1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 7.6 Properties of Real Numbers

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Apply the properties of real numbers. o Identify properties that justify given statements.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Applying the Properties of Real Numbers Properties of Addition and Multiplication In this table, a, b, and c are real numbers. For Addition Name of Property For Multiplication

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Applying the Properties of Real Numbers Properties of Addition and Multiplication (cont.) Addition Name of Property Multiplication

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Applying the Properties of Real Numbers Properties of Addition and Multiplication (cont.) Zero-Factor Law Distributive Property of Multiplication over Addition

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Applying the Properties of Real Numbers Notes The number 0 is called the additive identity because when 0 is added to a number the result is the same number. Likewise, the number 1 is called the multiplicative identity because when a number is multiplied by 1 the result is the same number. Also, the additive inverse of a number is its opposite and the multiplicative inverse of a number is its reciprocal.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Properties of Addition and Multiplication State the name of each property being illustrated. Solution commutative property of addition Solution associative property of addition Solution multiplicative identity

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Properties of Addition and Multiplication (cont.) Solution distributive property Solution zero-factor law

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Properties of Addition and Multiplication In each of the following equations, state the property illustrated and show that the statement is true for the value given for the variable by substituting the value in the equation and evaluating. a.x + 14 = 14 + x given that x = −4 Solution The commutative property of addition is illustrated.

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Properties of Addition and Multiplication (cont.) b. given that x = 5 Solution c. given that y = −2 Solution

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Determine the property being illustrated. 1. 2. 3. 2 + 7 = 7 + 24. 2(y + 5) = 2y + 10

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.associative property of multiplication 2.zero-factor law 3.commutative property of addition 4.distributive property