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.

Using Properties of Addition

a.

EXAMPLE 4

Tell whether the commutative or associative property ofaddition allows you to rewrite the problem as shown. Explain your choice.

4 + 2.75 + 11 = 2.75 + 4 + 11

Using Properties of Addition

a.

EXAMPLE 4

Tell whether the commutative or associative property ofaddition allows you to rewrite the problem as shown. Explain your choice.

4 + 2.75 + 11 = 2.75 + 4 + 11The order of the numbers haschanged. This is allowed bythe commutative propertyof addition.

Using Properties of Addition

a.

EXAMPLE 4

Tell whether the commutative or associative property ofaddition allows you to rewrite the problem as shown. Explain your choice.

4 + 2.75 + 11 = 2.75 + 4 + 11The order of the numbers haschanged. This is allowed bythe commutative propertyof addition.

b. (3.5 + 10) + 7 = 3.5 + (10 + 7)

Using Properties of Addition

a.

EXAMPLE 4

Tell whether the commutative or associative property ofaddition allows you to rewrite the problem as shown. Explain your choice.

4 + 2.75 + 11 = 2.75 + 4 + 11The order of the numbers haschanged. This is allowed bythe commutative property

b. (3.5 + 10) + 7 = 3.5 + (10 + 7)The grouping of the numbershas changed. This is allowedby the associative propertyof addition.

of addition.

Standardized Test Practice

EXAMPLE 5

SOLUTION

Standardized Test Practice

EXAMPLE 5

Write a verbal model to help you find the amount you earn.

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.

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

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.

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.

Subtract.

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.

Subtract.

Your sale earns you $36.01.ANSWER

The correct answer is A.

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.

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.

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

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 numbershas changed. This is allowedby the associative propertyof addition.

for Examples 4 and 5

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 numbershas changed. This is allowedby the associative propertyof addition.

for Examples 4 and 5

6. 9.3 + 2.9 = 2.9 + 9.3

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 + 9.3The order of the numbers haschanged. This is allowed bythe commutative property

The grouping of the numbershas changed. This is allowedby the associative propertyof addition.

of addition.

for Examples 4 and 5

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

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?