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that is, mint

22. What is the part of jy? į or j is and times as much, that is,

That is, à 5 =

is a

S as

23. Multiply

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Jlence, to multiply one fraction by another, multiply the numerators together for a new numerator, and the denominators together for a new denominator.

Arith. Art. XVII. 2 a

2 al 23. Multiply 3 c

6 cm 3 a d

I am 7a2d m 24. Multiply

460

5 c n rofe ? m

347"360

2by',m2 26. What is

2 a' m

8bfilos? Elm 5cd

3 m d se radi 4.6%d 27. What is

7bm ? 28 itd 38 9 am

13 n 1 ling? 23. Multiply

2 a cab.C. a'c ? 4 10

5 ab is a fè & sabel 2 am – 3 mm 5am? 29. Multiply

7 ks 4ac+20 2 a m - 5072 round reeman

25. Multiply

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25 a fe2.o act llabeathadt XVI. Multiplication and Division of Fractions. B7

2 ac +

3 3 abcc89, ac tu 30. Multiply

5b6-2 de oy 50c-2ado 2602-13 am

2a — m + 3 mm 31. Multiply

13 ac 7 am

17 am C+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 denomi-
nator, 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 bc 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 num-
ber of parts be used as at first, the value of the fraction will be
five times as great, and so on.
- 32. Multiply Song by 6. Ans. e .

33. Multiply by b.
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 b times as farge as
before.
34. Multiply : by 26.9

17 ab 35. Multiply

32 c 36. Multiply

7 a m'. 42 am 37. Multiply

ab

25 moc 38. Multiply

by 6...?

16

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46. Sac.

omes

39. Multiply são by ab. I

3 ac 40. Multiply 4 a 6' — 460

are 41. Multiply

17-4bc 1601 - 19. D o by 40.17-4*C

-366

23 m- 13 42. Multiply

35 m2 c d = mic + 42 m ad 23m-13 by

7 ma come 43. Multiply by 5.

mal Dividing the denominator by 5 it becomes t, or 3.. Altiply

by b. Dividing the denominator by b it becomes a., or a. 44. Multiply bad by 5bd. Ans. Sąc = 3 ac.

In fact multiplied by ő is š = 1, and of being a times as much as , must give a product a times as large, or a, times 1, which is a.

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

45. Multiply · Tacm by 56 d. laem 46. Multiply

25

by 36c. 25

18+ 47. Multiply,

46 me in 46 m 48. Multiply 12 mo yo

bd n r. ! 2 7 dni

m /

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49. Multiply 13 ab— n by 170.13 a town

17 am 50. Multiply

15 ac + 37 bc he

3700 by 10 ab2c. 15 aet?) 10 ab2C

47 a m® +36-C by am - 3 am +0.47 51. Multiply

a. *? — 3 am to Two ways have been shown to multiply fractions, and two ways to divide them. To multiply a fraction,

S the numerator To divide a fraction, S

multiply 3

the denominator. To divide a fraction, ?

S the numerator.
To multiply a fraction, S

the denominator.
Arith. Art. XVIII.

Reducing Fractions to Lower Terms. XVII. If both numerator and denominator he 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, a signifies that a contains b a certain number of times, if a is as large or larger than b; or a part of ontime, 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 X3 _21 _ 3 xb _ 36 852 510 - 70 535 5 x D - 56° .a _ 20 - 5a _ac_2acd

b c 2 b c d
6 ab _ 36 x 2 a 2 a
966-36 X 3630

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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.

vam to its lowest terms. Ans.

15 b c AL 2. Reduce

12 a c
to its lowest terms. An

40 x

1. Reduce 9 am

16 ana to its lowes

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3. Reduce 20m to its lowest terms. Ans.

30 7 m 4. Reduce 32 6 m y to its lowest terms.

ice 16 borgi toit 5. Reduce 52 a bázia

to its lowest terms. .

13 a*b* 6. Reduce 15 a* c — 25 a?

to its lowest terms. 5 abc + 55 7. Reduce 27 mör- 54 zria

- to its lowest terms. · 108 a x + 81 x 90 m za 8. Divide 35 ao b m® 2. by 7 aon mo x.

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

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