Multiplying and Dividing Multiplying and Dividing Fractions Fractions

Section 4.3

Multiplying FractionsMultiplying Fractions

34

12 of is

38

00 1134

38

68

The word “of” means The word “of” means multiplicationmultiplication and “is” means and “is” means equal toequal to..

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34

12 ofof isis

38

meansmeans

1 3 32 4 8

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Multiplying Two FractionsMultiplying Two Fractions

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

a c a c

b d b d

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

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ExamplesExamples

15

14

3 5 3 5

2 7 2 7

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

3 2 3 2

4 5 2 2 5

3

10

3 2

4 5 3

102

1

or

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3 8

4 5 x

x

ExamplesExamples

3 4 2

4 5

x

x

3 8

4 5 x

x

1

2

6

5

6

5 or

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

Helpful Hint

,8

5xwe assume that the variable we assume that the variable is not 0.is not 0.

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Evaluating Expressions with Evaluating Expressions with Fractional BasesFractional Bases

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

23

3FHIK 23

23

23

2 2 23 3 3

8

27

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Reciprocal of a FractionReciprocal of a Fraction

a

b

b

a

becausebecause

1a b a b ab

b a b a ab

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

is

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Dividing Two FractionsDividing Two Fractions

If If bb, , cc, and , and dd are not 0, then are not 0, then

a c a d a d

b d b c b c

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

3 2 3 7 21

5 7 5 2 1010

Martin-Gay, Prealgebra, 5ed

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

Helpful Hint

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

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Helpful Hint

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

12

23

12

32

34

Do not try to divide out these two 2s.

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Multiplying and Dividing with Multiplying and Dividing with Fractional Replacement ValuesFractional 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

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