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chase ?

16. James is to learn forty-two verses of Scripture in a
week : how many must he learn each day ?

17. How many times is 4 contained in 50, and how many
over?

PRINCIPLES AND EXAMPLES.

60. 1. Let it be required to divide 86 by 2.

Set down the number to be divided and write
the other number on the left, drawing a curved
line between them. Now there are 8 tens and
6 units to be divided by 2. We say, 2 in 8, 4
times, which being tens, we write it in the tens'
place. We then say, 2 in 6, 3 times, which
being units, are written in the units' place.
The result, which is called a quotient, is there-
fore, 4 tens and 3 units, or 43.

2. Let it be required to divide 729 by 3.

OPERATION.

2) 86

43 quotie't.

ANALYSIS. We say, 3 in 7, 2 times and 1 over. OPERATION.

Set down the 2, which are hundreds, under the 7.
But of the 7 hundreds there is 1 hundred, or 10 tens,
not yet divided. We put the 10 tens with the 2

3)729
1243

tens, making 12 tens, and then say, 3 in 12, 4 times, and write the
4 of the quotient in the tens' place ; then say, 3 in 9, 3 times.
The quotient, therefore, is 243.

3. Let it be required to divide 466 by 8.

ANALYSIS. We first divide the 46 tens
by 8, giving a quotient of 5 tens, and 6 tens
over. These 6 tens are equal to 60 units,
to which we add the 6 in the units' place.
We then say, 8 in 66, 8 times and 2 over ;
hence, the quotient is 58, and 2 over, which
we caU a remainder. This remainder is
written after the last quotient figure, and
the 8 paced under it; the quotient is read,
58 and 2 divided by 8-

OPERATION.

8)466

58-2 remain.

58f quotient.

50. Ex. 1. When you divide 8 tons* by 2, is the unit of the quotient
tens or units ? When 6 units are divided by 2, what is the unit ?

SIMPLE NUMBERS. 59

ANALYSIS. In the first example 86 is divided into 2 equal parts,
and the quotient 43 is one of the parts. If one of the equal parts
be multiplied by the number of parts 2, the product will be 86, the
number divided.

In the third example 466 is divided into 8 equal parts, and two
units remain that are not divided. If one of the equal parts 58,
be multiplied by the number of parts, 8, and the remainder 2 be
added to the product, the result will be equal to 466, the number
divided.

61. DIVISION is the operation of dividing a number into
two equal parts ; or, of finding how many times one number
contains another.

The first number, or number by which we divide, is called
the divisor.

The second number, or number to be divided, is called the
dividend.

The third number, or result, is called the quotient

The quotient shows how many times the dividend contains
the divisor.

If anything is left after division, it is called a remainder.

62. There are three parts in every division, and sometimes
four : 1st, the dividend ; 2d, the divisor ; 3d, the quotient ;
and 4th, the remainder.

There are three signs used to denote division ; they are the
following :

lS-f-4 expresses that 18 is to be divided by 4.
-^ 8 expresses that 18 is to be divided by 4.
4)18 expresses that 18 is to be divided by 4.
When the last sign is used, if the divisor does not exceed
12, we draw a line beneath, and set the quotient under it. If
the divisor exceeds 12, we draw a curved line on the right of
the dividend, and set the quotient at the right.

2. When the seven hundreds are divided by 3, what is the unit of
the quotient? To how many tens is the undivided hundred equal?
When the 13 tens arc divided by 8, what is the unit of the quotient?
Whun the 9 uuits arc divided by #, what is the quotient ?

- How is the division of the remainder expressed ? Read the
quotient. If there be a remainder after division, how must it be written ?

61. What is division ? What is the number to be divided called ?
What is the number called by which we divide? What is the answer
called ? What is the number oalled which is left ?

62. Plow many parts arc there in division ? Name them. How
many signs are there in division ? Make and name them ?

60 SHORT DIVISION.

SHORT DIVISION.

63. SHORT DIVISION is the operation of dividing when the
work is performed mentally, and the results only written
down. It is limited to the cases in which the divisors do not
exceed 12.

Let it be required to divide 30456 by 8.

ANALYSIS We first say, 8 in 3 we cannot. Then, OPERATION.

