1. Using Properties of Addition Tell whether the commutative or associative property of addition allows you to rewrite the problem as shown. EXAMPLE 4 Explain your choice.

2. Using Properties of Addition a. EXAMPLE 4 Tell whether the commutative or associative property of addition allows you to rewrite the problem as shown. Explain your choice. 4 + 2.75 + 11 = 2.75 + 4 + 11

3. Using Properties of Addition a. EXAMPLE 4 Tell whether the commutative or associative property of addition allows you to rewrite the problem as shown. Explain your choice. 4 + 2.75 + 11 = 2.75 + 4 + 11 The order of the numbers has changed. This is allowed by the commutative property of addition.

4. Using Properties of Addition a. EXAMPLE 4 Tell whether the commutative or associative property of addition allows you to rewrite the problem as shown. Explain your choice. 4 + 2.75 + 11 = 2.75 + 4 + 11 The order of the numbers has changed. This is allowed by the commutative property of addition. b. (3.5 + 10) + 7 = 3.5 + (10 + 7)

5. Using Properties of Addition a. EXAMPLE 4 Tell whether the commutative or associative property of addition allows you to rewrite the problem as shown. Explain your choice. 4 + 2.75 + 11 = 2.75 + 4 + 11 The order of the numbers has changed. This is allowed by the commutative property b. (3.5 + 10) + 7 = 3.5 + (10 + 7) The grouping of the numbers has changed. This is allowed by the associative property of addition.

6. Standardized Test Practice EXAMPLE 5

7. SOLUTION Standardized Test Practice EXAMPLE 5 Write a verbal model to help you find the amount you earn.

8. SOLUTION Standardized Test Practice Money earned Selling price – Purchase price – Fees EXAMPLE 5 Write a verbal model to help you find the amount you earn.

9. SOLUTION Standardized Test Practice EXAMPLE 5 Write a verbal model to help you find the amount you earn. = 141.82 – 97.56 – 8.25 Substitute. Money earned Selling price – Purchase price – Fees

10. SOLUTION Standardized Test Practice Money earned Selling price – Purchase price – Fees EXAMPLE 5 Write a verbal model to help you find the amount you earn. = 141.82 – 97.56 – 8.25 = 44.26 – 8.25 Substitute. Subtract.

11. SOLUTION Standardized Test Practice Money earned Selling price – Purchase price – Fees EXAMPLE 5 Write a verbal model to help you find the amount you earn. = 141.82 – 97.56 – 8.25 = 44.26 – 8.25 = 36.01 Substitute. Subtract.

12. SOLUTION Standardized Test Practice Money earned Selling price – Purchase price – Fees EXAMPLE 5 Write a verbal model to help you find the amount you earn. = 141.82 – 97.56 – 8.25 = 44.26 – 8.25 = 36.01 Substitute. Subtract. Your sale earns you $36.01. ANSWER The correct answer is A.

13. Standardized Test Practice EXAMPLE 5 Check - Use estimation to check that your answer is reasonable.Round $141.82 to $142, $97.56 to $98, and $8.25 to $8.Because 142 – 98 – 8 = 36, the answer is reasonable.

14. GUIDED PRACTICE for Examples 4 and 5 Tell whether the commutative or associative property allows you to rewrite the problem as shown. Explain your choice. Then find the sum.

15. GUIDED PRACTICE Tell whether the commutative or associative property allows you to rewrite the problem as shown. Explain your choice. Then find the sum. 5. (6.4 + 4.8) + 5.2 = 6.4 + (4.8 + 5.2) for Examples 4 and 5

16. GUIDED PRACTICE Tell whether the commutative or associative property allows you to rewrite the problem as shown. Explain your choice. Then find the sum. 5. (6.4 + 4.8) + 5.2 = 6.4 + (4.8 + 5.2) The grouping of the numbers has changed. This is allowed by the associative property of addition. for Examples 4 and 5

17. GUIDED PRACTICE Tell whether the commutative or associative property allows you to rewrite the problem as shown. Explain your choice. Then find the sum. 5. (6.4 + 4.8) + 5.2 = 6.4 + (4.8 + 5.2) The grouping of the numbers has changed. This is allowed by the associative property of addition. for Examples 4 and 5 6. 9.3 + 2.9 = 2.9 + 9.3

18. GUIDED PRACTICE Tell whether the commutative or associative property allows you to rewrite the problem as shown. Explain your choice. Then find the sum. 5. 6. (6.4 + 4.8) + 5.2 = 6.4 + (4.8 + 5.2) 9.3 + 2.9 = 2.9 + 9.3 The order of the numbers has changed. This is allowed by the commutative property The grouping of the numbers has changed. This is allowed by the associative property of addition. for Examples 4 and 5

19. GUIDED PRACTICE Suppose you bought the book in Example 5 for $78.45, you sold the book for $126.78, and the auction fees were the same. How much would you earn selling the book? 7. What if? for Examples 4 and 5

20. ANSWER GUIDED PRACTICE Suppose you bought the book in Example 5 for $78.45, you sold the book for $126.78, and the auction fees were the same. How much would you earn selling the book? Your sale earns you $40.08. for Examples 4 and 5 7. What if?