7.4 Properties of identity, inverses, and zero  (Page 3/7)

$101+0=101$

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

$\mathrm{-9}·1=\mathrm{-9}$

$0+64=64$

$8$

$14$

$\mathrm{-17}$

$\mathrm{-19}$

$\frac{7}{12}$

$\frac{8}{13}$

$-\frac{3}{10}$

$-\frac{5}{12}$

$0.8$

$0.4$

$\mathrm{-0.2}$

$\mathrm{-0.5}$

$48·0$

$\frac{0}{6}$

$\frac{3}{0}$

$22·0$

$0÷\frac{11}{12}$

$\frac{6}{0}$

$\frac{0}{3}$

$0÷\frac{7}{15}$

$0·\frac{8}{15}$

$(\mathrm{-3.14})(0)$

$5.72÷0$

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

$19a+44-19a$

$27c+16-27c$

$38+11r-38$

$92+31s-92$

$10(0.1d)$

$100(0.01p)$

$5(0.6q)$

$40(0.05n)$

$\frac{0}{r+20},\text{where}r\ne \mathrm{-20}$

$\frac{0}{s+13},\text{where}s\ne \mathrm{-13}$

$\frac{0}{u-4.99},\text{where}u\ne 4.99$

$\frac{0}{v-65.1},\text{where}v\ne 65.1$

$0÷\left(x-\frac{1}{2}\right),\text{where}x\ne \frac{1}{2}$

$0÷\left(y-\frac{1}{6}\right),\text{where}y\ne \frac{1}{6}$

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

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

$\frac{2.1+0.4c}{0},\text{where}2.1+0.4c\ne 0$

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

$\frac{9}{10}·\frac{10}{9}(18p-21)$

$\frac{5}{7}·\frac{7}{5}(20q-35)$

$15·\frac{3}{5}(4d+10)$

$18·\frac{5}{6}(15h+24)$

Insurance copayment Carrie had to have $5$ fillings done. Each filling cost $\text{\$80}.$ Her dental insurance required her to pay $20\%$ of the cost. Calculate Carrie’s cost

ⓐ by finding her copay for each filling, then finding her total cost for $5$ fillings, and

ⓑ by multiplying $5(0.20)(80).$

ⓒ Which of the Properties of Real Numbers did you use for part (b)?

Cooking time Helen bought a $\text{24-pound}$ 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.

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

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

ⓒ Which of the Properties of Real Numbers allows you to multiply $24\left(20·\frac{1}{60}\right)$ instead of $(24·20)\frac{1}{60}?$

In your own words, describe the difference between the additive inverse and the multiplicative inverse of a number.

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