7.2 Commutative and Associative Properties

Before you get started, take this readiness quiz.

Simplify: $7 y + 2 + y + 13 .$
If you missed this problem, review the reference.

Multiply: $\frac{2}{3} \cdot 18 .$
If you missed this problem, review the reference.

Find the opposite of $15 .$
If you missed this problem, review the reference.

Use the commutative properties to rewrite the following expressions:

1. ⓐ $−1 + 3 = _____$

2. ⓑ $4 \cdot 9 = _____$

Use the commutative properties to rewrite the following:

1. ⓐ $−4 + 7 = _____$
2. ⓑ $6 \cdot 12 = _____$

Use the commutative properties to rewrite the following:

1. ⓐ $14 + \left(−2\right) = _____$
2. ⓑ $3 \left(−5\right) = _____$

Use the associative properties to rewrite the following:

1. ⓐ $\left(3 + 0.6\right) + 0.4 = __________$

2. ⓑ $\left(−4 \cdot \frac{2}{5}\right) \cdot 15 = __________$

Use the associative properties to rewrite the following:
ⓐ $\left(1 + 0.7\right) + 0.3 = __________$ ⓑ $\left(−9 \cdot 8\right) \cdot \frac{3}{4} = __________$

Use the associative properties to rewrite the following:
ⓐ $\left(4 + 0.6\right) + 0.4 = __________$ ⓑ $\left(−2 \cdot 12\right) \cdot \frac{5}{6} = __________$

Use the Associative Property of Multiplication to simplify: $6 \left(3 x\right) .$

Use the Associative Property of Multiplication to simplify the given expression: $8 \left(4 x\right) .$

Use the Associative Property of Multiplication to simplify the given expression: $−9 \left(7 y\right) .$

Evaluate each expression when $y = \frac{3}{8} :$ⓐ $y + 0.84 + \left(- y\right)$ ⓑ $y + \left(- y\right) + 0.84 .$

Evaluate each expression when $f = \frac{17}{20} :$ⓐ $f + 0.975 + \left(- f\right)$ ⓑ $f + \left(- f\right) + 0.975 .$

Evaluate each expression when $p = 24 :$ⓐ $\frac{5}{9} \left(\frac{9}{5} p\right)$ ⓑ $\left(\frac{5}{9} \cdot \frac{9}{5}\right) p .$

Evaluate each expression when $q = 15 :$ⓐ $\frac{7}{11} \left(\frac{11}{7} q\right)$ ⓑ $\left(\frac{7}{11} \cdot \frac{11}{7}\right) q$

Simplify: $−84 n + \left(−73 n\right) + 84 n .$

Simplify: $−27 a + \left(−48 a\right) + 27 a .$

Simplify: $39 x + \left(−92 x\right) + \left(−39 x\right) .$

Simplify: $\frac{7}{15} \cdot \frac{8}{23} \cdot \frac{15}{7} .$

Simplify: $\frac{9}{16} \cdot \frac{5}{49} \cdot \frac{16}{9} .$

Simplify: $\frac{6}{17} \cdot \frac{11}{25} \cdot \frac{17}{6} .$

Simplify: $\left(\frac{5}{13} + \frac{3}{4}\right) + \frac{1}{4} .$

Simplify: $\left(\frac{7}{15} + \frac{5}{8}\right) + \frac{3}{8} .$

Simplify: $\left(\frac{2}{9} + \frac{7}{12}\right) + \frac{5}{12} .$

Simplify: $\left(6.47 q + 9.99 q\right) + 1.01 q .$

Simplify: $\left(5.58 c + 8.75 c\right) + 1.25 c .$

Simplify: $\left(8.79 d + 3.55 d\right) + 5.45 d .$

Simplify the expression: $\left[1.67 \left(8\right)\right] \left(0.25\right) .$

Simplify: $\left[1.17 \left(4\right)\right] \left(2.25\right) .$

Simplify: $\left[3.52 \left(8\right)\right] \left(2.5\right) .$

Simplify: $6 \left(9 x\right) .$

Simplify: $8 \left(3 y\right) .$

Simplify: $12 \left(5 z\right) .$

Simplify: $18 p + 6 q + \left(−15 p\right) + 5 q .$

Simplify: $23 r + 14 s + 9 r + \left(−15 s\right) .$

Simplify: $37 m + 21 n + 4 m + \left(−15 n\right) .$

Use the commutative properties to rewrite the given expression.

