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4.3

Multiplying and Dividing Fractions

Martin-Gay, Prealgebra, 6ed 22

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Multiplying Fractions

34

12 of is

38

00 1134

38

68

The word “of” means multiplicationThe word “of” means multiplication and “is” means equal to.and “is” means equal to.

Martin-Gay, Prealgebra, 6ed 33

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34

12 ofof isis

38

meansmeans

1 3 32 4 8

Multiplying Fractions

Martin-Gay, Prealgebra, 6ed 44

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Multiplying Two Fractions

If If aa, , bb, , cc, and , and dd are numbers and are numbers and bb and and dd are not 0, are not 0, thenthen

a c a c

b d b d

In other words, to multiply two fractions, multiply the In other words, to multiply two fractions, multiply the numerators and multiply the denominators.numerators and multiply the denominators.

Martin-Gay, Prealgebra, 6ed 55

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Examples

15

14

3 5 3 5

2 7 2 7

If the numerators have common factors with the If the numerators have common factors with the denominators, divide out common factors before denominators, divide out common factors before multiplying.multiplying.

3 2 3 2

4 5 2 2 5

3

10 3 2

4 53

102

1

or

Martin-Gay, Prealgebra, 6ed 66

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3 8

4 5

x

x

Examples

3 4 2

4 5

x

x 3 8

4 5

x

x

1

2

6

5

6

5or

Martin-Gay, Prealgebra, 6ed 77

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Recall that when the denominator of a fraction contains a variable, such as

,85x

we assume that the variable is not 0.

Helpful Hint

Martin-Gay, Prealgebra, 6ed 88

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Expressions with Fractional Bases

The base of an exponential expression can also be a fraction.

23

3FHIK 23

23

23

2 2 23 3 3

827

Martin-Gay, Prealgebra, 6ed 99

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Reciprocal of a Fraction

a

b

b

a

becausebecause

1a b a b ab

b a b a ab

Two numbers are reciprocals of each other if their product is 1. The reciprocal of the fraction

is

Martin-Gay, Prealgebra, 6ed 1010

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Dividing Two Fractions

If b, c, and d are not 0, then

a c a d a d

b d b c b c

In other words, to divide fractions, multiply the first In other words, to divide fractions, multiply the first fraction by the reciprocal of the second fraction.fraction by the reciprocal of the second fraction.

3 2 3 7 21

5 7 5 2 10

Martin-Gay, Prealgebra, 6ed 1111

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Every number has a reciprocal except 0. The number 0 has no reciprocal. Why?

There is no number that when multiplied by 0 gives the result 1.

Helpful Hint

Martin-Gay, Prealgebra, 6ed 1212

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When dividing by a fraction, do not look for common factors to divide out until you rewrite the division as multiplication.

12

23

12

32

34

Do not try to divide out these two 2s.

Helpful Hint

Martin-Gay, Prealgebra, 6ed 1313

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Fractional Replacement Values

x y

56

25

Replace x with and y with .

If x = and y = , evaluate . 56

25

x y

56

25

56

52

2512