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48 and these, joined to their respective whole numbers,

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give the following expressions, viz.

OPERATION.

Cwt.

192

Cwt. 193 202013 223 2248

=

Ans. 6287 cwt.

By adding together all the 60ths, viz. 45, 12 and 40, we have 7-17; then writing the 3 down, and carrying the whole number, 1, to the amount of the column of whole numbers, makes 62, which, joined with 3, makes 6237, Ans.

2. How much is § of †, and }, added together? } of}=}; and, reduced to a common denoininator, give 24 and

then

18, which, added together as before, give

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14, Ans.

From these illustrations we derive the following

RULE.

Q. How do you prepare fractions to add them?

A. Reduce compound fractions to simple ones, then all the fractions to a common or least common denominator.

Q. How do you proceed to add?

A. Add their numerators.

More Exercises for the Slate.

3. What is the amount of 16 yards, 17 yds. and 34 yards? 4. 373.

4. Add together and 4.

5. Add together, & and 11. 6. Add together, and 1. 7. Add together 14 and 158.

A. 1.

A. 233.

A. 118.

A. 307.

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2. Harry had of a dollar, and Rufus ; what part of a dollar has Rufus more than Harry? How much does from leave?

3. How much does 18 from 1 leave?

4. How much does from

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leave?

leave?

leave?

6. How much does 15% from 7

From the foregoing examples, it appears that fractions may be subtracted by subtracting their numerators, as well as added, and for the same reason.

1. Bought 20 yards of cloth, and sold 15 yards; how much remained unsoid?

OPERATION.
and, reduced to a com-
mon denominator, make
and 1; then,

203=20

15=15

4 yards, Ans.

In this example, we cannot take 12 from 12, but, by borrowing 1 (unit), which is 1, we can proceed thus, and 1 are, from which taking

, or 9 parts from 20 parts, leaves 11 parts, that is, 12 then, carrying 1 (unit, for that which I borrowed) to 15.

makes 16; then, 16 from 20 leaves 4, which, joined with 1,

makes 41, Ans.

2. From taket.

and t, reduced to a common denomi eator, give 13 and fo; then, f from 13 leaves 36, Ans.

From these illustrations we derive the following

Q. What is the rule ?

RULE.

A. Prepare the fractions as in addition, then the difference of the numerators written over the denominator, will give the difference required.

More Exercises for the Slate

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XLVI. TO DIVIDE A WHOLE NUMBER BY
FRACTION.

Lest you may be surprised, sometimes, to find in the fol-' lowing examples a quotient very considerably larger than the dividend, it may here be remarked, by way of illustration, that 4 18 contained in 12, 3 times, 2 in 12, 6 times, 1 in 12, 12 times; and a half (1) is evidently contained twice as many times as 1 whole that is, 24 times. Hence, when the divisor is 1 (unit,) the quotient will be the same as the dividend; when the divisor is more than 1 (unit), the quo tient will be less than the dividend; and when the divisor is less than 1 (unit), the quotient will be more than the dividend.

1. At of a dollar a yard, how many yards of cloth can you buy for 6 dollars? 1 dollar is †, and 6 dollars are 6 times, that is, then,, or 3 parts, are contained in 24, or 24 parts, as many times as 3 is contained in 24, that is, 8 times. A. 8 yards.

In the foregoing example the 6 was first brought into 4ths, or quarters, by multiplying it by the denominator of the divisor, thereby reducing it to parts of equal size with the divisor; hence we derive the following

RULE.

Q. How do you proceed to divide a whole number by a fraction! A. Multiply the dividend by the denominator of the dividing fraction, and divide the product by the numerator.

Exercises for the Slate.

2. At of a dollar a bushel, how many bushels of rye can I have for 80 dollars?

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3. If a family consume of a quarter of flour in one week, weeks will 48 quarters last the same family?

how many

A. 128 weeks. 4. If you borrow of your neighbor of a bushel of meal at one time, how many times would it take you to borrow 96 bushels? A. 960 times.

5. How many yards of cloth, at of a dollar a yard, may be bought for 200 dollars? 4. 1000 yards.

6. How many times is 26 contained in 720? A. 140.

7. How many times is 8 contained in 300?

an improper fraction. A. 36.

8. Divide 620 by 87.

9. Divide 84 by 28.

10. Divide 92 by 44. 11. Divide 100 by 2}.

12. Divide 86 by 15%.

13. How many rods in 220 yards?

14. How many sq. rods in 1210 sq. yards? 15. How many barrels in 1260 gallons?

IXLVII.

Reduce 8 to

A. 75%.

A. 160.

A. 204.

A. 36.

A. 5.
A. 40 rods.

A. 40 sq. rods.
A. 40 barrels.

TO DIVIDE ONE FRACTION BY ANOTHER.

1. At of a cent an apple, how many apples may be bought for of a cent? How many times

many times in?

in? How

2. William gave of a dollar for one orange; how many oranges, at that rate, can he buy for § of a dollar? How many for of a dollar? For ? For 24? For 21? For $?

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Then,

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times as 4 is contained in 9,21.

Into the denominator of the dividend, and the denominator of the divisor into the numerator of the dividend. But it will be found to be more convenient, in practice, to invert the divisor, then multiply the upper terms together for a numerator, and the lower terms for a denominator; thus, taking the last example,

and, by inverting the divisor, become and ; then, +4=-21 yards, as be

fore, Ans.

PROOF., the quotient, multiplied by, the divisor, thus,, gives 2-2, the

divisor.

From these illustrations we derive the following

RULE.

Q. How do you proceed to divide one fraction by another t A. I invert the divisor, then multiply the upper terms together for a new numerator, and the lower for a new denominator.

Note.-Mixed numbers must be reduced to improper fractions, and compound to simple terms.

PROOF. It would be well for the pupil to prove each result, as in Simple Multiplication, by multiplying the divisor and quotient together, to obtain the dividend.

More Exercises for the Slate.

2. At of a dollar a peck, how many pecks of salt may be bought for of a dollar?

3. Divide by
4. Divide by.

A. 43 pecks.

A.

=2.

A. 42=217.

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