8 in 30, 3 times and 6 over; then 8 in 64, 8 times ; 8)30456
then 8 in 5, times; then, 8 in 50. 7 times: hence,

/ ooOT

RULE I. Write the divisor on the left of the dividend.
Beginning at the left, divide each figure of the dividend by
the divisor, and set each quotient figure under its dividend

II. If there is a remainder, after any division, annex (o it
the next figure of the dividend, and divide as hcfnrp , ^

III. Jf any dividend is less than the divisor, write 0/br the
quotient figure and annex the next figure of the dividend, for
a new dividend.

IV. If there is a remainder, after dividing the last figure,
set the divisor under it, and annex the result to the quotient.

PROOF. Multiply the divisor by the quotient, and to the
product add the remainder, when there is one ; if the work
is right the result will be equal to the dividend.

/

EXAMPLES.

(1.) (2.) (3,) (4)
3)9369 4)73684 5)673420 6)825467

Ans. 3123 18421 134684 137577f

3 4 5 6_

Proof 9369 73684 673420 825467"

5. Divide 86434 by 2.

6. Divide 416710 by 4.
7 Divide 641 40 by 5.

8. Divide 278943 by 6.

9. Divide 95040522 by 6.

10. Divide 75890496 by 8.

11. Divide 6794108 by 3.

12. Divide 21090431 by 9.

13. Divide 2345678964 by 6
14 Divide 570196382 by 12

15. Divide 67897634 by 9.

16. Divide 75436298 by 12.

17. Divide 674189904 by 9.

18. Divide 1404967214 by 11.

19. Divide 27478041 by 10
20 Divide 167484329 by 12.

EQUAL PARTS. 61

21. A man sold his farm for 6756 dollars, and divided the
amount equally between his wife and 5 children : how much
did each receive ?

22. There are 576 persons in a train of 12 cars : how
many are there in each car ?

23. If a township of land containing 2304 acres be equally
divided among 8 persons, how many acres will each have ?

24. If it takes 5 bushels of wheat to make a barral of flour,
how many barrels can be made from 65890 bushels ?

25. Twelve things make a dozen : how many dozens are
therein 2167284?

26. Eleven persons are all of the same age, and the sum
of their ages is 968 years : what is the age of each ?

27. How many barrels of flour at 7 dollars a barrel can be
bought for 609463 dollars ?

28. An estate worth 2943 dollars, is to be divided equally
among a father, mother, 3 daughters and 4 sons : what is
the portion of each ?

29. A county contains 207360 acres of land lying in 9 town-
ships of equal extent : how many acres in a township ?

30. If 11 cities contain an equal number of inhabitants,
and the whole number is equal to 3800247 : how many will
there be in each ?

EQUAL PARTS OF NUMBERS.

64. 1. If any number or thing be divided into two equal
parts, one of the parts is called one-half: one half of a single
thing is written thus ; J.

2. If any number is divided into three equal parts, one of
the parts is called one-third, which is written thus ; \ ; two
of the parts are called two-thirds: which are written thus ; f .

3. If any number is divided into four equal parts, one of
the parts is called one-fourth, which is written thus ; J ; two
of the parts are called two-fourths, and are written thus ; ;
three of them are called three-fourths, and written J ; and
similar names are given to the equal parts into which any
number may be divided.

63. What is short division ? How is it generally performed ? Give
the rule ? How do you prove short division ?

62 EQUAL PARTS

4. If a number is divided into five equal parts, what is one
of the parts called ? Two of them ? Three of them ? Pour
of them ?

5. If a number is divided into 7 equal parts, what is one
of the parts called ? What is one of the parts called when
it is divided into 8 equal parts ? When it is divided into 9
equal parts ? When it is divided into 10 ? When it is divided
into 11 ? When it is divided into 12 ? -

6. What is one-half of 2? of4? of6? ofS? of 10? of 12?
of 14? of 16? of 18?

7. What is two-thirds of 3 ?

ANALYSTS Two-thirds of three are two times one third of
three. ODe-third of three is 1 , therefore, two-thirds of three are
two times 1, or 2.

Let every question be analyzed in the same manner.

What is one-third of 6 ? 2 thirds of 6 ? One-third of 9 ?
2 thirds of 9 ? One-third of 12 ? two-thirds of 12 ?

8. What is one-fourth of 4 ? 2 fourths of 4 ? 3 fourths of 4 ?
What is one-fourth of 8 ? 2 fourths of 8 ? 3 fourths of 8 ? What
is one-fourth of 12 ? 2 fourths of 12 ? 3 fourths of 12 ? One-
fourth of 16 ? 2 fourths of 16 ? 3 fourths ?

