9
8
7, 6
5
4. 3
2
I.
Millions
Thousands,
Units.
This is read nine hundred and eighty-seven
million, six hundred and fifty-four thousand,
three hundred and twenty-one.
5. Recite the table. Copy and read i
(6.) (7.) (8.) (9.) (10.)
131 190 3176 1021
118 600 1041 9010
636 1 309 6360 3007
Write in figures nine thousand and thirty-
117
234
607
ii.
four.
12.
Six thousand, one hundred and four.
13. Ninety thousand, seven hundred, and
twenty-nine.
14. One million, one thousand, one hundred
and twenty-five.
FIRST LESSONS ix NU
AH EXEECISE WITH OOTJ1TTEBS.
LESSON XVI.
ORDINAL XUMBERS.
The words first, second, third, etc., are called
Ordinal Numbers. They denote the order in
which objects are arranged.
Name the seven days of the week.
What day of the week is Sunday ? Monday ?
Tuesday ? Wednesday ? etc.
Name the first month, second, etc.
What is the name of the first period, second,
third, etc.
FIRST LESSONS IN NUMBERS.
ADDITION.
LESSOR I.
1. Addition is the process of, uniting several
numbers into one sum.
2. The Sum, or Amount, is tlio result or num-
ber obtained. It is equal to all the numbers
added.
3. The Sign of Addition is a perpendicular
cross +, and is called plus, which means more.
Placed between two numbers, it shows that they
are to be added together.
28 FIRST LESSORS /.v X
LESSOX II.
Principles,!. Only like Numbers can be
added, 2. The sum and the numbers added
must be like numbers.
and i are i. 6 and i are 7.
1 " i " 2. 7 " i " 8.
2 " I " 3. S " I " 9.
3 " i " 4. 9 " i " 10.
4 '*' i " 5. 10 '' i " ii.
5 " i " 6. ii " i <; 12.
1. George has 2 books on the seat and i book
in his hand : how many has he in all ?
Solution. 2 books and 1 book are 3 books.
2. How many are 4 horses and one horse ?
3. If you have 5 pencils and your teacher gives
you one more, how many will you have ?
Solution. I will have the sum of five pencils
and one pencil, which is six pencils.
(4.) (5.) (6.) (7.) (8.) (9.) (10.) (n.)
01234 o 6
111111 1 1
12. The sign of equality is two short parallel
lines zi. It is read equals or equal. Placed
between two numbers, it denotes that they equal
each other. It may be read 5+1 are 6.
13. The dollar sign is an S and two parallel lines
drawn through it : thus, $.
FIRST LESSORS ix NUMBERS. 29
LESSON III.
and z are 2. 6 and 2 are 8.
1 " 2 " 3. 7 " 2 " 9.
2 " 2 " 4. 8 " 2 " 10.
'3 " 2 " 5. 9 " 2 " II.
4 " 2 " 6. 10 " 2 " 12.
5 " 2 " ?. ii " 2 " 13.
1. Three windows and one window are how
many ?
2. If John has 4 books, and buys 2 more, how
many will he have ?
3. How many are 5 slates and 2 slates ?
4. How many are 7 desks and 2 desks ?
5. Show that 8 pencils and 2 pencils are 10
pencils.
6. A boy had 9 cents, and earned two more :
how many did he then have ?
7. Mary has n cherries, and Kate has 2 cher-
ries : how many cherries have both girls ?
8. John had 2 apples, his sister had 5, and his
brother had two : how many had all ?
Copy and complete the following :
(9.) (10.) (ii.) (12.) (13.) (14.) (15.) (16.)
01234 567
22222222
20. Count by twos till you reach 60.
30 FIRST LESSONS IN NUMBERS.
LESSON IV.
and 3 are 3. 6 and 3 are 9.
1 " 3 " 4- 7 " 3 " i-
2 " 3 " 5- 8 " 3 " ii.
3 " 3 " 6 - 9 " 3 " J 2-
4 " 3 " 7. 10 " 3 " 13.
5 " 3 " 8- ii " 3 " 14-
1. Two coats and three coats are how many ?
2. Show that 4 pencils and 3 pencils are 7
pencils.
3. There are 6 skates in one window and 3
skates in another : how many are in both win-
dows ?
4. There were 7 houses in one street, and they
are building 3 new houses: IIOAV many will there
be when these are finished ?
5. A man had 9 cows, and bought three more :
how many did he then have ?
6. Count by threes, beginning with three:
thus, 3, 6, 9, etc.
7. Count by threes, from one. From two.
8. Eleven cents and three cents are how many ?
9. Write the table thus : 0+3=3.
Copy and complete the following :
(10.) (n.) (12.) (13.) (14.) (15.) (16.) (17.)
0123456 7
FIRST LESSONS IN NUMBERS. 31
LESSON V.
and 4 are 4. 6 and 4 are 10.
1 " 4 " 5- 7 " 4 " ii.
2 " 4 " 6. . 8 " 4 " 12.
3 " 4 " 7. 9 " 4 " 13-
4 " 4 " 8. 10 " 4 " 14.
5 " 4 " 9- ii " 4 " 15-
1. One ship and four ships are how many ?
2. Two masts and four masts are how many ?
3. Five ropes and four ropes are how many ?
4. Show that 3 books and 4 books are seven
books.
5. Six houses and four houses are how many ?
6. Seven men were in one boat and four in an-
other : how many were in both ?
7. The tail of a boy's kite was ten feet long ;
lie tied on four feet : what was its whole length ?
8. A man had 4 dollars, and he earned 9 dol-
lars : how many did he then have ?
Solution. He had the sum of $4 and $9,
which is 13 dollars ; Or he had $13, because $4
and $9 are $13.
Copy and complete the following :
(9.) (10.) (n.) (12.) (13.) (HO (15-) (16.)
? 3 I ,5 6 7 8 9
44444444
(17.}, l
20. Count by fours till you reach 60.
'32 FIRST LESSONS IN L
LESSON VI.
and 5 are 5. 6 and 5 are n.
1 5 " 6. 7 <' 5 " 12.
2-5-7. 8-5 13.
3 " 5 " 8 - 9 " 5 " H.
4 " 5 " 9- I0 " 5 " T 5-
5 " 5 " 10. ii " 5 " 1 6.
1. Two boys and five boys are how many ?
2. Show by lines on the black-board that three
and five are eight.
3. One room has 5 windows, and another has
6 : how many windows in both rooms ?
4. There are 5 houses in one row and 7 in
another : how many in both ?
5. I counted 8 apples on one branch and 5 on
the next : how many on both ?
6. There are 5 peaches in one basket and 9 in
another : how many in both ?
7. James caught 10 fish, and his brother caught
5 : how many did both catch ?
8. Edward is 7 years old : how old will he be
5 years hence ?
9. If you are 9 years old and your brother is
5 years older than you, how old is your brother ?
(10.) (n.) (M.M.I3.) (14-) (15.) (16.) (17.)
0123 4 > # 7
1 111 1 J 11
o ~> .7 -7 -7 5 5 5
FIRST LESSONS IN NUMBERS. 33
LESSON VII.
o and 6 are 6.
6 and 6 are 12.
i 6 " 7.
7 6 13.
2 " 6 " 8.
8 " 6 " 14.
3 6 " 9.
9 6 15.
4 " 6 " 10.
10 " 6 " 1 6.
5 " 6 "ii.
ii " 6 " 17.
1. If you have 3 peaches and buy 6 more, how
many will you have ?
2. How many are 6 cents and 7 cents.
3. There are 4 buds on one bush and 6 on an-
other : how many on both ?
4. Charles paid 6 cents for ink and 8 cents for
paper: how many cents did he spend ?
5. How many cents must a boy have to buy
ten cents' worth of cake and 6 cents' worth of
candy ?
6. How many cents must I give a boy if I wish
him to buy a spool of thread at 6 cents and a
yard of muslin at 1 1 cents ?
Copy and complete the following :
(7.) (8.) (9.) (10.) (ii.) (12.) (13.) (14.)
67896 6 66
11110 1 23
66662 2 22
(15.) 4
17. Count by lives till you reach 60, By 6's.
34 FIRST LESSONS IN NUMBERS.
LESSON VIII.
and 7 are 7. 6 and 7 are 13.
1 " 7 " 8. 7 " 7 " 14.
2 " 7 " 9- 8 " 7 " J 5.
3 " 7 " jo. 9 " 7 " 16.
4 " 7 " ii. 10 " 7 " 17.
5 " 7 " 12. ii " 7 " 18.
1. How many are 3 cents and 7 cents ?
2. Count by sevens till you reach 70.
3. How many are $5 and $7 ?
4. Three sheep are in one field and seven in
another : how many are in both ?
