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fractions, find the least common multiple of the denominators, for the common denominator, which, multiplied by each frac tion, will give the new numerator for said fraction.

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14. Reduce 14 and 13 to the least common denominator A. 1412, 131.

Fractions may be reduced to a common, and even to the least common denominator, by a method much shorter than either of the preceding, by multiplying both the terms of a fraction by any number, that will make its denominator like the other denominators, for a common denominator; or by di viding both the terms of a fraction by any numbers that wil make the denominators alike, for a common denominator This method oftentimes will be found a very convenient one in practice.

Reduce and to a common, nominator.

X2; then & and

2); then and

and to a least common,

de

common denominator, A.

least common denominator, A.

In this example both the terms of one fraction are multiplied, and both the terms of the other divided, by the same number, consequently, (¶ XXXVII.,) the value is not altered.

Reduce and to the least common denominator

.9.12, 1. Reduce and to the least common denominator.

500

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ADDITION OF FRACTIONS.

↑ XLIV. 1. A father gave money to his sons as follows. to William of a dollar, to Thomas, and to Rufus ; how much is the amount of the whole How much are †,†, and I, added together?

2. A mother divides a pie into 6 equal pieces, or parts, and

gives to her son, and to her daughter; how much did she give away in all? How much are and added together? 3. How much are § +3 +3 ?

4. How much are

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5. How much are 12 + 15 + 1T?

6. How much are 2%+2%+2%?

When fractions like the above have a common denominator expressing parts of a whole of the same size, cr value, it in plain, that their numerators, being like parts of the same whole, may be added as in whole numbers; but sometimes we shall meet with fractions, whose denominators are unlike, as, for example, to add and together. These we cannot add as they stand; but, by reducing their denominators to a common denominator, by ¶ XLIII., they make and, which, added together as before, make §, Ans.

1. Bought 3 loads of hay, the first weighing 194 cwt., the second 20 cwt. and the third 22 cwt.: what was the weight of the whole ?

£, t, &, reduced to a common denominator, are equal to ff, 18 and 8: these, joined to their respective whole numbers, give the following expressions, viz.

Cwt.

OPERATION.
Cwt.

192 = 1948

201=2013

223=2248

=

By adding together all the 60ths, viz. 45, 12 and 40, we have 87-187; then writing the down, and carrying the whole number, 1, to the amount of the column of whole numbers, makes 62, which, joined with 7, makes 6287, Ans

2. How much is

Ans. 6287 cwt. of, and }, added together? of }=}; then } and 3, reduced to a commor. denominator, give and, which, added together as before, give=154, Ans.

From these illustrations we derive the following

RULE.

I. 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.

II How do you proceed to add? A. Add their numerators

FRACTIONS.

More Exercises for the Sute.

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

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SUBTRACTION OF FRACTIONS.

¶ XLV. 1. William, having Thomas; how much had he left? ¡eave?

of an orange, gave to

How much does from

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

3. How much does 18 from 1 leave?

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6. How much does

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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 unsold?

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In this example, we cannot take

from, but, by borrowing 1 (unit), which is 2, we can proceed thus and are, from which taking, or 9 parts from 20 parts, leaves 11 parts, that is,

; then, carrying 1 (unit, for that which I borrowed) to 15, makes 16; then, 16 from 20 leaves 4, which, joined with, makes 411, Ans.

2. From tor, give

take.and &, reduced to a common denomina and; then, from 1 leaves 36, Ans.

From these illustrations we derive the following

RULE.

1. What is the rule? A. Prepare the fractions as in addition then, the difference of the numerators, written over the denom inator, will give the difference required.

More Exercises for the Slate.

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DIVISION OF FRACTIONS.

↑ XLVI. To divide a Whole Number by a Fraction.

Lest you may be surprised, sometimes, to find in the following examples a quotient very considerably larger than the dividend, it may here be remarked, by way of illustration, that 4 is contained in 12, 3 times, 2 in 12, 6 times, 1 in 12, 12 times; and a half (4) 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 quotient 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 dellars? 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.

I How do you proceed to divide a whole number by a frac tion? A. Multiply the dividend by the denominator of the dividing fraction, and divide the product by the numerator.

2. At

Exercises for the Slate.

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

OPERATION.

80 dividend.
16 denominator.

480
80

Numer. 5)1280

Quotient, 256 bushels, Ans.

3. If a family consume

In this example, we see more fully illustrated the fact that division is the opposite of multiplication; for, to multiply 80 by, we should multiply by the numer ator, and divide by the denominator, 1 XXXIX

of a quarter of flour in one week, now many weeks will 48 quarters last the same family?

A. 128 weeks.

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

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

6. How many times is 36 contained in 720? A. 140.

7. How many times is 83 contained in 300

improper fraction. A. 36.

Reduce 8} to an

8. Divide 620 by 8

A. 757.

9. Divide 84 by 198.

A. 160.

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12. Divide 86 by 157.

12. How many rods in 220 yards? A. 49 rods.

A. 51297.

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