9. What is one-seventh of 7 ? What is 2 sevenths of 7 ? 5
sevenths? 6 sevenths? What is one-seventh of 14? 3 sev-
enths ? 5 sevenths ? 6 sevenths ? What is one-seventh of 21 ?
of 28 ? of 35 ?

10. What is one-eighth of 8? of 16? of 24? of 32? of
40? of 56?

1 1 . What is one-ninth of 9 ? 2 ninths ? 7 ninths ? 6 ninths ?
5 ninths? 4 ninths? What is one-ninth of 18? of 27? of
54? of 72? of 90? of 108?

12. How many halves of 1 are there in 2 ?

ANALYSIS There are twice as many halves in 2 as there are
in 1. There are two halves in 1 ; therefore, there are 2 times 2
''halves in 2, or 4 halves.

13 How many halves of 1 are there in 3 ? In 4 ? In 5 ?
In 6? In 8? In 10? In 12?

14 How many thirds are there in 1 ? How many thirds
of 1 in 2? In 3? In 4? In 5? In 6? In 9? In 12?

15. How many fourths are there in 1 ? How many fourths
of 1 in 2? In 4? In 6? In 10? In 12?

OF NUMBERS.

16. How many fifths are there in 1 ? How many fifths of

1 are there in 2 ? In 3 ? In 6 ? In 1 ? In 11 ? In 12 ?

17. How many sixths are there in 2 and one-sixth ? In 3
and 4 sixths ? In 5 and 2 sixths ? In 8 and 5 sixths ?

18. How many sevenths of 1 are there in 2 ? In 4 and 3
sevenths how many ? How many in 5 and 5 sevenths ? In fc
5 and 6 sevenths ?

19. How many eighths of 1 are there in 2 ? How many
in 2 and 3 eighths ? In 2 and 5 eighths ? In 2 and 7 eighths?
In 3 ? In 3 and 4 eighths ? In 9 ? In 9 and 5 eighths ? In

10 ? In 10 and 7 eighths ?

20. How many twelfths of 1 are there in 2 ? In 2 and 4
twelfths how many ? How many in 4 and 9 twelfths ? How
many in 5 and 10 twelfths? In 6 and 9 twelfths? In 10 and

11 twelfths?

21. What is the product of 12 multiplied by 3 and one
half, (which is written 3J) ?

ANALYSIS. Twelve is to be taken 3 and one-half times (Art
45). Twelve taken times is 6 ; and 12 taken three times is 36 ;
therefore, 12 taken ty times is 42.

22. What is the product of 10 multiplied by 5J ?

23. What is the product of 12 multiplied by 3J ?

24. What is the product of 8 multiplied by 4 J ?

25. What will 9 barrels of sugar cost at 2 dollars a
barrel?

ANALYSIS. Nine barrels of sugar will cost nine times as
much as 1 barrel. If one barrel of sugar costs 2f dollars, 9
barrels will cost 9 times 2f dollars, which are 24 dollars. For,

2 thirds taken 9 times gives 18 thirds, which are equal to 6 ; then
9 times 2 are 18, and 6 added gives 24 dollars.

26. What will 6 yards of cloth cost at 5 dollars a yard ?

27. What will 12 sheep cost at.4J dollars apiece ?

28. What will 10 yards of calico cost at 9f cents a yard ?

29. What will 8 yards of broadcloth cost at 7-J dollars
a yard ? / -

30. What will 9 tons of hay cost at 9^ dollars a ton ?

31. How many times is 2J contained in 10 ?

ANALYSIS. Two and one-half is equal to 5 halves ; and 10 is
equal to 20 halves ; then 5 halves is contained in 20 halves 4
times: hence.

LONG DIVISION.

In all similar questions change the divisor and dividend
to the same fractional unit. (Art. 144).

32. How many yards of cloth, at 3J dollars a yard, can
you buy for 14 dollars ? how many for 21 dollars ?

33. If oranges are 3| cents apiece, how many can you buy
for 20 cents ? ' , :

34. If 1 yard of nbbon costs 2f cents, how many yards
can you buy for 12 cents ?

35. If 1 yard 'of broadcloth costs 3| dollars, how many-
yards can be bought for 33 dollars ?

36. If 1 pound of sugar costs 4J cents, how many pounds
can be bought for 36 cents ? /

37. How many times is 5J contained in 44 ?

38. How many times is 2| contained in 24 ?

39. How many lemons, at 2| cents apiece, can you buy
for 32 cents ?

40. How many yards of ribbon, at 1^ cents a yard, can
you buy for 12 cents ?

LONG DIVISION.