5. There are 6 trees in one row and 7 in an-
other : how many are there in the two rows ?
6. James spent 7 cents for pencils and 8 for a
slate : how much money did he spend ?
7. A boy had 9 cents left after spending 7
cents : how many cents did he have at first ?
8. There are 10 boys in one line and 7 in
another ; how many in both ?
9. A boy missed 7 words and recited 1 1 : how
many words was he asked to spell ?
10. A railroad train was made up of 7 passen-
ger cars, and 10 freight cars : how many in all ?
(n.) (12.) (13.) (14.) (15.) (16.) (17.) (18.)
01234 50 7
77777 77
FIRST LESSONS IN fi
LESSOR IX.
and 8 are 8. 6 and 8 are 14.
1 8 9. 7 " 8 15.
2 " 8 " 10. 8 " 8 " 16.
3 " 8 " n. 9 " 8 " 17.
4 " 8 " 12. 10 " 8 " 1 8.
5 " 8 " 13. ii " 8 " 19.
1. How many are $i and $8 ?
2. There are 2 birds on the fence and 8 on the
tree : how many are there in all ?
3. A sponge cost 3 cents and a rubber 8 cents :
how many cents did both cost ?
4. There are 8 windows in the front of a house
and 4 in the rear : how many are there in all ?
5. John gaye away 5 peaches and has 8 left :
how many had he at first ?
6. Six years ago John was 8 years old : how
old is he now ?
7. How many are 7 yards and 8 yards ?
8. After selling 8 turkeys, a farmer has 8 left :
how many had he at first ?
9. How many are 9 and 8 ? 10 and 8 ? n and
8 ? 12 and 8 ?
10. Count by eights till you reach 80.
(ii.) (12.) (13.) (14.) (I5-) (16.) (17-) (18.)
01334507
88888888
(19.) 8+4+8+2=? (20.) f)+l+3+S+l=:?
LESSON A.
and 9 are 9. 6 and 9 are 15.
1 *' 9 <% 10. 7 "' 9 " *6.
2 " 9 " ii. 8 " 9 " 17.
3 " 9 " 12. 9 " 9 " 18.
4 " 9 " J 3- J o " 9 " I 9-
5 " 9 " 14. ii " 9 " 20.
i A boy was sent for one pound of tea and 9
pounds of sugar: how many pounds must lie
carry home ?
2. There are 9 persons in one family and 8 in
another: how many persons in the two families ?
3. Henry's hat cost 2 and his coat $9 : how
many dollars did both cost ?
4. Count by nines till you reach 90.
5. Mary is four years old, and Kate was nine
years \vhen Mary was born : how old is Kate ?
6. After giving away 5 roses, Jane has 9 left :
how many had she at first ?
7. If a quart of apples cost 6 cents and a quart
of pears cost 9 cents, what will both cost ?
8. Count by tens till you reach 100.
9. Paid 88 for a tableland 89 for six chairs:
how many dollars did I spend ?
10. Charles and Edward had 9 marbles each;
Charles gave his to Edward : how many did Ed-
ward then have ?
11. Ten persons sat on one side -of a car and 9
on the other : how many persons were in the car ?
FIKST LESSONS /.Y NUMBERS. 37
LESSON XL
To add single columns.
i. Find the amount of 8, 3, i, 4, 9. Slatework.
ANALYSIS. i. Write the numbers one under 8
another, in a perpendicular column, and draw 3
a line underneath. i
2. Begin at the bottom and add the numbers 4
to one another, thus: 9, 13, 14, 17, 25. 9
3. Write the amount underneath.
Hence the sum is 25. 25 Ans.
NOTES. i. In adding, name the results only. Avoid
this style: 9 and 4 are 13, and i are 14.
2. Require the pupil to add without counting fingers or
other objects.
3. Insist on neat figures and perpendicular columns.
(*) (3.) (4.) (5-) (6.) (7.) (3.) (9-)
3 345
222224_c6
67899567
12 4 5 6 7 8
(10.) (II.) (12.) (I 3 .) (I 4 .) (I S .) (.6.) (I 7 .)
5
6
7
8
9
7
8
9
4
4
4
4
4
8
9
7
6
6
6
6
6
9
7
8
7
9
7
9
8
7
8
9
9
8
9
6
5
8
9
8
2
3
4
5
6
9
8
7
38 FIRST LESSONS ix XUXHKKS.
LESSON XII.
(i.) (2.) (3.) (4.) (5.) (6.) (7.) (3.)
6
6
6
6
6
6
6
6
5
8
7
9
4
6
6
7
6
6
6
6
6
7
6
7
8
7
8
6
8
7
7
6
6
6
6
7
9
8
7
8
7
5
9
9
8
8
8
8
5
8
8
7
7
8
8
6
6
4
9
8
9
9
9
9
7
8
9
6
8
9
9
9
7
8
9
8
9
9
9
9
(9-)
(10.)
(n.)
(12.)
(13.)
(14.)
('5-)
(16.)
3
7
9
7
4
i
H
9
6
14
12
i
9
9
8
3
8
9
7
H
7
8
13
16
ii
3
i
9
13
15
9
4
4
i
4
4
8
6
7
8
(~)
(18.)
(190
(20.)
(21.)
(22.)
(23.)
(24.)
8
5
8
5
6
8
7
9
7
9
5
6 '
5
9
8
6
9
16
7
T 7
7
2 5
9
18
15
8
6
9
J 3
9
6
5
9
7
9
8
9
7
18
9
4
6
13
7
8
6
9
8
FIRST LESSONS IN NUMBERS. 39
LESSON XIII.
When the sum of each column is less than 10.
i. What is the amount of 521 and 126 ?
ANALYSIS. i. Write the numbers one un- Slate work.
der another, units under units, tens under 521
tens, etc., and draw a line underneath. 126
2. Add the figures in the units' column,
and write the sum, which is 7 units, under 647 Ans.
units' place.
3. Add the figures in the tens' column, and write the
sum, which is 4 tens, under the tens' place.
Continue thus until all the columns are added.
Hence the sum is 647.
(2.) (3.) (4.) (5.) (6.) (7.) (8.)
12
22
3 2
48 15
17
234
13
23
33
10 71
40
123
14
24
34
21 12
3 1
43
( 9 .)
(10.)
(n.)
( I2 -) (I3-)
( I4 .)
(is-)
I0 5
341
301
142 364
132
307
56i
"3
65
32O 2O2
43
172
3 2 3
202
5^3
5 l6 423
704
520
(16.)
(I?-)
(i&;
) ' (190
(20.)
(21.)
$ Pounds. Men
Miles.
Acres.
Horses.
234
2 3
561
35
802
240
140
614
*5
9*3
9 l
5 '4
405
*35
33
S 1
1 06
H3
40 FIRST LESSOXS /.v NUMB EPS.
LESSON XIV.
When the sum of a column equals or exceeds 10.
1. What is the amount of 365, $944, and $422?
ANALYSIS. i. Write the numbers one un- Slate work.
der another, units under units, tens under $365
tens, etc., and draw a line underneath. 944
2. Add the figures in the units' column. 423
The sum is 12 units, equal to i ten and 2 units.
Write the 2 units under units' place, and add $1732 Am.
the i ten to the tens' column, because it is of the same
order.
3. The sum of the tens is 13 tens, equal to i hundred
and 3 tens. Write the 3 tens under tens' place, and add
the i hundred to the hundreds' column, because it is of the
same order.
4. The sum. of the hundreds is 17, and this being the
last column we set down the whole amount.
Hence the sum is 1732.
NOTE. At first give examples in which one column
amounts to ten, or more.
2. One school has 308 pupils, another 96, and
another 435 : how many have all ?
3. A merchant gained $450 the first year, $573
the second year, and 695 the third year: what
was the whole gain ?
4. Find the sum of 590 tons, 817 tons, 904
tons, and 1325 tons.
5. Three men sold a steamboat; the first re-
ceived 82125 as his share, the second 8936, and the
third $3688 : what was the value of the steamboat?
FIRST LESSONS IN NUMBERS. 41
6. Add 508, 7009, and 60,306.
7. A captain sold his vessel for $3425, which
was $2050 less than cost: what did it cost ?
8. A man gave his property to his wife, son,
and daughter; to his daughter 1*3 gave $3475,
to his son 5150, and to his wife as much as he
gave to his children : what was the value of his
property ?
9. A grocer bought 4 hogsheads of molasses;
the first contained 95 gallons, the second 6 gal-
lons more than the first, the third 7 gallons more
than the second, and the fourth 27 gallons more
than the third: how many gallons did he
purchase ?
RULE FOR ADDITION.
1. Write the numbers one under another, units
under units, tens under tens, hundreds under
hundreds, etc.
