7.4 Properties of Identity, Inverses, and Zero

Before you get started, take this readiness quiz.

Find the opposite of $−4 .$
If you missed this problem, review the reference.

Find the reciprocal of $\frac{5}{2} .$
If you missed this problem, review the reference.

Multiply: $\frac{3 a}{5} \cdot \frac{9}{2 a} .$
If you missed this problem, review the reference.

Identify whether each equation demonstrates the identity property of addition or multiplication.

1. ⓐ $7 + 0 = 7$

2. ⓑ $−16 \left(1\right) = −16$

Identify whether each equation demonstrates the identity property of addition or multiplication:

ⓐ $23 + 0 = 23$ⓑ $−37 \left(1\right) = −37 .$

Identify whether each equation demonstrates the identity property of addition or multiplication:

ⓐ $1 \cdot 29 = 29$ⓑ $14 + 0 = 14 .$

Find the additive inverse of each expression: ⓐ $13$ ⓑ $- \frac{5}{8}$ ⓒ $0.6$.

Find the additive inverse: ⓐ $18$ ⓑ $\frac{7}{9}$ ⓒ $1.2$.

Find the additive inverse: ⓐ $47$ ⓑ $\frac{7}{13}$ ⓒ $8.4$.

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

Find the multiplicative inverse: ⓐ $5$ ⓑ $- \frac{1}{7}$ ⓒ $0.3$.

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

Simplify: ⓐ $−8 \cdot 0$ ⓑ $\frac{5}{12} \cdot 0$ ⓒ $0 \left(2.94\right)$.

Simplify: ⓐ $−14 \cdot 0$ ⓑ $0 \cdot \frac{2}{3}$ ⓒ $\left(16.5\right) \cdot 0 .$

Simplify: ⓐ $\left(1.95\right) \cdot 0$ ⓑ $0 \left(−17\right)$ ⓒ $0 \cdot \frac{5}{4} .$

Simplify: ⓐ $0 \div 5$ ⓑ $\frac{0}{−2}$ ⓒ $0 \div \frac{7}{8}$.

Simplify: ⓐ $0 \div 11$ ⓑ $\frac{0}{−6}$ ⓒ $0 \div \frac{3}{10}$.

Simplify: ⓐ $0 \div \frac{8}{3}$ ⓑ $0 \div \left(−10\right)$ ⓒ $0 \div 12.75$.

Simplify: ⓐ $7.5 \div 0$ ⓑ $\frac{−32}{0}$ ⓒ $\frac{4}{9} \div 0$.

Simplify: ⓐ $16.4 \div 0$ ⓑ $\frac{−2}{0}$ ⓒ $\frac{1}{5} \div 0$.

Simplify: ⓐ $\frac{−5}{0}$ ⓑ $96.9 \div 0$ ⓒ $\frac{4}{15} \div 0$

Simplify: $3 x + 15 - 3 x .$

Simplify: $−12 z + 9 + 12 z .$

Simplify: $−25 u - 18 + 25 u .$

Simplify: $4 \left(0.25 q\right) .$

Simplify: $2 \left(0.5 p\right) .$

Simplify: $25 \left(0.04 r\right) .$

Simplify: $\frac{0}{n + 5}$, where $n \neq −5$.

Simplify: $\frac{0}{m + 7}$, where $m \neq −7$.

Simplify: $\frac{0}{d - 4}$, where $d \neq 4$.

Simplify: $\frac{10 - 3 p}{0} .$

Simplify: $\frac{18 - 6 c}{0} .$

Simplify: $\frac{15 - 4 q}{0} .$

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

Identify whether each example is using the identity property of addition or multiplication.

$\frac{3}{5} \left(1\right) = \frac{3}{5}$

Identify whether each example is using the identity property of addition or multiplication.

$0 + 64 = 64$

Find the multiplicative inverse.

$14$

Find the multiplicative inverse.

$−19$

Find the multiplicative inverse.

$\frac{8}{13}$

Find the multiplicative inverse.

$- \frac{5}{12}$

Find the multiplicative inverse.

$0.4$

Find the multiplicative inverse.

$−0.5$

Simplify using the properties of zero.

$\frac{0}{6}$

Simplify using the properties of zero.

$22 \cdot 0$

Simplify using the properties of zero.

$\frac{6}{0}$

Simplify using the properties of zero.

$0 \div \frac{7}{15}$

Simplify using the properties of zero.

$\left(−3.14\right) \left(0\right)$

Simplify using the properties of zero.

$\frac{\frac{1}{10}}{0}$

Simplify using the properties of identities, inverses, and zero.

$27 c + 16 - 27 c$

Simplify using the properties of identities, inverses, and zero.

$92 + 31 s - 92$

Simplify using the properties of identities, inverses, and zero.

$100 \left(0.01 p\right)$

Simplify using the properties of identities, inverses, and zero.

$40 \left(0.05 n\right)$

Simplify using the properties of identities, inverses, and zero.

$\frac{0}{s + 13}$, where $s \neq −13$

Simplify using the properties of identities, inverses, and zero.

$\frac{0}{v - 65.1}$, where $v \neq 65.1$

Simplify using the properties of identities, inverses, and zero.

$0 \div \left(y - \frac{1}{6}\right)$, where $y \neq \frac{1}{6}$

Simplify using the properties of identities, inverses, and zero.

$\frac{28 - 9 b}{0}$, where $28 - 9 b \neq 0$

Simplify using the properties of identities, inverses, and zero.

$\frac{1.75 + 9 f}{0}$, where $1.75 + 9 f \neq 0$

Simplify using the properties of identities, inverses, and zero.

$\left(\frac{5}{16} n - \frac{3}{7}\right) \div 0$, where $\frac{5}{16} n - \frac{3}{7} \neq 0$

Simplify using the properties of identities, inverses, and zero.

$\frac{5}{7} \cdot \frac{7}{5} \left(20 q - 35\right)$

Simplify using the properties of identities, inverses, and zero.

$18 \cdot \frac{5}{6} \left(15 h + 24\right)$

Cooking time Helen bought a $\text{24}-\text{pound}$ turkey for her family’s Thanksgiving dinner and wants to know what time to put the turkey in the oven. She wants to allow $20$ minutes per pound cooking time.

1. ⓐ Calculate the length of time needed to roast the turkey by multiplying $24 \cdot 20$ to find the number of minutes and then multiplying the product by $\frac{1}{60}$ to convert minutes into hours.

2. ⓑ Multiply $24 \left(20 \cdot \frac{1}{60}\right) .$

3. ⓒ Which of the Proper…

How can the use of the properties of real numbers make it easier to simplify expressions?