1. Objectives Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Adding and Subtracting Fractions, Mixed Numbers, and Rational Expressions 1. Add and subtract fractions with the same denominator. 2. Add and subtract rational expressions with the same denominator. 3. Add and subtract fractions with different denominators. 4. Add and subtract rational expressions with different denominators 5.6

2. Objectives Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Adding and Subtracting Fractions, Mixed Numbers, and Rational Expressions 5. Add and subtract mixed numbers. 6. Add and subtract negative mixed numbers. 7. Solve equations. 8. Solve applications. 5.6

3. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 3 Objective 1 Add and subtract fractions with the same denominator.

4. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 4 To add or subtract fractions with the same denominator: Procedure 1.Add or subtract the numerators and keep the same denominator. 2.Simplify.

5. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 5 Example 1 Add or subtract. a. b.

6. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 6 Example 2 Add. a. b.

7. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 7 Example Subtract. a.b.

8. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 8 Objective 2 Add and subtract rational expressions with the same denominator.

9. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 9 Example 4 Add. a.b.

10. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 10 Example 4 Add. c. a.

11. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 11 Objective 3 Add and subtract fractions with different denominators.

12. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 12 To add or subtract fractions with different denominators: Procedure 1.Write the fraction as equivalent fractions with a common denominator. 2.Add or subtract the numerators and keep the common denominator. 3.Simplify. Note: Any common multiple of the denominators will do, but using the LCD makes the numbers more manageable.

13. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 13 Example 6 Add, three cases.

14. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 14 Objective 4 Add and subtract rational expressions with different denominators.

15. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 15 Example 7 Add or subtract. a. b.

16. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 16 Objective 5 Add and subtract mixed numbers.

17. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 17 Method 1: Write them as improper fractions.

18. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 18 Method 2: Because mixed numbers are, by definition, the result of addition, we can use the commutative property of addition and add the integers and fractions separately. Use the definition of mixed numbers. Use the commutative property of addition. Add the integers and fractions separately. Write as a mixed number.

19. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 19 Example 8 Add.

20. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 20 To add or subtract mixed numbers: Procedure Method 1: Write as improper fractions then follow the procedure for adding or subtracting fractions. Method 2: Add or subtract the integers and fractions separately.

21. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 21 Objective 6 Add and subtract negative mixed numbers.

22. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 22 Example 10 Add or subtract.

23. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 23 Objective 7 Solve equations.

24. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 24 Example 11 Solve and check.

25. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 25 Objective 7 Solve applications.

26. Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 5.6 - 26 Example 12 In a poll, ¼ of the respondents said they agreed with the passing of a certain bill, 1/5 said the disagreed, and the rest said they had no opinion. What fraction of the respondents had no opinion?