2. Begin at the right-hand or units' column,
and add each column separately.
3. When the sum of a column is less than ten,
write it under the column added.
4. Where the sum of a column is 10, or more,
write the units' figure under the column added,
and add the remaining figure or figures to the
next higher order.
5. When the last column is added, set down the
whole amount.
Proof. Repetition is the only proof of addition.
42 FIRST LESSONS IN NUMBERS.
SUBTRACTION.
LESSON I.
Subtraction is the process of finding the differ-
ence between two numbers.
The Difference, or remainder, is the number
lef fc after subtracting.
The Minuend is the number from which the
subtraction is made.
FIRST LESSONS IN NUMBERS. 43
The Subtrahend is the number to be subtracted.
The Sign of Subtraction is a short horizontal
line , called minus, which means less.
It shows that the number on the right is to be
taken from the number on the left.
LESSON II.
Principle. Only like Numbers can be subtracted.
i from i leaves o. i from 6 leaves 5.
i " 2 " i. i " 7 " 6.
i " 3 " 2. i " 8 " 7.
i " 4 " 3. i " 9 8.
i < 5 " 4. i " 10 " 9.
1. Draw 3 chalk-lines on the black-board ;
erase one : how many are left ?
2. Draw 4 lines ; erase one : how many are
left?
3. John had 5 cents and spent one cent for an
apple : how many cents had he left ?
Solution. He had left the difference between 1
cent and 5 cents, which is four cents.
Copy and subtract the following :
(4.) (5-) (6.) (7-) (8.) (90 (10.) (n.) (12.)
123 4 3 678 9
11111 11 11
44 FIRST LESSORS IN NUMBERS.
LESSON III.
2 from 2 leaves o. 2 from 7 leaves 5.
2 " 3 " i. 2 " 8 " 6.
2 " 4 f; 2. 2 " 9 "' 7.
2 " 5 " 3. 2 10 " 8.
2 " 6 " 4. 2 "' XI 4i 9.
1. Draw three lines on the black-board ; erase
two : how many are left ?
2. Place four books in a row ; take away two :
how many are left ?
3. Jane bought 5 apples and ate 2 : how many
had she left ?
Solution. 2 apples from 5 apples leave 3 apples.
4. Joseph earned 7 cents ; he spent two, and
saved the rest : how many did he save ?
5. If there are 9 roses in a bouquet, and Peter
takes out two, how many will remain ?
6. If you have 6 marbles and lose 2, how many
have you left ?
7. If there are 10 eggs in a nest, and a boy
takes out two, how many are left ?
8. A hunter saw 12 ducks on a pond ; he shot
two : how many escaped ?
9. Write the table thus: 2 2=0.
10. What number is two less than n ?
(ii.) (12.) (13.) (14.) (15-) (16.) (i7-) (18.)
3 3 1 ' 6 78 9
FIRST LESSONS IN NUMBERS. 45
LESSON IV.
3 from 3 leaves o. 3 from 8 leaves 5.
5 " 4 " i. 3 k * 9 " 6.
3 " 5 " 2. 3 " 10 " 7.
3 - 6 " 3. 3 ii " 8.
3 " 7 " 4 3 " 12 9.
1. Charles had 3 oranges and gave one to each
of his three sisters : how many has he left ?
2. John had 4 birds,, and the cat killed 3 of
them : how many were left ?
3. If you have 5 rabbits, and give away three,
how many will remain ?
4. If yon had 6 cents, and spent 3, how many
cents will you have left ?
5. A gentleman built 7 houses in a row ; he
sold 3 : how many still belong to him ?
6. 3 boys out of 9 were promoted : how many
were not ?
7. Louise bought 8 oranges and gave away 3 :
how many had she left ?
8. A carpenter had n chisels, and broke 3 :
how many remained ?
9. Willie had ten cents ; he bought a top' for
two cents, and a cord for i cent : how much had
he left ?
(10.) (n.) (12.) (13.) (14.) (15.) (16.)
12 /-,' 14 15 16 17 18
46 FIRST LESSONS IN NUMBERS.
LESSON V.
4 from 4 leaves o. 4 from 9 leaves 5.
4 5 " i. 4 " 10 " 6.
4 '' 6 <' 2. 4 ^ ii " 7.
4 " 7 " 3. 4 " 12 " 8.
4 " 8 " 4. 4 13 - 9.
1. If a boy had 4 cents, and bought 4 cents'
worth of candy, how much money would he have
left ?
2. A boy bought 5 pencils and broke 4: how
many has he left ?
3. John promised to make 6 kites ; he has 4
of them done : how many more must he make ?
4. Edward picked 7 quarts of berries, and sold
4 quarts : how many had he left ?
5. George caught 9 fish and his brother caught
4: how many did George catch more than his
brother ?
6. A hen had 10 chickens; four died: how
many are still alive ?
7. A farmer had 12 sheep; he sold 3 and i
died : how many had he left ?
8. A box of crackers weighed 13 pounds, and a
box of candy 4 pounds : what is the difference in
weight ?
( 9 .) (10.) (II.) (12.) (I 3 .) (I 4 .) (I S .)
U -4 .-J 26 27 28 20
5
leaves
0.
5 from
10
leaves
5-
6
<
i.
5
t k
1 1
*'*
6.
7
( .
2.
5
*
12
7-
8
"
3<
5
ft
J 3
8.
9
4-
5
*
14
"'<'
9-
er
ic had
6
rabbits,
and
sold 5 ;
how
FIRST LESSORS rx NUMBERS.
LESSON VI.
5 from
5 "
5
5 "
5 "
1. Fred
many had he left ?
2. If he has i left, how many must he buy so
as to have 8 rabbits ?
3. A pail filled with water weighed 9 pounds ;
without the water it weighed 4 pounds : how
many pounds did the Avater weigh ?
4. A merchant paid n cents a pound for
sugar and sold it for 5 cents a pound : what was
the loss on each pound ?
5. A carpenter earned $12, and spent $5* for a
saw: how many dollars had he left ?
6. A grocer paid 5 cents a pound for cheese,
and sold it for 13 cents : what was the gain ?
7. John had $14, and he spent $5 for a hat:
how many dollars had he left ?
8. William is 14 years old, and his sister is 5
years younger: how old is his sister ?
(9.) (10.) (ii.) (12.) (13.) (14.) (15.) (16.)
21 22 23 24. 25 26 27 28
ft -5 5 5 5555
48 FIRST LESSORS ix NUMBERS.
LESSON VII.
6 from 6 leaves o. 6 from 1 1 leaves 5.
6 " 7 " i. 6 " 12 < 6.
6 ' 8 " 2. 6 V* 13 " 7.
6 " 9 " 3. 6 " 14 " 8.
6 ** 10 <' 4. 6 * 15 9.
1. Jane carried 7 quarts of berries to market,
and sold 6 : how many quarts were left ?
2. Charles rises at 6 o'clock, and studies till 8 :
how many hours does he devote to study ?
3. If you pay 6 cents for an orange, and sell it
for 9 cents, how much will you gain ?
4. If a grocer pays 10 a barrel for flour, and
sells it for $6, how much will he lose ?
5. There were n chairs in a room, and Mary
removed 6 : how many were left ?
6. -If you had 12 cents, and spent 4 for cake
and 2 for apples, how many cents will remain ?
7. 6 and how many make 14 ? Why ?
8. 13 is the minuend, and 6 is the subtrahend:
what is the remainder ?
9. A farmer owned 15 sheep, but a wolf killed
six: how many were left ?
10. 6 and how many will make 20 ?
(ii.) (12.) (13.) (4.) (15.) (16.) (17.) (18.)-
27
FIRST LESSONS IN NVMBBX& 49
LESSON VIII.
7 from 7 leaves o. 7 from 12 leaves 5.
7 " 8 " i. 7 " 13 " 6.
7 " 9 " 2. 7 " 14 " 7.
7 " 10 " 3. 7 " 15 " 8.
7 " ii "4. 7 " 16 " 9.
1 . A traveller started in the 7 o'clock train and
reached home at 9 : how long was he in the cars ?
2. Frank passes 10 barns on his way to school ;
7 are old : how many are new ?
3. There were n chickens in a brood, and the
rats killed all but 7 : how many were killed ?
4. Tom is now twelve years old, and he has
been to school 7 years : how old was he when he
began to go to school ?
5. If I earn 13 cents and spend 7, how many
cents will I have left ?
6. A dress cost $14 and a hat cost $6 less : what
was the cost of ihe hat ?
7. There were 15 children in the park, but 7
have gone home : how many remain ?
8. Jane is 16 years old, and Louise is 7 years
younger : how old is Louise ?
9. What is the difference between 7 and 17 ?
(10.) (n.) (12.) (13.) (14.) (IS-) (16.)