$7 + 6 = ___$

Use the commutative properties to rewrite the given expression.

$7 \left(−13\right) = ___$

Use the commutative properties to rewrite the given expression.

$\left(−12\right) \left(−18\right) = ___$

Use the commutative properties to rewrite the given expression.

$−15 + 7 = ___$

Use the commutative properties to rewrite the given expression.

$y + 1 = ___$

Use the commutative properties to rewrite the given expression.

$−3 m = ___$

Use the associative properties to rewrite the given expression.

$\left(21 + 14\right) + 9 = ___$

Use the associative properties to rewrite the given expression.

$\left(14 \cdot 6\right) \cdot 9 = ___$

Use the associative properties to rewrite the given expression.

$\left(−2 + 6\right) + 7 = ___$

Use the associative properties to rewrite the given expression.

$\left(13 \cdot \frac{2}{3}\right) \cdot 18 = ___$

Use the associative properties to rewrite the given expression.

$4 \left(7 x\right) = ___$

Use the associative properties to rewrite the given expression.

$\left(17 + y\right) + 33 = ___$

Evaluate each expression for the given value.

If $z = \frac{7}{8} ,$ evaluate:

1. ⓐ $z + 0.97 + \left(- z\right)$
2. ⓑ $z + \left(- z\right) + 0.97$

Evaluate each expression for the given value.

If $d = - \frac{9}{4} ,$ evaluate:

1. ⓐ $d + 2.375 + \left(- d\right)$
2. ⓑ $d + \left(- d\right) + 2.375$

Evaluate each expression for the given value.

If $k = 21 ,$ evaluate:

1. ⓐ $\frac{4}{13} \left(\frac{13}{4} k\right)$
2. ⓑ $\left(\frac{4}{13} \cdot \frac{13}{4}\right) k$

Evaluate each expression for the given value.

If $n = −8 ,$ evaluate:

1. ⓐ $- \frac{5}{21} \left(\frac{21}{5} n\right)$
2. ⓑ $\left(- \frac{5}{21} \cdot \frac{21}{5}\right) n$

Simplify.

$9 y + 23 + \left(−9 y\right)$

Simplify.

$\frac{2}{5} + \frac{5}{12} + \left(- \frac{2}{5}\right)$

Simplify.

$\frac{13}{18} \cdot \frac{25}{7} \cdot \frac{18}{13}$

Simplify.

$\frac{3}{10} \cdot \frac{13}{23} \cdot \frac{50}{3}$

Simplify.

$−36 \cdot 11 \cdot \frac{4}{9}$

Simplify.

$\left(\frac{1}{12} + \frac{4}{9}\right) + \frac{5}{9}$

Simplify.

$\frac{8}{15} + \frac{5}{7} + \frac{2}{7}$

Simplify.

$\left(5.89 d + 2.75 d\right) + 1.25 d$

Simplify.

$36 \left(0.2\right) \left(5\right)$

Simplify.

$\left[9.731 \left(4\right)\right] \left(0.75\right)$

Simplify.

$9 \left(8 w\right)$

Simplify.

$−23 \left(2 n\right)$

Simplify.

$20 \left(\frac{3}{5} q\right)$

Simplify.

$15 u + 11 v + 27 u + 19 v$

Simplify.

$−22 p + 17 q + \left(−35 p\right) + \left(−27 q\right)$

Simplify.

$\frac{5}{6} a + \frac{3}{10} b + \frac{1}{6} a + \frac{9}{10} b$

Simplify.

$9.6 m + 7.22 n + \left(−2.19 m\right) + \left(−0.65 n\right)$

Counting Cash Grant is totaling up the cash from a fundraising dinner. In one envelope, he has twenty-three $\$\text{5}$ bills, eighteen $\$\text{10}$ bills, and thirty-four $\$\text{20}$ bills. In another envelope, he has fourteen $\$\text{5}$ bills, nine $\$\text{10}$ bills, and twenty-seven $\$\text{20}$ bills.

1. ⓐ How much money is in the first envelope?

2. ⓑ How much money is in the second envelope?

3. ⓒ What is the total value of all the cash?

4. ⓓ What is the va…

In your own words, state the Associative Property of Multiplication and explain why it is useful.