1.9 Properties of Real Numbers

Simplify: $18 p + 6 q + 15 p + 5 q .$

Simplify: $23 r + 14 s + 9 r + 15 s .$

Simplify: $37 m + 21 n + 4 m - 15 n .$

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

Use the associative property to simplify $6 \left(3 x\right) .$

Use the associative property to simplify 8(4x).

Use the associative property to simplify $−9 \left(7 y\right) .$

Find the additive inverse of ⓐ $\frac{5}{8}$ ⓑ $0.6$ ⓒ $−8$ ⓓ $- \frac{4}{3} .$

Find the additive inverse of: ⓐ $\frac{7}{9}$ ⓑ $1.2$ ⓒ $−14$ ⓓ $- \frac{9}{4} .$

Find the additive inverse of: ⓐ $\frac{7}{13}$ ⓑ $8.4$ ⓒ $−46$ ⓓ $- \frac{5}{2} .$

Find the multiplicative inverse of ⓐ $9$ ⓑ $- \frac{1}{9}$ ⓒ $0.9 .$

Find the multiplicative inverse of ⓐ $4$ ⓑ $- \frac{1}{7}$ ⓒ $0.3$

Find the multiplicative inverse of ⓐ $18$ ⓑ $- \frac{4}{5}$ ⓒ $0.6 .$

Simplify: ⓐ $−8 \cdot 0$ ⓑ $\frac{0}{−2}$ ⓒ $\frac{−32}{0} .$

Simplify: ⓐ $−14 \cdot 0$ ⓑ $\frac{0}{−6}$ ⓒ $\frac{−2}{0} .$

Simplify: ⓐ $0 \left(−17\right)$ ⓑ $\frac{0}{−10}$ ⓒ $\frac{−5}{0} .$

Simplify: ⓐ $\frac{0}{n + 5} ,$ where $n \neq − 5$ ⓑ $\frac{10 - 3 p}{0} ,$ where $10 - 3 p \neq 0 .$

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: ⓐ $\frac{0}{m + 7} ,$ where $m \neq − 7$ ⓑ $\frac{18 - 6 c}{0} ,$ where $18 - 6 c \neq 0 .$

Simplify: ⓐ $\frac{0}{d - 4} , \text{where} d \neq 4$ ⓑ $\frac{15 - 4 q}{0} , \text{where} 15 - 4 q \neq 0 .$

Simplify: $\frac{3}{4} \cdot \frac{4}{3} \left(6 x + 12\right) .$

Simplify: $\frac{2}{5} \cdot \frac{5}{2} \left(20 y + 50\right) .$

Simplify: $\frac{3}{8} \cdot \frac{8}{3} \left(12 z + 16\right) .$

Simplify: $3 \left(x + 4\right) .$

Simplify: $4 \left(x + 2\right) .$

Simplify: $6 \left(x + 7\right) .$

Simplify: $6 \left(\frac{5}{6} y + \frac{1}{2}\right) .$

Simplify: $12 \left(\frac{1}{3} n + \frac{3}{4}\right) .$

Simplify: $100 \left(0.7 + 0.15 p\right) .$

Simplify: $100 \left(0.04 + 0.35 d\right) .$

Simplify: $−3 \left(6 m + 5\right) .$

Simplify: $−6 \left(8 n + 11\right) .$

Simplify: $−5 \left(2 - 3 a\right) .$

Simplify: $−7 \left(8 - 15 y\right) .$

Simplify: $− \left(y + 5\right) .$

Simplify: $− \left(z - 11\right) .$

Simplify: $− \left(x - 4\right) .$

Simplify: $8 - 2 \left(x + 3\right) .$

Be sure to follow the order of operations. Multiplication comes before subtraction, so we will distribute the 2 first and then subtract.

Simplify: $9 - 3 \left(x + 2\right) .$

Simplify: $7 x - 5 \left(x + 4\right) .$

Simplify: $4 \left(x - 8\right) - \left(x + 3\right) .$

Simplify: $6 \left(x - 9\right) - \left(x + 12\right) .$

Simplify: $8 \left(x - 1\right) - \left(x + 5\right) .$

Use the associative property to simplify.

3(4x)

Use the associative property to simplify.

$\left(y + 12\right) + 28$

Simplify.

$\frac{1}{2} + \frac{7}{8} + \left(- \frac{1}{2}\right)$

Simplify.

$\frac{3}{20} \cdot \frac{49}{11} \cdot \frac{20}{3}$

Simplify.

$−24 \cdot 7 \cdot \frac{3}{8}$

Simplify.

$\left(\frac{5}{6} + \frac{8}{15}\right) + \frac{7}{15}$

Simplify.