80 32 34 35 36 38 39
7 7 7- 7 7 7 7
50 FIRST
LESSON IX.
8 from 8 leaves o. 8 from 13 leaves 5.
8 " 9 " i. 8 14 " 6.
8 " 10 " 2. S " 15 " 7.
8 " ii " 5 8 " 16 " 8.
8 ^ 12 " 4. 8 " 17 " 9.
1 . A farmer paid $8 dollars a barrel for flour
and sold it for $9 : how much did he gain ?
2. What is the difference between $8 and $10 ?
3. ii passengers were riding in a cat : S got
out : how many continued to ride ?
4. .What mv aw from a 1 2-foot
board to make it 8 feet long ?
5. Charles is 8 years old ; how many years will
pass before he will be 13 ?
6. Francis saw 14 ducks on a lake, and shot 5 :
how many escaped ?
7. If William has $8 and can save $i a day:
how long must he work to have $15 ?
8. A sloop sailed 8 miles in an hour, and a
steamer 16 miles : how far were they apart at the
end of the first hour ?
9. Two men paid $17 for a boat ; one agreed to
pay $8 : what must the second ma
(10.) (II.) (12.) (I 3 .) (I 4 .) (150 06.) (I
31 32 S3 -? 37
S S S S S S S S
FIRST LESSONS ix NUMBERS. 51
LESSON X.
9 from 9 leaves o. 9 from 14 leaves 5.
9 " 10 " i. 9 4 * 1 S 6i 6.
9 "'' ii " 2. 9 " 1 6 " 7.
9 " 12 - 3. 9 " 17 W 8.
9 ? 13 K 4- 9 " l8 " 9-
1. Harry bought a knife for 10 cents and sold
it for 9 cents : how many cents did he lose ?
2. Charles borrowed n cents and paid back 9,
how many does he still owe ?
3. A farmer planted 12 pear-trees, and 9 of
them bear fruit : how many do not ?
4. A grocer paid 9 cents a pound for cheese
and sold it for 13 cents : what did he gain on each
pound ?
5. School opens at 9 o'clock : how many hours
till noon ?
6. A scholar answered 9 questions out of 14 :
how many did he miss ?
7. James saved 15 cents ; he bought a copy-
book for 8 cents, and a pen for i cent : how much
had he left ?
8. A boy had 16 marbles and won 4; then he
lost 9 : how many had he left ?
(9.) (10.) (n.) (12.) (13.) (14.) (150 (16.)
9 19 29 30 32 34 36 38
9 9999999
FufST LESSOXS IN Xm
LESSON XL
To subtract when each figure in the subtra-
hend is less than the one above it.
i. Find the difference between 75 and 21.
ANALYSIS. i. Write the less number un- Slate wwk.
der the greater, units under units, tens under 75
tens, etc., and draw a line underneath. 21
2. Subtract the units thus : i unit from 5
units leaves 4 units. Write the remainder 54 Ans.
under the units' place, because it is units.
3. Subtract the tens, and write the remainder under the
tens' place, because it is tens.
Hence the remainder is 54.
(*) (3-) (4-) (S-)
From 59 74 295 359
Take 27 31 134 214
(7-) (8.) (9.)
From 176 pounds. 346 sheep. 569 horses.
Take 162 *' 313 '* 266 '
(6.)
842
5 21
(10.)
138
(II.) (12.) (I 3 .)
From 694 men. 359 miles. 189 tons.
Take 684 " 45 " 72 "
(HO
$394
103
(150 (16.) (17.)
From 468 barrels. 963 trees. 277 feefc.
Take 57 " 32 6 4
(18.)
$543
241
Fiitsr LESSOXS ix NUMBERS. 5;i
LESSON XII.
When a figure in the subtrahend is greater
than the orie above it.
1. What is the difference between 575 and 327?
ANALYSIS. i. Write the less num- Slate work.
ber under the greater, units under IB
units, tens under tens, etc., and 5 "^N^
draw a line underneath. 327
2. Seven units from 5 units can-
not be taken ; we must take one 248 Am.
ten from the ten's figure and add it to the 5 units, which
makes 15 units. 7 units from 15 units leave 8 units, which
we write under units' place, because it is units.
3. Since we took i ten from the 7 tens, there are 6 tens
left ; and 2 tens from 6 tens leave 4 tens, which we write
under tens' place, because it is tens.
4. Three hundreds from 5 hundreds leave 2 hundreds.
Hence the remainder is 248.
NOTE. i. Take one from the next figure : do not bor-
row and pay back.
2. It is necessary at first to mark this change in the
slate work. In review, however, insist on a dot being
placed over the figure from which i is taken (575).
2. I sold a watch for $i 10 which cost $75 : what
was the gain ?
3. If I pay 35 cents for a brush, how much
change will I receive out of a $2 bill ?
4. A farmer sold a horse for $75, and bought a
cow for $35 and a calf for $15: how many dol-
lars had he left ?
5. A gentleman planed $1250 in bank ; lie drew
54 FIRST Lf:sso.\'fi /.v
out at one time $360, and at another $237 : what
sum remains in bank ?
6. I purchased a house for $'18572, and sold it
for $20000 : what did I gain ?
ANALYSIS. i. Two units from o unit State work.
cannot be taken. We must take one iVS^X^io
from the next significant figure. ^X.o o o o
2. i ten thousand from 2 ten thou- 18572
sands added to the thousands makes -
10 thousands, leaving i ten thousand. i 4 2
i thousand from 10 thousand added to the hundreds
makes 10 hundreds, leaving 9 thousands, i hundred
from 10 hundreds added to the tens makes 10 tens,
leaving 9 hundreds, i ten from 10 tens added to the
units makes 10 units, leaving 9 tens.
3. 2 units from 10 units leave 8 units. 7 tens from 9
tens leave 2 tens. 5 hundreds from 9 hundreds leave 4
hundreds, etc. Hence the gain is $1428.
RULE FOR SUBTRACTION".
1. Write the less number wider the greater,
units under units, tens under tens, etc.
2. Begin at the right or units' place, and sub-
tract each figure of the longer number from the
one above it, setting the remainder under the
column subtracted.
3. If the lower figure Is greater than the upper
figure, increase the latter by ten, and consider the
next higher figure one less ; then subtract.
Proof. The sum of the remainder and subtra-
hend should equal the minuend.
FTI?ST .LKHHOXS r.v Nr
MULTIPLICATION.
LESSON I.
Multiplication is the process of taking one of
two numbers as many times as there are units in
the other.
The Multiplicand is the number to be multi-
plied.
The Multiplier is the number which shows how
many times the multiplicand is to be taken.
r>fi FIRST LFSSOXS rx
The Product is the result obtained.
The Sign of multiplication is an oblique cross
X- It is read multiplied by. or times.
LESSON II.
Principles. 1. The multiplier is an abstract
number. 2. The multiplicand and product are
like numbers.
2 times i are 2. 2 times 7 are 14.
2 " 2 " 4. 2 " 8 ** 1 6.
2 " 3 " 6. 2 " 9 " 18.
2 " 4 " 8. 2 {; 10 " 20.
2 "' '' 5 * * I O. 2 * k I I ' 22.
2 " 6 " 12. 2 *" 12 " 24.
1. Draw a line on the black-board each time
that I give the signal. When two lines were
drawn, how many times was the signal given ?
2. Two times one line are how many ?
3. What is the cost of 2 apples at 5 cents each ?
Solution. Since 1 apple cost 5 cents, 2 apples
will cost 2 times 5 cents, which are ten cents.
4. If you can hold 8 chestnuts in one hand.
how many can you hold in both ?
5. Each boy has ten fingers : how many fin-
ers have two bovs ?
FTKST LESSONS IN N
LESSON III.
3 times i are 3. 3 times 7 are 21.
3 ff 2 " 6. 3 " 8 " 24.
3 " 3 " 9- 3 " 9 " 2 7-
3 " 4 " 12. 3 " 10 " 30.
3 " 5 " J 5- 3 " IJ " 33-
3 6 18. 3 " 12 36.
1. One ox has 2 horns : how many horns have
3 oxen ?
2. In each of 3 beats there are 3 men : how
many are there in all ?
3. How many feet are in 4 yards ?
4. A truckman can carry 6 barrels at a load :
how many barrels can he take in 3 loads ?
5. Mary is 7 years old, and her brother is 3
times as old : what is the age of her brother ?
6. When pine-apples are 8 cents each, what
will 3 pine-apples cost ?
7. At $10 each what will be the price of 3
stoves ?
8. What will 3 yards of muslin cost at n
cents per yard ?
9. If a copy-book contains 12 leaves, how
many leaves will 3 copy-books contain ?
