Objectives

Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Dividing Fractions, Mixed Numbers, and Rational Expressions

1. Divide fractions.2. Divide mixed numbers.3. Divide rational expressions.4. Find the square root of a fraction.5. Solve equations involving fractions.6. Solve applications involving division of

fractions.

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Objective 1 Divide fractions.

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Definition Reciprocals: Two numbers whose product is 1.

1 1 444 4 1

1

1

1

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Example 1 Find the reciprocal.

a. 34

b. 15

c. 6 d. 57

e. 0

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To divide fractions: Procedure

1. Change the operation symbol from division to multiplication and change the divisor to its reciprocal.

2. Divide out any numerator factor with any like denominator factor.

3. Multiply the remaining factors (numerator by numerator and denominator by denominator).

4. Simplify as needed.

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Example 2 Divide. Write the quotient in lowest terms.

a. 5 38 4

b. 4 129

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Definition Complex fraction: A fractional expression with a fraction in the numerator and/or denominator.

For example…5834

is a complex fraction equivalent to… 5 3

8 4

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Objective 2 Divide mixed numbers.

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To divide mixed numbers:Procedure

1. Write the mixed numbers as improper fractions.

2. Write the division statement as an equivalent multiplication statement using the reciprocal of the divisor.

3. Divide out any numerator factor with any like denominator factor.

4. Multiply the remaining factors (numerator by numerator and denominator by denominator).

5. Simplify as needed.

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Example 3 Estimate, then find the actual quotient expressed as a mixed number in simplest form.

a. 2 18 25 4

b.

357133

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Objective 3 Divide rational expressions.

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Example 5 Divide. Write the quotient in lowest terms.

3

4 26 1535 14

a b ac c

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Objective 4 Find the square root of a fraction.

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To find the square root of a fraction, try the following:Procedure

Find the square root of the numerator and denominator separately, then simplifyorSimplify the fraction, then find the square root.

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You can find the square root of a fraction by finding the square root of numerator and denominator.

You can find the square root of a fraction by simplifying first to see if the simplified number is a perfect square.

916

34

because 34

2

34g34

9

16

6 1 1 124 4 24

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Example 6 Simplify.

a. 2536

b. 455

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Objective 5 Solve equations involving fractions.

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Example 8 Solve and check.

3 524 8

x x32

143

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Objective 6 Solve applications involving division of fractions.

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Whenever we are given a total amount represented by either the size of the parts or the number of parts, we can write an equation with an unknown factor using the following formula.

size of each part ● number of parts = whole amount

If you know what you are doing…go directly to the related division… size of each part = whole amount ÷ number of parts

or

number of parts = whole amount ÷ size of each part

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Example 9 Solve.

a. A board is 35 ¾ inches long. The board is to be cut into pieces that are each 6 ½ inches long. How many pieces can be cut?