65. LONG DIVISION is the operation of finding the quotient
of one number divided by another, and embraces the case of
Short Division, treated in Art. 63.

1. Let it be required to divide 7059 by 13.

ANALYSIS. The divisor, 13, is not OPERATION.

contained in 7 thousands ; therefore, . ^

there are no thousands in the quotient. & ^ J J& ' m -3

We then consider the to be annex- J2 s g '3 a g *3

ed to the 7, making 70 hundreds, and EH W EH P W EH P

call this a partial dividend. 13)70 5 9(5 43

The divisor, 13, is contained in 70 65

hundreds, 5 hundreds times and some- ^ -
thing over. To find how much over,

multiply 13 by 5 hundreds and subtract 5 2

the product 65 from 70, and there will r 3 g

remain 5 hundreds, to which bring q

down the 5 tens and consider the 55 _r__
tens a new partial dividend.

65. What is long division ? Does it embrace the case of short divi-
sion ? What is u partial dividend ?

SIMPLE NUMBERS. 65

Then, 13 is contained in 55 tens, 4 tens times and something
over. Multiply 13 by 4 tens and subtract the product, 52, from
55, and to the remainder 3 tens bring down the 9 units, and con-
sider the 39 units a new partial dividend.

Then, 13 is contained in 39, 3 times. Multiply 13 by 3, and
subtract the product 39 from 39, and we find that nothing remains.

66. PROOF. Each product that has arisen from multiply-
ing the divisor by a figure of the quotient, is a partial product,
and the sum of these products is the product of the divisor
and quotient (Art. 51, XOTE). Each product has been taken,
separately, from the dividend, and nothing remains. But,
taking each product away in succession, leaves the same re-
mainder as would be left if their sum were taken away at
once. Hence, the number 543, when multiplied by the
divisor, gives a product equal to the dividend : therefore, 543
is the quotient (Art. 61) : hence, to prove division,

Multiply the divisor by the quotient and add in the remain-
der, if any. If the work is right, the result will be the same
as the dividend.

67. Let it be required to divide 2756 by 26.

We first say, 26 in 27 once, and place 1 in OPERATION.

the quotient. Multiplying by 1, subtracting, 26)2756(106

and bringing down the 5, we have 15 for the 26

first partial dividend. We then say, 26 in 15, "^

times, and place the in the quotient. We 156

then bring down the 6, and find that the divisor 156
is contained in 156, 6 times.

If anyone of the partial dividends is less than the divisor, write
for the quotient figure, and then bring down the next figure,
forming a new partial dividend.

Hence, for Long Division, we have the following
KULE. I. Write the divisor on the left of the dividend.

II. Note the fewest figures of the dividend, at the left,
that will contain the divisor, and set the quotient figure at
the right.

66. What is a partial product ? What is the sum of all the partial
products equal to ? How do you prove division ?

67. What do you do if any partial dividend is less than the divisor ?
What is the rule for long division ?

66

LONG DIVISION.

III. Multiply the divisor by the quotient figure, subtract
the product from the first partial dividend, and to the re-
mainder annex the next figure of the dividend, forming a
second partial dividend.

TV. find in the same manner the second and succeeding
figures of the quotient, till all the figures of the dividend
are brought down.

NOTE 1. There arc five operations in Long Division. 1st. To
write down the numbers : 2d. Divide, or find how many times :
3d. Multiply : 4th. Subtract : 5th. Bring down, to form the partial
uividends.

2. The product of a quotient figure by the divisor must never
be larger than the corresponding partial dividend : if it is, the
quotient figure is too large and must be diminished.

3. When any one of the remainders is greater than the divisor,
the quotient figure is too small and must be increased.

4. The unit of any quotient figure is the same as that of the
partial dividend from which it is obtained. The pupil should
always name the unit of every quotient figure.

EXAMPLES.

1. Divide 7574 by 54.

OPERATION.

54)7574/140

54

2. Divide 67289 by 261.

OPERATION.

261)67289(257
522

1508
1305

2039
1827
212 Remainder,

PROOF.