Write the table, thus :
(A) 3x1=3. (B) 1x3=3.
3x2=6. 2x3=0.
3x3=9. 3x3=9.
58 FIRST LESSONS IN NUMBERS.
LESSON IV.
4 times i are 4. 4 times 7 are 28.
4 " 2 " 8. 4 " 8 " 32.
4 " 3 " 12. 4 " 9 " 3<5.
4 . " 4 " 1 6. 4 " 10 " 40.
4 " 5 " 20. 4 " ii " 44-
4 " 6 " 24. 4 " 12 " 48.
1. What will 4 yards of silk cost at $7 a yard ?
2. If a boy works 5 hours each day, how many
hours does he work in 4 days ?
3. How many feet have 3 dogs ?
4. There are 4 gills in one pint: how many
gills in 6 pints ?
5. If one table cost $7, what will 4 tables cost ?
6. If one pound of sugar cost 8 cents,, how
many cents will 4 pounds cost ?
7. I have 4 boards, each 9 feet long : what is
the united length of the boards ?
8. Bought 4 pounds of sugar at 10 cents a
pound, and sold it at 12 cents a pound ; what did
I gain ?
9. At the rate of 7 for a cent, how many mar-
bles can be bought for 4 cents ?
10. In form A, which is the multiplier ?
11. In form B, which is the multiplier ?
12. Write the table in both forms.
(13.) (14.) (15.) (16.) (17.) (18.) (19.)
Multiply 5 9 11 8 12 21 ..'.>
By . -. 33 4 4 4
LESSONS IN NUMBERS. 59
LESSON V.
5 times i arc 5. 5 times 7 are 35.
5 " 2 " 10. 5 " 8 40. '
5 " 3 " 15- 5 " 9 " 45-
5 " 4 (i 20. 5 " 10 " 50.
5 ki 5 " 25. 5 " ii " 55.
5 " 6 " 30. 5 " 12 " 60.
1. What will be the cost of 5 hats at $2 each ?
2. At 3 cents each, what will be the cost of
three oranges ?
3. Frank lives 2 miles from school : how many
miles does he walk in 5 days ? Ans. 20 miles.
4. If a man earns $4 a day, how many dollars
will he earn in 5 days ?
5. If 6 marbles can be bought for one cent,
how many can be bought for 5 cents ?
6. There are 7 days in i week : how many
days are there in 5 weeks ?
7. Ten cents make one dime : how many cents
in 5 dimes ?
8. "What will 11 quarts of chestnuts cost at
5 cents a quart ?
9. How many inches in 5 feet ? In 4 feet ?
10. How many fives make 20 ? etc.
11. Write the table in both forms.
(12.) (13.) (14.) (15.) (16.) (17.)
Multiply 11 12 21 27 31 111
By 555555
FIRST LESSONS IN XUMBE.
LESSON
V
[Jl
6
6
times i are 6.
2 " : 12.
6
6
times 7
*' 8
6
6
6
6
" 3 " 18.
- " 4 " 24.
" 5 " 3-
6 - 36.
6
6
6
6
" 9
" 10
" ii
" 12
GO
are 42.
" 48.
" .54-
" 60.
" 66.
" 7 2.
1. A workman earned $2 a day: how many
dollars did he earn in 6 days ?
2. Sarah saved $3 each month : how many dol-
lars had she at the end of 6 months ?
3. A grocer paid $5 a barrel for flour, and sold
it for 89 : what did he gain on 6 barrels ?
4. A carpenter built 6 fences, each fence having
5 posts : how many posts did he use ?
5. He built 6 houses, each house having 6 win-
dows : how many window-frames were required ?
6. If one sheet of paper makes 8 leaves of a
copy-book, how many leaves will 6 sheets make ?
7. A gentleman hired 5 workmen at $2 a day :
how much must he pay them for 6 days' work ?
8. A farmer carried 6 dozen of eggs to mar-
ket, and sold them for i cent apiece : what did
he get for them ?
(9.) (10.) (n.) (12.) (13.) (14.)
Multiply .9 11 21 111 201 311
Bv '> 6 6 6 6 6
FIRST LESSONS IN NUMBERS. 61
LESSON VII.
7 times i are 7. 7 times 7 are 49.
7 " 2 " 14. 7 " 8 " 56.
7 -' 3 " 21. 7 " 9 63.
7 *'' 4 * 28. 7 ** 10 *' 70.
7 "' 5 " 35- 7 " ii " 77-
7 M 6 " 42. 7 " 12 <f 84.
1. A jeweller paid $3 apiece for rings, and
sold them for $4 : what did he gain on 7 rings ?
2. Each room in a hotel is lighted by 2 gas-
jets : how many jets are in 7 rooms ?
3. How many horseshoes will a blacksmith
use in shoeing 7 horses ?
4. If a barrel will hold 3 bushels of apples,
how many bushels will 7 barrels hold ?
5. What will 7 pairs of boots cost at $5 a pair ?
6. How many feet in 7 boards each 6 feet long?
7. How many days are there in 7 weeks ?
8. Alice is 8 years old, and her father is 7 times
as old as she is : what is her father's age ?
9. 7 tens are how many units ?
10. If a family use n pounds of sugar in one
week, how many pounds will they use in 7 weeks ?
11. What will be the price of a dozen spools of
cotton at 7 cents a spool ?
(12.) (13.) (14.) (15.) (16.) (17-)
Multiply 11 9 101 201 211 311
BY 777 7 7 7
6x5 FIRST LESKOXS ix
LESSON A
8 times i are S. 8 times 7 are 56.
8 " 2 k * 16. 8 *' 4 ' 8 " 64.
8 " 3 " 24. 8 " 9 " 72.
8 " 4 " 32. 8 " 10 " 80.
8^5 " 40. 8 " ii " 88.
8 " 6 " 48. 8 " 12 " 96.
1. 8 quarts make a peck : how many quarts in
8 pecks ?
2. What will be the cost of 8 yards of muslin,
at 4 cents a yard ?
3. Five boards, each 8 feet long, reach from the
door of a cottage to the gate : what is the length
of the yard ?
4. An agent rented a house at 7 a month :
how much did he receive in 8 months ?
5. A carpenter made 8 ladders, each having
12 rungs : how many rungs did he use ?
6. What will a boy receive for 8 quarts of ber-
ries at 9 cents a quart ?
7. At 10 cents each what will 8 oranges cost ?
8. 8 times 1 1 miles are how many miles ?
9. What will a dozen copy-books cost at 8
cents each ?
(10.) (n.) (12.) (i 3 .) (i 4 :) (i 5 .)
9 11 7 101 111 210
<S* S 8 8 8 8
FIRST LESSORS IN NUMBERS. 63
LESSON IX,
9 times i are 9. 9 times 7 are 63.
9 " 2 " 1 8. 9 " 8 " 72.
9 " 3 " 27. 9 " 9 " 81.
9 " 4 " 36. 9 " 10 " 90.
9 " 5 " 45- 9 " ii rt 99-
9 " 6 " 54. 9 " 12 " 1 08.
1. Sold 9 barrels of flour at a profit of $2 a
barrel : what did I gain ?
2. A carriage-maker finished 9 carriages : how
many wheels did he use ?
3. How many shelves can be made out of 9
boards, if one board will make three shelves ?
4. What is the cost of 9 tables at $5 each ?
5. Paid 5 cents each for pears, and sold them at
a gain of i cent : what were 9 pears sold for ?
6. What will 9 yards of velvet cost at $7 a yd. ?
7. Each of 9 boys answered 8 questions ; how
many questions were answered ?
8. 9 times naught are how many ?
9. Bought 9 yards of muslin at n cents a yard:
how much change did I receive out of a dollar ?
10. What will 9 calves cost at $12 each ?
11. Write the table in both forms.
(12.) (13.) (14.) (15.) (16.) (17.)
7 9 11 1001 1010 2001
9 9 9 9 9
G4 FIRST LESSONS AV Nui
LESSON X.
10 times i are 10. 10 times 7 are 70.
IO
f ( 2
a
20.
10 "
8 "
80.
IO
" 3
ft
3-
IO "
9 "
9 0.
IO
" 4
a
40.
IO "
10 "
IOO.
IO
" 5
ti
5-
IO "
n (i
IIO.
IO
" 6
a
60.
10 "
12 "
120.
LESSON XL
n times i are n.
II " 2
ii " 3
n
n
n
4
5
6
II.
n
times 7
are 77.
22.
n
8
" 88.
33-
n
" 9
' 9-
44.
n
I O
" IIO.
55-
n
n
" 121.
66.
n
" 12
X i3 2 -
LESSON XII.
12 times i are 12.
12 ff 2 " 24.
12 3 36.
12 fi 4 " 48.
12 " 5 " 60.
