1. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 1 Section 1.5 Addition of Real Numbers

2. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 2 Objective 1 Add numbers with a number line.

3. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 3 Adding with a Number Line Using the Number Line to Find a Sum Let a and b represent real numbers. To find using the number line, 1. Start with a. 2. a. If b is positive, move b units to the right. b. If b is negative, move units to the left. c. If b is 0, stay at a. 3.The number where we finish on the number line represents the sum of a and b.

4. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 4 Adding Real Numbers Using a Number Line Add using the number line. -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Finish at Move 9 units left. Start at 7.

5. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 5 Objective 1: Example 1a.Find the sum using a number line: Start at 4 and move 7 units to the left. Thus,

6. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 6 Objective 1: Example 1b.Find the sum using a number line: Start at and move 3 units to the left. Thus,

7. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 7 Objective 1: Example 1c.Find the sum using a number line: Start at and move 3 units to the right. Thus,

8. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 8 Objective 2 Find sums using identity and inverse properties

9. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 9 PropertyMeaningExamples Identity Property of Addition Zero can be deleted from a sum. Identity and Inverse Properties of Addition Let a be a real number, a variable or an algebraic expression. Properties of Addition

10. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 10 PropertyMeaningExamples Inverse Property of Addition The sum of a real number and its additive inverse gives 0, the additive identity. Properties of Addition (cont)

11. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 11 Objective 2: Example 2. Use the Inverse Property of Addition to add: The sum of a real number and its additive inverse, or opposite, gives 0, the additive identity.

12. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 12 Objective 3 Add numbers without a number line.

13. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 13 Addition Adding Two Numbers with the Same Sign 1. Add the absolute values. 2. Use the common sign as the sign of the sum. Use the common sign. Add the absolute values:

14. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 14 Addition Adding Two Numbers with Different Signs 1. Subtract the smaller absolute value from the greater absolute value. 2. Use the sign of the number with the greater absolute value as the sign of the sum. Use the sign of the number with the greater absolute value. Subtract the absolute values:

15. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 15 Example We are adding numbers having like signs. So we just add the absolute values and take the common sign as the sign of the sum.

16. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 16 Example We are adding numbers having unlike signs. We just take the difference of the absolute values (difference is 4) and then take the sign of the number that has the largest absolute value (that’s the 14 and it is positive).

17. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 17 Objective 3: Example 3a.Add without using a number line:

18. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 18 Objective 3: Example 3b.Add without using a number line: 3c.Add without using a number line:

19. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 19 Objective 4 Use addition rules to simplify algebraic expressions.

20. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 20 Objective 4: Example 4a.Simplify:

21. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 21 Objective 4: Example 4b.Simplify:

22. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 22 Objective 4: Example 4c.Simplify:

23. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 23 Objective 5 Solve applied problems using a series of additions.

24. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 24 Series of Additions Positive and negative numbers are used in everyday life to represent such things as gains and losses in the stock market, rising and falling temperatures, deposits and withdrawals on bank statements and ascending and descending motion. Positive and negative numbers are used to solve applied problems involving a series of addition.

25. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 25 Series of Additions One way to add a series of positive and negative numbers is to use the commutative and associative properties. Add all the positive numbers. Add all the negative numbers. Add the sums obtained in the first two steps.

26. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 26 Objective 5: Example 5.The water level of a reservoir is measured over a five-month period. During this time, the level rose 2 feet, then fell 4 feet, then rose 1 foot, then fell 5 feet, and then rose 3 feet. What was the change in the water level at the end of the five months? The level rose 2 feet: 2 then fell 4 feet: then rose 1 foot: 1 then fell 5 feet: and then rose 3 feet: 3

27. Copyright © 2017, 2013, 2009 Pearson Education, Inc. 27 Objective 5: Example (cont) At the end of 5 months the water level was down 3 feet.