140 Quotient.
54 Divisor.

560
700
7560

14 Remainder.
7574 Dividend.

PROOF.

261 Divisor.
257 Quotient.

1827
1305
522

212 Remainder.
-#7289 Dividend.

SIMPLE NUMBERS. 67
3. Divide 119836687 by 39407.

OPERATION. PROOF.

39407)119836687(3041 39407 Divisor.

118221 3041 Quotient.

161568 39407

157628 157628

39407 . 118221

39407 119836687 Dividend.

4. Divide 7210473 by 37.

5. Divide 147735 by 45.

6. Divide 937387 by 54.

7. Divide 145260 by 108

8. Divide 79165238 by 238.

9. Divide 62015735 by 78.

10. Divide 14420946 by 74.

11. Divide 295470 by 90.

12. Divide 1874774 by 162.

13. Divide 435780 by 216.

14. Divide 203812983 by 5049.

15. Divide 20195411808 by 3012.

16. Divide 74855092410 by 949998.

17. Divide 47254149 by 4674.

18. Divide 119184669 by 38473.

19. Divide 280208122081 by 912314.

20. Divide 293839455936 by 8405.

21. Divide 4637064283 by 57606.

22. Divide 352107193214 by 210472.

23. Divide 558001172606176724 by 2708630425.

24. Divide 1714347149347 by 57143.

25. Divide 6754371495671594 by 678957

26. Divide 71900715708 by 37149. 1

27. Divide 571943007145 by 37149.

28. Divide 671493471549375 by 47143.

29. Divide 571943007645 by 37149.

30. Divide 171493715947143 by 57007.

31. Divide 121932631112635269 by 987654321.

NOTES. 1. How many operations are there in long division ? Name
them.

2. If a partial product is greater than the partial dividend, what does
it indicate ? What do you do ?

3. What do you do when any one of the remainders is greater than
the divisor ?

4. What is the unit of any figure of the quotient ? When the divisor
is contained in simple units, what will be the unit of the quotient figure ?
When it is contained in tens, what will be the unit of the quotient
figure ? When it is contained in hundreds ? In thousands ?

68 LONG DIVISION.

08. PRINCIPLES RESULTING FROM DIVISION.

NOTES. 1st. When the divisor is 1, the quotient will be equal
to the dividend.

2d. When the divisor is equal to the dividend, the quotient
' will be 1.

3d. "When the divisor is less than the dividend, the quotient
will be greater than 1. The quotient will be as many times
greater than 1, as the dividend is times greater than the divisor.

4th. When the divisor is greater than the dividend, the quotient
will be less than 1. The qaot'ent will be such a part of 1, as
the dividend is of the divisor.

PROOF OF MULTIPLICATION.

69. Division is the reverse of multiplication, and they
prove each other. The dividend, in division, corresponds to
the product in multiplication, and the divisor and quotient to
the multiplicand and multiplier, Avhich are factors of the pro-
duct : hence,

If the product of two numbers be divided by the multipli-
cand, the quotient will be the multiplier ; or, if it be divided
by the multiplier, the quotient will be the multiplicand.

EXAMPLES.

3679 Multiplicand 3679J1203033(327

327 -Multiplier. 11037

25753 9933

7358 7358

11037 25753

1203033 Product. 25753

2. The multiplicand is 61835720, and the product
8162315040 : what is the multiplier ?

3. The multiplier is 270000 ; now if the product be
1315170000000, what will be the multiplicand?

4. The product is 68959488, the multiplier 96 : what is
the multiplicand ?

5. The multiplier is 1440, the product 10264849920 :
what is the multiplicand ?

6. The product is 6242102428164, the multiplicand
6795634 : what is the multiplier ?

CONTRACTIONS IN MULTIPLICATION. G9

CONTRACTIONS IN MULTIPLICATION.

70. To multiply by 25.
1. Multiply 275 by 25.'

ANALYSIS. If we annex two ciphers to the mul- OPERATION-.

tiplicand, we multiply it by 100 (Art. 55): this 4)27500

product is 4 times too great ; for the multiplier is /,, 7 -
but one-fourth of 100 ; hence, to multiply by 25,

Annex two ciphers to the multiplicand and divide the
result by 4.

EXAMPLES.

