1. 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. 5.4

2. 5.4 - 2 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 1 Divide fractions.

3. 5.4 - 3 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definition Reciprocals: Two numbers whose product is 1.

4. 5.4 - 4 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 1 Find the reciprocal. a.b. c. d. e.

5. 5.4 - 5 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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.

6. 5.4 - 6 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 2 Divide. Write the quotient in lowest terms. a. b.

7. 5.4 - 7 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Definition Complex fraction: A fractional expression with a fraction in the numerator and/or denominator. For example…is a complex fraction equivalent to…

8. 5.4 - 8 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 2 Divide mixed numbers.

9. 5.4 - 9 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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.

10. 5.4 - 10 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 3 Estimate, then find the actual quotient expressed as a mixed number in simplest form. a.b.

11. 5.4 - 11 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 3 Divide rational expressions.

12. 5.4 - 12 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 5 Divide. Write the quotient in lowest terms.

13. 5.4 - 13 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 4 Find the square root of a fraction.

14. 5.4 - 14 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley To find the square root of a fraction, try the following: Procedure Find the square root of the numerator and denominator separately, then simplify or Simplify the fraction, then find the square root.

15. 5.4 - 15 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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.

16. 5.4 - 16 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 6 Simplify. a. b.

17. 5.4 - 17 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 5 Solve equations involving fractions.

18. 5.4 - 18 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example 8 Solve and check.

19. 5.4 - 19 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective 6 Solve applications involving division of fractions.

20. 5.4 - 20 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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

21. 5.4 - 21 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 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?