12 '' 6 *' 72.
12 times 7 are 84.
12 " 8 " 96.
12 " C) " 1 08.
12 " 10 fi 120.
12 ig II itf 132.
12 " 12 ' 144.
FIRST LESSONS IN NUMBERS. 65
LESSON XIII.
To multiply by one figure when the partial
products are less than 10.
i. What will 3 houses cost at $1213 each ?
ANALYSIS. i. Write the multiplier under Slate work.
the right-hand figure of the multiplicand. $1213
2. Multiply the units figure of the multi- 3
plicand by the multiplier. 3 times 3 units
are 9 units ; which we write under units' $3639 Ans.
place, because it is units.
3. 3 times i ten are 3 tens ; which we write under tens'
place, because it is tens.
Continue thus until each figure of the multiplicand has
been multiplied. Hence the product is $3639.
NOTE. Show that multiplication is a short method of
adding equal numbers.
When a partial product is 10, or more,
What will 5 carriages cost at $417 each ?
ANALYSIS. i. Write the multiplier under Slate work.
the right-hand figure of the multiplicand. $417
Begin at units' place to multiply. 5
2. 5 times the 7 units are 35 units, equal
to 3 tens and 5 units. Write the 5 units $2085 Ans.
under the figure multiplied, and add the 3 tens to the pro-
duct of the tens.
3. 5 times i ten are five tens, and 3 tens make 8 tens.
Write the 8 under the figure multiplied.
4. 5 times 4 hundreds are 20 hundreds : this being the
last figure to be multiplied, we set down the whole amount.
NOTE. Teach multiplication by 10, n, arid 12 by one
operation.
66 FIRST LESSORS AV S UMBERS.
LESSON XIV.
When the multiplier is more than 12.
What will 24 pianos cost at $638 each ?
ANALYSIS. i. Write the multiplier under Slate work.
the multiplicand, units under units, tens $638
under tens, etc. 24
2. 4 times 8 units are 32 units, or 3 tens
and 2 units. Write the 2 units under the 2552
figure multiplied, and add the 3 tens to the 1276
product of the tens.
3. 4 times 3 tens are 12 tens, and 3 tens $15312 Ans.
are 15 tens, or i hundred and 5 tens. Write the tens in tens'
place, and add the hundreds to the product of the hundreds.
4. Continue thus until each figure of the multiplicand
has been multiplied by the units figure of the multiplier.
5. 2 tens times 8 units" are 16 tens, or i hundred and 6
tens. Write the tens under the figure multiplied by, and
add the i hundred to the next product.
6. 2 tens times 3 tens are 6 hundreds, and i hundred
are 7 hundreds. Write the 7 in hundreds' place, etc.
7. Add the partial products.
RULE TOR MULTIPLICATION.
i. Write the multiplier under the multiplicand,
units under units, etc.
2.' Multiply the multiplicand by each figure of
the multiplier, and set the first figure of each
partial product under the figure multiplied by.
3. Add the partial product*.
Proof. Repetition is the only proof of multipli-
cation until division has been taught.
LESSONS rx LUMBERS.
67
DIVISION.
LESSON I.
Division is the process of finding how many
times one number is contained in another.
Or, Division is the process of finding one of
the equal parts of a number.
The Dividend is the number to be divided.
The Divisor is the number to divide by.
The Quotient shows how many times the divisor
is contained in the dividend.
68 . FIRST LESSONS ix NUMBERS.
The Remainder is the part of the dividend left
over when the division is not exact. It is always
less than the divisor. When there is no remain-
der the division is said to be exact.
The Sign of Division is a short horizontal line
between two dots -*-. It is read divided by.
Placed between two numbers, it shows that the
one on the left is to be divided by the one on the
right.
LESSOR. II.
2 in 2, i time. 2 in 12, 6 times.
2,
i
time.
2
in
12,
6
4,
2
times.
2
(t
14,
7
6,
3
<e
2
16,
8
8,
4
{(
2
((
18,
9
10,
5
ft
2
ef
20,
10
1. How many times 2 horses are 12 horses ?
2. How many apples at 2 cents each can you
buy for 4 cents ?
Solution. You can buy as many apples for 4
cents as 2 cents, the price of one apple, is con-
tained times in 4 cents, which is 2 times ; there-
fore, 2 apples can be bought.
3. How many peaches at 2 cents each can yon
buy for 6 cents ?
4. How many $2 bills make twenty dollars ?
5. If 2 dresses cost 18, what will i dress cost ?
FTRST LESSONS ix NUMBERS. 69
LESSON III.
3 in 3, i time. 3 in 1 8, 6 times.
3 " 6, 2 times. 3 " 21, 7 "
3 " 9, 3 " 3 " 24, 8 '
3 12, 4 " 3 v < 27, 9
3 " J 5> 5 " 3 " 3? I0 "
1. How many kites at 3 cents each can you
buy for 6 cents ?
2. 3 feet make a yard : how many yards are
there in 9 feet ?
3. If one boat holds 3 boys, how many boats
will be required for 12 boys ?
4. If you can buy a ring f qr 3 cents, how many
can you buy for 15 cents ?
5. A kite-frame requires 3 sticks : how many
kites can be made with 18 sticks ?
6. A plate holds 3 apples: how many places
will be required for 2 1 apples ?
7. How many bags will be required to hold 24
bushels of potatoes, if one bag holds 3 bushels ?
8. How many times 3 cents are 27 cents ?
9. 30 is how many times 3 ?
10. How many threes in 15 ?
11. 3 is contained in 21 how many times ?
12. Continue: 3+3=1. 6+3=2. 9+3=3.
(13.) (14.) (15.) (16.) (17.) (18.)
3)6 3)12 3)15 3)18 3)2 4 3)30
70 FIRST LESSOXS i.\ XC
LESSOX IV.
4 in 4> i time. 4 in 24, 6 times.
4 " 8, 2 times. 4 " 28, 7 "
4 " 12, 3 " 4 32, 8
4 " 16, 4 " 4 '" 36, 9 ".
4 " 20, 5 ?f 4 " 40,. 10
1. If 4 hats cost $8, what will one hat cost ?
Solution. If 4 hats cost $8, one hat will cost
one-fourth of $8, which is 2 dollars.
2. If 4 yards of silk cost 12 dollars, what will
one yard cost ?
3. If 4 copy-books cost 16 cents, what will one
copy-book cost ?
4. If 4 panes of glass cost 20 cents, what will
one pane cost ?
5. If 4 wheels are needed for one carriage, how
many carriages will 24 wheels supply ?
6. If one bench will seat 4 boys, how many
benches will seat 28 boys ?
7. How many dresses will 32 yards of ribbon
trim, if it takes 4 yards to trim one dress ?
8. If 4 boys earn 40 cents, what will be each
boy's share ?
9. Continue: 4+4=*- 8+4=2- 12+4=3.
(10.) (ii.) (12.) (13.) (14.) (15.)
4)8 4)1* 4)20 4)32 4)40 4)44
FIRST LESSOXS ix NVMBEKX. 71
LESSON V.
5 in 5, i time.
5 in 30, 6 times.
5 " 10, 2 times.
5 ^ 35, 7 "
5 " '5, 3 "
5 " 4o, 8 "
5 " 2 o, 4 "
5 ik ' 45 ? 9 "
5 " 25, 5 "
5 " 50, 10 "
1. How many fans at 5 c6nts eacli can you buy
for 5 cents ?
2. How many spools of thread at 5 cents each
can be bought for 10 cents ?
3. How many times can 5 cents be taken from
15 cents ?
4. If the railroad fare is 5 cents a mile, how far
can you ride for 20 cents ?
5. If you pay $5 apiece for sheep, how many
sheep can you buy for $25 ?
6. An orchard contains 30 trees, and has 5 trees
in each row : how many rows in the orchard ?
7. How many fives in 35 ?
8. How many bouquets, each containing 5
roses, can you make with 35 roses ?
9. A lady bought 5 cups for 40 cents: what did
one cup cost ?
10. If 5 tables cost $45, what will one table
cost ?
(ii.) (12.) (13.) (14.) (IS-) (16.)
5)15 5)25 5)30 5)35 5)45 5)50
FIRST Lxs
LKSSOX VI
6 in 6, i time. 6 in 36, 6 times.
6 " 12, 2 times. 6 " 42, 7 "
6 << 18, 3 "' 6 " 48, 8 -
6 " 24, 4 " 6 54, 9
6 " 30, 5 " 6 " 60, 10 tftf
1. How many pineapples at 6 cents each can
be bonght for 12 cents ?
2. I paid 1 8 cents for 6 kites: what was the
cost of each ?
3. If 6 pounds of flour cost 24 cents, what is
the cost of one. pound ?
