1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 7.3 Complex Fractions

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objective o Simplify complex fractions.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Simplifying Complex Fractions (First Method) To Simplify Complex Fractions (First Method) 1.Simplify the numerator so that it is a single rational expression. 2.Simplify the denominator so that it is a single rational expression. 3.Divide the numerator by the denominator and reduce to lowest terms.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: First Method for Simplifying Complex Fractions Simplify the complex fraction To divide, multiply by the reciprocal of the denominator.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: First Method for Simplifying Complex Fractions Simplify the following complex fractions. Solution Combine the fractions in the numerator and in the denominator separately.

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: First Method for Simplifying Complex Fractions (cont.) To divide, multiply by the reciprocal of the denominator.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: First Method for Simplifying Complex Fractions (cont.) Solution Add the two fractions in the denominator.

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: First Method for Simplifying Complex Fractions (cont.) Multiply by the reciprocal of the denominator.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Simplifying Complex Fractions (Second Method) To Simplify Complex Fractions (Second Method) 1.Find the LCM of all the denominators in the numerator and denominator of the complex fraction. 2.Multiply both the numerator and denominator of the complex fraction by this LCM. 3.Simplify both the numerator and denominator and reduce to lowest terms.

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Second Method for Simplifying Complex Fractions Simplify the following complex fractions. Solution Multiply by x(x + 3), the LCM of {x, x+3}. This multiplication can be done because the net effect is that the fraction is multiplied by 1.

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Second Method for Simplifying Complex Fractions (cont.) Note that this matches the result found in Example 2a using Method 1.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Second Method for Simplifying Complex Fractions (cont.) Solution Multiply by xy, the LCM of {1, x, y}.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Second Method for Simplifying Complex Fractions (cont.)

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Simplifying Complex Algebraic Expressions Simplify the following expression. Solution In a complex algebraic expression such as the rules for order of operations indicate that the division is to be done first.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Simplifying Complex Algebraic Expressions (cont.)

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Simplify each of the following expressions.

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers