1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 7.2 Addition with Real Numbers

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Add real numbers. o Add real numbers in a vertical format. o Determine if a given real number is a solution to an equation.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Addition with Real Numbers Rules for Addition with Real Numbers 1.To add two real numbers with like signs, a. add their absolute values, and b. use the common sign. 2. To add two real numbers with unlike signs, a. subtract their absolute values (the smaller from the larger), and b. use the sign of the number with the larger absolute value.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Addition with Like Signs

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Addition with Unlike Signs

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Adding More Than Two Real Numbers One technique to add more than two real numbers is to add the numbers from left to right.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Addition in a Vertical Format Notes The positive sign ( + ) may be omitted when writing positive numbers, but the negative sign ( − ) must always be written for negative numbers. Thus, if there is no sign in front of a real number, the real number is understood to be positive.

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Addition on a Vertical Format Find each sum.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Addition in a Vertical Format Find each sum. Solution One technique for adding several real numbers is to mentally add the positive and negative real numbers separately and then add these results. (We are, in effect, using the commutative and associative properties of addition.)

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Addition in a Vertical Format (cont.) Solution

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Determining Possible Solutions Determine whether or not the given real number is a solution to the given equation by substituting for the variable and adding. a. given that x = −7 Solution is true, so −7 is a solution.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Determining Possible Solutions (cont.) b. 1.8 + z = −3.9 given that z = 2.1 Solution c. |x| + (−7) = −3 given that x = −4 Solution 1.8 + 2.1 = −3.9 is false since 1.8 + 2.1 = +3.9 So 2.1 is not a solution. |−4| + (−7) = 4 + (−7) = −3 is true, so −4 is a solution.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Determining Possible Solutions (cont.) d. given that Solution is true, so is a solution.

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Find each sum. Add from left to right if there are more than two numbers. 1. +16 + (−10)2. −12 + (8) 3.4. −1.3 + (1.3) 5.6. +6 + (−7) + (−1) 7. +100 +(−100) + (+10)

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems (cont.) Find the indicated sum. 8.9. 10.Determine whether or not x = −3 is a solution to the equation

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.62. −43. 4.05. 6. −2 7.108. −339. 2 10. yes