4. How many days will 30 apples last, if you
eat 6 each day ?
5. How many boards 6 feet long will reach
across a yard which is 36 feet in length ?
6. If a stage holds 6 persons, how many stages
will be required to carry 42 persons ?
7. If 48 trees are planted in 6 equal rows, how
many trees will there be in each row ?
8. If James saves 6 cents a week, how long will
it take him to save 54 cents ?
9. If 6 trunks cost $60, what is the price
of one ?
10. Continue : 6+6=1. 12+6=2. 18+6=3.
(11.) (12.) (13.) (14.) (15.) (16.)
6)12 6)24 6)30 6)42 6)54 6)60
FIRST LESSONS ix NUMBERS.
LESSON VII.
7
in
7,
i
time.
7
in
42,
6
times*
7
((
H,
2
times.
7
(C
49 ?
7
ft
7
t(
2I >
3
f<
7
(
56,
8
a
7
a
28,
4
7
it
63,
9
<e
7
((
35.
5
tt
7
a
7,
io
"
1. If i pound of sugar costs 7 cents, how many
pounds can be bought for 14 cents ?
2. 7 days make a week : how many weeks in
21 days ?
3. I tied 28 cherries in bunches of 7 cherries
each : how many bunches did I make ?
4. How many sevens in 35 ? How many fives
in 35 ?
5. If 7 pencils cost 42 cents, what will one
cost ?
6. At $7 each, how many calves can be bought
for 49 dollars ?
7. How many yards at 7 cents a yard can be
bought for 56 cents ?
8. 63 is seven times what number ?
9. John spent 63 cents in one week : how much
did he spend each day ?
10. How many times $7 is $49 ?
11. Continue: 77=1. 14+7=2.. 21+7=8.
(12.) (13.) (14.) (is-) (16.) (17.)
7)U' 7)21 7)28 7)35 7)49 7)70
74 FIKST LESSOXS ix XU
LESSOX VIII.
8 in 8/1 time. 8 in 48, 6 times.
8 " 16, 2 times. 8 " 56, 7 "
8 " 24, 3 " 3 64, 8
8 " 32, 4 " 8 " 72, 9 "
8 " 40, 5 " 8 " So, 10 "
1. At 8 cents a quart, how many quarts of milk
can be bought for 16 cents ?
2. If one slate cost 8 cents, how many can be
bought for 24 cents ?
3. 8 boys earned 32 cents : what was each boy's
share ?
4. I paid 40 cents for 8 bouquets : what was
the price of one ?
5. 8 quarts make a peck : how many pecks in
48 quarts of corn ?
6. 8 pounds of oatmeal cost 56 cents : what
was the price of one pound ?
7. How many pews, each seating 8 children,
will seat 64 boys ?
8. How many eights in 72 ? In 80 ? In 88 ?
In 96 ? In 800 ? '
9. How many yards of velvet at 88 a yard can
be bought for 872 ?
10. How many times 88 is 840 ?
11. Continue: 8+8=1. 16+8=2. 24+8-3.
(12.) (13.) (14.) (15.) (16.) (17.)
>
LESSORS ix NCMBEHS.
LESSON IX.
9 in
9,
I
time.
10 ill
IO,
i
time.
9 "
18,
2
times.
10 *'
20,
2
times.
9 "
27,
3
a
10 ' *'
30,
3
"
9 "
36,
4
10 "
40,
4
"
9 "
45.
5
a
10 4i
5,
5
a
9 "
54,
6
a
10 "
60,
6
a
9 "
63,
7
a
10 "
70,
7
"
9 "
72,
8
ii
I O
80,
8
a
9 "
81,
9
a
10 "
90,
9
tt
9 "
90,
10
ii
10 "
100,
10
ff
LESSON X.
ii in
Ir ,
i
time. 12 in
I2 >
i
time.
n "
22,
2
times. 12 "
24,
2
times.
ii "
33,
3
12 "
36,
3
a
ii "
44,
4
" 12 '*
48,
4
"
ii "
55,
5
a
12 "
60,
5
ii "
66,
6
66
12 "
72,
6
"
a "
77,
7
ii
12 "
8 4 ,
7
"
ii "
88,
8
it
12 "
96,
8
a
n "
99.
9
ii
12 "
1 08,
9
a
ii "
IIO,
10
ii
12 "
120,
10
66
ii "
121,
1 1
ii j fj it
132,
n
a
ii "
!3 2 ,
12
it 12
T 44,
12
n
70 FIRST LESSORS IN
LESSON XL
When the divisor consists of one figure.
How many chairs, at $2 each, can be bought
for 246 ?
ANALYSIS. i. Write the divisor to the Slate work.
left of the dividend, with a curve line be- 2)246
tween them, and begin at the left to Chairs 123 Ans.
divide.
2. 2 is contained in 2 hundreds i hundred times ; write
the i under the figure divided, for it is of the same order.
3. 2 is contained in 4 tens, 2 tens times ; write the 2
under the figure divided, for it is of the same order.
4. Continue thus until each figure is divided.
Hence the quotient is 123.
To divide by one figure when the divisor is
not contained an even number of times.
Slate work.
ANALYSIS. i. Write the divisor to the left 4)3369
of the dividend, with a curve line between them. 842^
2. 4 is not contained hi 3 thousands any thousands times ;
unite the 3 thousands and 3 hundreds, making 33 hun-
dreds. 4 is contained in 33 hundreds, 8 hundred times,
and a remainder ; write the 8 under the figure divided.
3. i hundred and 6 tens make 16 tens. 4 is contained in
1 6 tens, 4 tens times ; write the 4 under the figure divided.
4. 4 is contained in 9 units, 2 times ; write the 2 under
the figure divided. 9 is the last figure ; write the last re-
mainder over the division, and annex it to the quotient.
Hence the quotient is 8424.
LESSONS IN NUMBERS. Tl
LESSON XII.
When the divisor exceeds 12.
Divide 48352 by 3 2 -
1. 32 is contained in 48 thousands, 32)48352(1511
i thousand time. Write the i thou- 32" *
sand in the quotient ; multiply the
divisor by it ; subtract the product from 163
the figures divided, and annex to the re- 160
mainder the next figure of the dividend
for a partial dividend. 35
2. 32 is contained in 163 hundreds, 5 32
hundreds times. Write the 5 hundreds
in the quotient, and continue the above 32
process until all the figures of the dividend 32
have been brought down.
Hence the quotient is 1511.
11ULE FOR DIVISION.
1 . Write the divisor to the left of the dividend, and
draw a curve line for the quotient.
2. Find Jww many times the divisor is contained in,
the least number of left-hand figures that will contain
it, and write the result in the quotient.
3. Multiply the divisor by the quotient figure ; sub-
tract the product from the figures divided, and to the
remainder annex the next figure of the dividend for a
partial dividend.
4. Divide as before, until all the figures of the divi-
dend have been brought down.
5. If any partial dividend ivill not contain the
divisor, tvrite a cipher in the quotient, annex the next
figure of the dividend to the partial divisor, and divide
as before.
6. If tJiere be a final remainder, ivrite it over the
divisor, and annex it to the quotient.
Proof, Multiply the quotient by the divisor.
78 FIRST LESSORS iy ^'
STATES MONEY.
A coin is a piece of metal bearing n legal
stamp. Each coin lias a lixed value.
Paper money consists of notes and bills issued
by a government or a bank, as substitutes for
coin. Notes and bills are promises to pay stated
sums of money.
United States Money is the legal currency of
the United States.
The denominations are eagles, dollars, dimes,
cents, and mills.
The Unit of United
States money is the
Dollar.
TABLE.
10 mills (m.) make i cent, ct.
10 cents " i dime, d.
10 dimes " i dollar, 8.
10 dollars " i eagle, E.
The coin of the United States consists of gold,
silver, nickel, and bronze.
The gold coins are the double-eagle, eagle, half-
eagle, quarter-eagle, three dollars, and one-dollar
pieces.
The silver coins are the trade dollar, half-dollar,
quarter -dollar, and dime.
The nickel coins are the live-cent and three-
cent pieces.
The bronze coins are the two-cent and one-
cent pieces.
FIRST LESSORS IN
ENGLISH MONEY.
English Sterling Money is the legal currency of
Great Britain.
The denominations are pounds, shillings, pence,
and farthings.
The Unit of
["English money is
the pound ster-
ling or Sovereign.
TABLE.
4 farthings (far.) make i penny, cl.
12 pence
20 shillings
2 shillings i florin.
5 "
i crown,
i guinea.
i shilling,
\ i pound, ,
/ i sovereign, sov.
i pound $4.866^.
i shilling =2 4 cents
i penny = 2 cents.
FBENCH MONEY.
French Money is the legal currency of France.
