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21. What is for you. I of q, is it and”; is twice as much,

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22. What is the part of of į is biar and my is a

ас

a

That is, à

ас

by

2m

3 am

by

times as much, that is,


X. o 응
d

bd
Hence, to multiply one fraction by another, multiply the nume-
rators together for a new numerator, and the denominators together
for a new denominator.

Arith. Art. XVII. 2 a b

2 a 3 23. Multiply

Ans. 3 c

6 с т 3 ad 24. Multiply

4 b c

5 cén 12 ani

3 аа? 25. Multiply

by

2by 2 a' m 26. What is

of 5cd

3 m d 47 d

76m 27. What is

of

? 9 a

2 ac-bc 29. Multiply

by 3b +c

5 ab 2 am – 3 am 5 å m2 29. Multiply

4ac +2c

2 am 50

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13 b ry

8bf?

13 na

2 a

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by

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2 ac + 3 3ab — с 30. Multiply

by
5bc2d 5 ac 2 ad
2a-m +3 m

13ac 31. Multiply

by na ma

17 am +5 We have seen that a fraction may be divided by multiplying its denominator, because the parts are made smaller; on the contrary, a fraction may be multiplied by dividing its denominator, because the parts are made larger. Arith. Art. XVIII. If the denominator be divided by 2, the unit is divided into only one half as many parts ; consequently the parts must be twice as large as before. If the denominator be divided by 5, the unit is divided into only one fifth as many parts ; hence the parts must be five times as large as before, and if the same number of parts be used as at first, the value of the fraction will be five times as great and so on.

3a 32. Multiply

by 5. 20

4

3 a

Ans.

a

b.

a

33. Multiply

by

b c If we divide the denominator by b, the fraction becomes

in which a is divided into [ part as many parts ; hence the parts, and consequently the fraction is bitimes-as-large as before. 34. Multiply

by

3 a

2.C.

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8 a b

3 ac

7 m c.

by

a

40. Multiply

by 46. 4 a 6 - 400

17-4bc 41. Multiply

by 4a. 16 a' — 12 ab-4a

23 m - 13 42. Multiply

35 mcd- 7 mo c + 42 m* a ca

by 43. Multiply

5. Dividing the denominator by 5 it becomes ļ, or 3. Multiply o by

b. ī Dividing the denominator by b it becomes a 44. Multiply by 56 d. Ans. 3 ac = 3 ac. 56d

1 In factmultiplied by b is į = 1, and being a times

1 as much as

must give a product a times as large, or a

7 times 1, which is a.

Hence, if a fraction be multiplied by its denominator, the product will be the numerator.

7acm 45. Multiply

by 5bd. 5bd

or a.

3 ac

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49. Multiply

13 ab

17 a

by

17 a?.

by

50. Multiply
15 ac + 37bc

10 ab_2c.
10 ab2c

47 a m* +36-C 51. Multiply

by a 2 - 3 aam+b. a n-3 am + b Two ways have been shown to multiply fractions, and two ways to divide them. To multiply a fraction,

the numerator To divide a fraction,

multiply

the denominator. To divide a fraction,

the numerator.

divide To multiply a fraction,

the denominator. Arith. Art. XVIII.

Reducing Fractions to Lower Terms.

XVII. f both numerator and denominator be multiplied by the same number, the value of the fraction will not be altered.

Arith. Art. XIX. For multiplying the numerator multiplies the fraction, and multiplying the denominator divides it; hence it will be multiplied and the product divided by the multiplier, which reproduces the multiplicand.

In other words, signifies that a contains b a certain number of times, if a is as large or larger than b; or a part of one time, if b is larger than a. Now it is evident that 2 a will contain 2 b just as often, since both numbers are twice as large as before.

So dividing both numerator and denominator, both divides and multiplies by the same number. 2 x 3 6 7 X 3_21

3 x 6

36
2 X 5
10 7 x 5

35

5 x 6 56
5a

2 acd
6
26 56

2bcd
6 a b

36 x 2 a 9bc 36 x 30

a

2a

ac

bc

2 a 30

Hence, if a fraction contain the same factor both in the numerator and denominator, it may be rejected in both, that is, both may be divided by it. This is called reducing fractions to lower terms.

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15 ac 25 a? 6. Reduce

to its lowest terms. 5 a' bc + 55 a 6

27 mx 54 x 7. Reduce

to its lowest terms. 108 a x + 81 x 90 mm 8. Divide 35 a' b m® x3 by 7 aon mo x.

Write the divisor under the dividend in the form of a fraction, and reduce it to its lowest terms.

56 mir Ans.

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