1. Multiply 127 by 25.

2. Multiply 4269 by 25.

3. Multiply 87504 by 25.

4. Multiply 7-04963 by 25.

71. To multiply by 12 J
1. Multiply 326 by m.

ANALYSIS. Since 12^ is one-eighth of 100, OPERATION.

Annex two ciphers to the multiplicand and di- 8)32600

vide the result by 8. 4.075

EXAMPLES.

1. Multiply 284 by 12J.

2. Multiply 376 by 121.

3. Multiply 4740 by 12.

4. Multiply 70424 by 12

72. To multiply by 33*
1. Multiply 675 by 33J.

ANALYSIS. Annexing two ciphers to the mul- OPERATION.
tiplicand, multiplies it by 100: but the multiplier 3)67500
is but one-third of 100 : hence,

Annex two ciphers and divide the result ly 3.

EXAMPLES.

1. Multiply 889626 by 33J.
2 Multiply 740362 by 33J.

3. Multiply 5337756 by 33J.

4. Multiply 2221086 by 33i.

68. When the divisor is 1, what is the quotient? Wheii the divisor
is equal to the dividend, what is the quotient ? When the divisor is less
than the dividend, how does the quotient compare with 1 ? When the di-
visor is greater than the dividend, how doas the quotient compare with 1 ?

09. If a product be divided by one of the factors, what is the quotient ?

70

CONTRACTIONS IN MULTIPLICATION.

73. To multiply by 125.
1. Multiply 375 by 125.

ANALYSIS. Annexing three ciphers to the mul-
tiplicand, multiplies it by 1000 : but 125 is but
one-eighth of one thousand : hence,

Annex three ciphers and divide the result by 8.

OPERATION.

8)375000

46875

EXAMPLES.

1. Multiply 29632 by 125.

2. Multiply 8796704 by 125.

3. Multiply 970406 by 125.

4. Multiply 704294 by 125.

74. By reversing the last four processes, we have the four
folio whig rules :

1. To divide any number by 25 ;

Multiply the number by 4, and divide the product by 100.

2. To divide any number by 12.

Multiply the number by 8, and divide the product by 100.

3. To divide any number by 33 \ :

Multiply the number by 3, and divide the product by 100.

4. To divide any number by 125 :

Multiply by 8, and divide the product by 1000.

EXAMPLES.

1.

2.
3.
4.
6.

6.

7.
8.

Divide
Divide
Divide
Divide
Divide
Divide
Divide
Divide

3175 by 25.
106725 by 25.
2187600 by 25.
2426225 by 25.
1762405 by 25.
4075 by 12J.
3550 bv 12J.
59262\$ by 12J.

9.
10.
11.
12.
,13.
14
15.
16.

Divide
Divide
Divide
Divide
Divide
Divide
Divide
Divide

880300 by 12i.
22500 by 33J.
654200 by 33J.
7925200 by 33.
4036200 by 33f .
93750 by 125.
3007875 by 125.
6758625 by 125.

70. What is the rule for multiplying by 25 ?

71. What is the rule for multiplying by 12* ?

72. What is the rule for multiplying by 88* ?

73. What is the rule for multiplying by 135?

CONTRACTIONS IN DIVISION. 71

CONTRACTIONS IN DIVISION.

75. Contractions in Division are short methods of finding
the quotient, when the divisors are composite numbers.

CASE I.

76. When the divisor is a composite number.

1. Let it be required to divide 1407 dollars equally among
2i rnen. Here the factors of the divisor are 7 and 3.

ANALYSIS. Let the 1407 dollars

be first divided into 7 equal piles. OPERATION.

Each pile will contain 201 dollars. 7)1407

Let each pile be now divided into 3 , .... . , , , .

equal park Each part will contain S) 201 lst quotient.

67 dollars, and the number of parts G7 quotient sought,
will bo 21 : hence the following

RULE. Divide the dividend by one of the factors of the
divisor ; tlien divide the quotient, thus arising, by a second
factor, and so on, till every factor has been used as a divisor :
the last Quotient will be the answer.

EXAMPLES.

Divide the following nnmbers by the factors ;

1. 1260 by 12 3x4.

2. 18576 by 48=4 x 12.

3. 9576 by 72 = 9x8.

4. 19296 by %=12x8.

5. 55728 by4x 9x4=14 4.

6. 92880 by 2x2x3x2x2.

7. 57888 by4x2x2x2.

8. 154368 by 3 x 2 x fc.

NOTE. It often happens that there are remainders after some

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