The denomi-
nations used in
business are na-
poleons, francs,
and centimes.
The Unit of
French money
is the Franc.
The value of the franc is 18 cents and 6 mills.
80 FIHST LESSORS AY LU
TEOY WEIGHT.
The Standard Unit of weight in the United
States is the Troy pound.
Troy Weight is used in weighing gold, silver,
coin, jewels, etc.
The denominations are pounds, ounce*?, penny-
weights, and grains.
TABLE,
24 grains (gr.) make i pennyweight, pwt.
20 pennyweights i ounce, oz.
12 ounces ' " i pound, Ib.
3-J- grains " i carat.
5760 grains *'' i pound.
|L
i grain. 24 grains. 480 grains. 5760 grains.
APOTHECARY WEIGHT.
Apothecary Weight is used in preparing
medicine, but all drugs are bought and sold
in large quantities by Avoirdupois Weight,
The denominations are pounds, ounces, drams,
scruples, and grains.
TABLE.
20 grains (gr.) make i scruple. $.
3 scruple? " i dram. 3.
^ drams >; i ounce. .
12 ounces " T ])oiuid. Ib.
5760 grains *'* i pound.
FIRST LESSORS IN LU
81
The pound, ounce, and grain of this weight
ure the same as those of Troy weight, the differ-
ence being in the subdivision of the ounce.
60 gr.
480 gr. 5760 gr.
AVOIRDUPOIS WEIGHT.
Avoirdupois Weight
is used to weigh all
coarse and heavy ar-
ticles.
The denominations
are tons, hundred-
weights, quarters,
pounds, and ounces.
The Long ton is used
in the United States
Custom-houses and in
selling coal at the
mines.
1 6 ounces (oz.) make
25 pounds "
4 quarters *'
20 hundredweight "
2240 pounds
7000 Troy grains "
Not used.
pound, Ib.
quarter, qr.
hundred weight, cwt.
ton, T.
Long ton, L. T.
avoirdupois pound.
437 Jgr-
7000 gr.
FIRST LESSOXS IN
LIQUID OK WINE MEASURE.
Liquid Measure is used in measuring wine,
liquor, milk, water, etc.
The denominations are hogsheads, barrels,
gallons, quarts, pints, and gills.
TABLE.
4 gills (gi.) n
2 pints
4 quarts
231 cubic inches
31 1 gallons
2 barrels
lake i pint,
i quart,
i gallon,
i gallon.
4 i barrel,
i hogshead,
pt.
qt.
gal.
bbl.
hhd.
Barrels and hogsheads are not fixed measures.
DRY MEASURE.
Dry Measure is used in measuring grain, fruit,
salt, etc.
The denominations are bushels, pecks, quarts,
and pints.
TABLE.
2 pints (pt.) make
quart,
qt.
8 quarts *'
peck,
nk.
4 pecks
bushel,
1m.
36 bushels
chaldron,
d.
2 quarts "
small measure.
LESSORS rx
The standard bushel contains 2150.42 cubic
inches. It is a cylindrical measure, i8| inches
in diameter and 8 inches deep.
LOKG MEASUKE.
Long Measure is used in measuring lines and
distances.
The denominations are leagues, miles, furlongs,
rods, yards, feet, and inches.
TABLE.
12 inches (in.) make i foot,
3
feet
feet
5i y ards
40 rods
8 furlongs
5280 feet
3 miles
ft.
yd.
rd.
i yard,
i rod,
i rod.
i furlong, fur.
i mile, " mi.
i mile.
i league.
OTHEK DENOMINATIONS.
4 inches make i hand, h.
6 feet " i fathom, fath.
i-t miles " i knot, k.
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Cloth Measure is no longer used. In measur-
ing dry-goods, etc., the yard is divided into
halves,' quarters, eighth?, etc.
84 FIRST LESSONS /.v Jfni
SURVEYORS' LONG MEASURE.
Surveyors' Long Measure is used in laying out
roads and measuring land.
The unit of measure is Gunter's Chain. It is
66 feet long, and consistsof 100 links. 80 chains
make one mile.
SURFACE, OR SQUARE MEASURE.
A surface has two dimensions
length and breadth.
A square is a plane figure
having four equal sides and four
right angles.
Surface, or Square Measure is
used in measuring the surface
of land, boards, plastering, etc.
The denominations are square miles, acres,
square rods, square yards, square feet, and square
inches.
TABLE.
144 square inches (sq.in.) make i square foot,sq.ft.
9 square feet make i square yard, sq. yd.
30^ square yards " i square rod, sq. rd.
272! square feet " i square rod.
1 60 square rods " i square acre, A.
640 acres '' i square mile, sq.
mi.
SURVEYORS' SQUARE MEASURE.
Surveyors' Square Measure is used by surveyors
in computing the area or surface of lands.
FIRST LKSSOXS ix
TABU-:.
1 6 square rods make i square chain, sq. eh.
10 square chains " i acre, A.
640 acres make i square mile or section.
36 square miles make i township.
Government lands are divided into townships
by parallels and meridians.
CUBIC, OR SOLID MEASURE.
A Solid has three dimensions length, breadth,
and thickness.
A Cube is a body bounded by six equal squares,
called faces.
The Volume, or contents of a solid is the space
included within the surfaces which bound it.
Cubic or Solid Measure is used in computing
the volume of solids, and the capacity of rooms,
cisterns, ships, etc.
The denominations are cubic yards, cubic feet,
and cubic inches.
TABLE.
1 728 cubic inches (en. in.) make i cubic foot, cu.fr.
27 cubic feet " i cubic yard,cu.yd.
1 28 cubic feet " i cord of wood.
A Cord
of Wood
i.s a pile
8 feet
long-, 4
fr. wide,
and 4
ft. hio-h.
FIRST LFXSOXS i.\ A'r.w;/
TIME MEASURE.
The denominations of Time Measure are years.
months, days, hours, minutes, and seconds.
TABLE.
60 seconds (sec.) make i minute, min.
60 minutes " i hour, hr.
24 hours " i day. d.
7 days " i week, w.
30 or 31 days " month. mo.
12 months
52 weeks
365 days
366 days
100 years
year, y.
year.
common year,
leap year,
centurv.
The exact length of a solar year is 365 days,
5 hrs.. 48 min., 46 sec., or nearly 365! days.
NAMES OF THE MONTHS.
1. January (Jan.) has 31 days.
2. February (Feb.) " 28 days.
3. March ' (Mar.) " 31 days.
4. April (Apr.) " 30 days.
5. May (May) " 31 days.
6. June (June) " 30 days.
7. July (July) " 31 days.
8. August (Aug.) " 31 days.
9. September (Sept.) " 30 days.
10. October (Oct.) " 31 days.
11. Xovember (Xoy.) '* 30 days.
12. December (Dec.) " 31 days.
FIRST LESSONS IN NUMBERS. 87
Thirty days hath September,
April, June, and November ;
All the rest have thirty-one, except February.
CIRCULAR, OR ANGULAR MEASURE.
A Circle is a plane figure bounded by a curve
line, every point of which is equally distant from
a point within, called the centre.
A Circumference is the curve line which bounds
the circle.
The circumference is 3j- times the diameter.
An Arc is any part of the circumference.
A Radius is any straight line drawn from the
centre to the circumference.
A Diameter is a straight line drawn through the
centre, and terminated both ways by the circum-
ference.
An Angle is the difference in the direction of
two lines drawn f 1:0111 the same point, called the
Vortex.
Circular, or Angular Measure is used in measur-
ing angles and arcs of circles. It is used in
astronomy, geography, navigation, surveying,
and for calculating difference of time.
TABLE.
60 seconds (") make i minute, '
60 minutes " i degree,
90 degrees " i quadrant, quad.
360 degrees " i circle.
69! miles '* i degree of latitude.
FIRST LKSSOXS IN XT
MISCELLANEOUS T A B LES.
POUXTTXO.
12 units
make
i dozen
t
i2 dozen
u
i gross.
12 gross
<.-
i great
gross.
20 units
.'
i score.
24 sheets make i quire. 2 reams make i bundle.
20 quires " i ream. 5 bundles '* i bale.
YA 02444
102
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Fleury's Historical Catechisrir.^. Abridged by Forn
Formby's Ilhistralsri Bible an I Olrarch History.
cdiiiou. With Questions.
Mylius's History of Ea^laid. Continued down -
sent Time by . . LL.D: %
Q-ahan's Chu .1 iau-%1 u
Time by J. G. Shea, LL.D.
Fredet's Ancient History.
ct Modera History.
Catechism rf Perseverance.
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Kerney'3 First Class Book of History.
Kerney's Compendium of- Ancient and Modem History.
Iiingard's England abridged.
of Philosophy, by Hill.
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