1. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 1 Section 1.6 Subtraction of Real Numbers

2. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 2 Subtraction For all real numbers a and b, In words: To subtract b from a, add the opposite, or additive inverse, of b to a. The result of the subtraction is called the difference. Definition of Subtraction

3. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 3 Objective 1 Subtract real numbers.

4. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 4 Subtraction Subtracting Real Numbers 1.Change the subtraction operation to addition. 2.Change the sign of the number being subtracted. 3.Add, using one of the rules for adding numbers with the same sign or different signs.

5. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 5 Example Change the sign to addition. Replace 15 with

6. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 6 Example Change the sign to addition. Replace with 9.

7. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 7 Objective 1: Example 1a.

8. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 8 Objective 1: Example 1b.

9. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 9 Objective 2 Simplify a series of additions and subtractions.

10. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 10 Subtraction Simplifying a Series of Additions and Subtractions 1.Change all subtractions to additions of opposites. 2.Group and then add all the positive numbers. 3.Group and then add all the negative numbers. 4.Combine the results of steps 2 and 3.

11. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 11 Example Simplify: Write as addition of additive inverses. Group the positive numbers and group the negative numbers. Add the positive numbers. Add the results.

12. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 12 Objective 2: Example 2.

13. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 13 Objective 3 Use the definition of subtraction to identify terms.

14. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 14 Subtraction and Algebraic Expressions We know that the terms of an algebraic expression are separated by addition signs. Let’s use this idea to identify the terms of the following algebraic expression: Because terms are separated by addition, we rewrite the subtractions in the algebraic expression as additions of opposites. Thus,

15. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 15 Objective 3: Example 3.

16. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 16 Objective 4 Use the subtraction definition to simplify algebraic expressions.

17. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 17 Example Simplify: Write as an addition. Rearrange terms. Apply the distributive property. Add within grouping symbols. Simplify.

18. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 18 Objective 4: Example 4a.

19. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 19 Objective 4: Example 4b.

20. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 20 Objective 5 Solve problems involving subtraction.

21. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 21 Objective 5: Example 5. The peak of Mount Everest is 8848 meters above sea level. The Marianas Trench, on the floor of the Pacific Ocean, is 10,915 meters below sea level.

22. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 22 Objective 5: Example (cont) What is the difference in elevation between the peak of Mount Everest and the Marianas Trench? The difference in elevation between the peak of Mount Everest and the Marianas Trench is 19,763 meters.