17(0.25)(4)

Simplify.

[2.48(12)](0.5)

Simplify.

7(4a)

Simplify.

$−15 \left(5 m\right)$

Simplify.

$12 \left(\frac{5}{6} p\right)$

Simplify.

$43 m + \left(−12 n\right) + \left(−16 m\right) + \left(−9 n\right)$

Simplify.

$\frac{3}{8} g + \frac{1}{12} h + \frac{7}{8} g + \frac{5}{12} h$

Simplify.

$6.8 p + 9.14 q + \left(−4.37 p\right) + \left(−0.88 q\right)$

Find the additive inverse of each number.

ⓐ $\frac{2}{5}$ ⓑ 4.3
ⓒ $−8$
ⓓ $- \frac{10}{3}$

Find the additive inverse of each number.

ⓐ $- \frac{7}{6}$ ⓑ $−0.075$ ⓒ 23 ⓓ $\frac{1}{4}$

Find the multiplicative inverse of each number.

ⓐ 6 ⓑ $- \frac{3}{4}$ ⓒ 0.7

Find the multiplicative inverse of each number.

ⓐ $\frac{11}{12}$ ⓑ $−1.1$ ⓒ $−4$

Simplify.

$\frac{0}{6}$

Simplify.

$0 \div \frac{11}{12}$

Simplify.

$\frac{0}{3}$

Simplify.

$\left(−3.14\right) \left(0\right)$

Simplify.

$19 a + 44 - 19 a$

Simplify.

$10 \left(0.1 d\right)$

Simplify.

$\frac{0}{u - 4.99} ,$ where $u \neq 4.99$

Simplify.

$0 \div \left(x - \frac{1}{2}\right) ,$ where $x \neq \frac{1}{2}$

Simplify.

$\frac{32 - 5 a}{0} ,$ where
$32 - 5 a \neq 0$

Simplify.

$\left(\frac{3}{4} + \frac{9}{10} m\right) \div 0$ where
$\frac{3}{4} + \frac{9}{10} m \neq 0$

Simplify.

$15 \cdot \frac{3}{5} \left(4 d + 10\right)$

Simplify using the distributive property.

$8 \left(4 y + 9\right)$

Simplify using the distributive property.

$6 \left(c - 13\right)$

Simplify using the distributive property.

$\frac{1}{4} \left(3 q + 12\right)$

Simplify using the distributive property.

$9 \left(\frac{5}{9} y - \frac{1}{3}\right)$

Simplify using the distributive property.

$12 \left(\frac{1}{4} + \frac{2}{3} r\right)$

Simplify using the distributive property.

$r \left(s - 18\right)$

Simplify using the distributive property.

$\left(y + 4\right) p$

Simplify using the distributive property.

$−7 \left(4 p + 1\right)$

Simplify using the distributive property.

$−3 \left(x - 6\right)$

Simplify using the distributive property.

$− \left(3 x - 7\right)$

Simplify using the distributive property.

$16 - 3 \left(y + 8\right)$

Simplify using the distributive property.

$4 - 11 \left(3 c - 2\right)$

Simplify using the distributive property.

$22 - \left(a + 3\right)$

Simplify using the distributive property.

$\left(5 m - 3\right) - \left(m + 7\right)$

Simplify using the distributive property.

$5 \left(2 n + 9\right) + 12 \left(n - 3\right)$

Simplify using the distributive property.

$9 \left(8 x - 3\right) - \left(−2\right)$

Simplify using the distributive property.

$14 \left(c - 1\right) - 8 \left(c - 6\right)$

Simplify using the distributive property.

$6 \left(7 y + 8\right) - \left(30 y - 15\right)$

Insurance copayment Carrie had to have 5 fillings done. Each filling cost $80. Her dental insurance required her to pay 20% of the cost as a copay. Calculate Carrie’s copay:

1. ⓐ First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings.
2. ⓑ Next, by multiplying [5(0.20)](80)
3. ⓒ Which of the properties of real number…

Buying by the case Trader Joe’s grocery stores sold a bottle of wine they called “Two Buck Chuck” for $1.99. They sold a case of 12 bottles for $23.88. To find the cost of 12 bottles at $1.99, notice that 1.99 is $2 - 0.01 .$

1. ⓐ Multiply 12(1.99) by using the distributive property to multiply $12 \left(2 - 0.01\right) .$
2. ⓑ Was it a bargain to buy “Two Buck Chuck” by the case?

In your own words, state the commutative property of addition.

Simplify $8 \left(x - \frac{1}{4}\right)$ using the distributive property and explain each step.