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RULE FOR COMPOUND DIVISION.

If the divisor does not exceed 12, divide each order sepa. rately, beginning with the highest, remembering to make the quotient figure of the same order as the dividend.

Whenever there is a remainder, change it and add it to the next lower order and divide as before.

If the divisor exceeds 12, either resolve it into factors and divide first by one and then by the other, or proceed after the manner of long Division. T. cwt. 16.

dr. Divide 29 13

25 12 13 by 6. 16.

pwt. grs. Divide 7 10 15 2 by 5.

yds. qrs. Divide. 76 3 2 by 4 deg.

fur. pol. ft. in. bar. Divide 97 55 7 35 66 4 5 2 1

oz.

66

oz.

na.

m.

by 7.

£ Divide 25

S. 16

d. 10

qrs.
3 by 9.

DIVISION WHERE ONLY THE DIVISOR IS A FRACTION.

If we have 3 apples, how many į in the whole ? Ans. In one apple there are two halves, and in three apples there are three times as many, or six halves.

If we have 6 dollars, how many { in the whole ? Ans. In one dollar there are three thirds, and in six dollars there are six times as many, or eighteen thirds ?

If we have 9 apples how many 1?
In 8 apples how many ; ?
In 12 apples how many {!
In 7 apples how many is?
It thus appears that when we divide by a fraction (un.

What is the rule for compound division when the divisor does not exceed 12? What is the rule, if it exceed 12 ?

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or 12.

less it be an improper fraction) the quotient is larger than the dividend.

Thus 12 divided by 1 is 48, for there are 48 one fourths in 12 units.

Again 9 divided by { is 27, for there are 27 one thirds in 9 units.

How many į in 8?
How many ă in 12 ?

Divide 7 by 4 Divide 6 byd. Divide 12 by į Divide 10 by } Divide 8 by $ Divide 11 by } Divide 12 by

Divide 9 by :
How many } in 8? How many in 7?

If you divide 8 by the answer is 24, for there are 24 one thirds in 8.

But if we are to divide 8 by there will be but half as many.

For there is but half as many two thirds as there are one thirds in a number. Therefore if 8 divided by } is 24, when divided by it is half as much,

How many in 3 ?

Ans. In 3 there are 18 one sixths and half as many two sixths, or 9.

How many in 12 ?
How many š in 2?
How many 4 in 4 ?
How many i in 6 ?
How many f in 3?

Divide 4 by ả Divide 5 by : Divide 3 by Divide 8 by s Divide 2 by Divide 7 by a Divide 5 by to Divide 12 by .

If you have 12 yards of long lawn and wish to cut a number of handkerchiefs of of a yard each, how many can you make from the whole piece ?

If you have 4 oranges and wish to give of an orange to your mates, to how many could you give them?

If you have 4 pounds of rice to distribute to the poor, and are to give of a pound to each person, to how many persons can you give ?

If a reservoir is filled by a spout in of an hour, how many

times would the cistern be filled in 9 hours? If a pound of raisins can be bought for of a dollar, how many pounds can you buy for 4 dollars ?

If of a barrel of flour will last a family one week, how loug will 6 barrels last ?

If a cow eats 4 of a ton of hay a month, how long would 4 tons last her?

If of a barrel of flour last a family one week, how long will 10 barrels last?

It is seen by the preceding examples, that when a num. ber is to be divided by a fraction, it is multiplied by its denominator, and divided by its numerator.

Thus if we are to divide 2 by we multiply by the de. nominator 4 to change 2 into fourths and then divided by the 3 to find how many three fourths there are.

Divide 3 by ..

Why do you multiply by the denominator? Why do you divide by the numerator?

RULE FOR FRACTIONAL DIVISION WHERE ONLY THE DI. VISOR IS A FRACTION.

Multiply the dividend by the denominator, and divide the product by the numerator.

Divide

66

8

66

EXAMPLES FOR THE SLATE.
23 by

4 Divide 364 by
25
12

24
32

21
12
325

486

16
75

4 2
9479
24

381

18

59 342 16

542

34

T15 681 15

. 232 42

65 3292 73

4285

13 516

10

9

80

84

DIVISION WHERE THE DIVIDEND ONLY IS A FRACTION. When the dividend only is a fraction, and we divide it How is a number divided by a fraction? Why do we multiply 2 by the denominator 4? Why do we divide by the numerator 3? What is the rule for fractional division where only the divisor is a fraction ?

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by a whole number, we are to find how many parts of a time, a certain number is contained in certain parts of a unit.

Thus if we divide į by 2, we know that does not con. tain 2 units once, but we can find what part of one time the contains the 2.

If į is divided by 1 unit, we find that it contains it, not once, but of once. It can contain two units but half as many times as one unit. Therefore { contains 1 one half a time, and it contains 2 just half as often, or of a time.

divided by 2 then is a: If is to be divided by 3, we reason in the same way. į contains 1, i a time. It contains 3 only a third as often. ļof į is į, and there. fore contains 3, 1 of a time.

Again, if is to be divided by 4, we reason thus : If i contains 1, } a time, it contains 4 only į as often. of į is š. Then contains 4 not one time, but I of one time.

Again let } be divided by 4, and we reason thus :

If is divided by 1, it contains it not 1 time, but 1 of one time. But it can contain 4 only $ as often. & of 1 is 'a:

The dividend } contains the divisor 4, not one time, but
I of one time.
Divide }, }, , , , , to, each by one.

Proceed thus : { contains 1 not one time, but } of one time. d contains 1 not one time, but of one time, &c.

Divide
} by 2 | Divide

i by 3
4

1

5
6
'7

is

7 ito

9 How often is 2 contained in ? ?

(Ans.) As I would be contained of a time, 2 is contained half as often, or is of one time.

How often is 3 contained in ??
How often is 5 contained in š?
How often is 6 contained in 1 ?

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8

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When we divide a fraction by a whole number what do we find ?

How often is 7 contained in jo ?
How often is 8 contained in i ?
How often is 9 contained in is

?
How often is 10 contained in } ?
How often is 11 contained in į?
How often is 12 contained in < ?
How often is 9 contained in ı ?
How often is 8 contained in ?
How often is 9 contained in į?

After finding how often 4 is contained in one part, we find by multiplying, how often it is contained in a given number of parts. For instance, 4 is contained in one fifth ab of one time. In two fifths it would be contained twice as often, or go of one time.

Again, let be divided by 4, and we reason thus : 4 is contained in one seventh one fourteenth of one time, in 2 sevenths it is contained twice as often, or two fourteenths of one time.

How often is 3. contained in 4 ?

(Ans.) 3 is contained in one eighteenth of one time. In dit is contained 4 times as often, or four eighteenths of one time.

How often is 4 contained in < ?
How often is 5 contained in g?
How often is 6 contained in ?
Divide to by 3. Divide by 5.
Divide f by 6. Divide by 7.
Divide is by 8. Divide by 9.
Divide by 11. Divide $ by 8.
How many times is 6 contained in ?
How many times is 4 contained in a ?
How many times is 7 contained in ?
How many times is 8 contained in ?
How many times is 9 contained in

? In all the above cases it will be observed that the an. swer is obtained by simply multiplying the denominator of the fraction by the divisor.

Thus is divided by 4 thus. 4 is contained in of one time, and in s twice as often, or i of one time. It

What method can always be taken in dividing a fraction by a whole number?

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