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Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

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

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

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

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

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

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

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

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

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

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

$\frac{9}{10}\cdot \frac{10}{9}(18p-21)$

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

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

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

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

Simplify Expressions using the Properties of Identities, Inverses, and Zero

In the following exercises, simplify using the properties of identities, inverses, and zero.

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

Insurance copayment Carrie had to have $5$ fillings done. Each filling cost $\char36 80.$ Her dental insurance required her to pay $20\%$ of the cost. Calculate Carrie’s cost

1. ⓐ by finding her copay for each filling, then finding her total cost for $5$ fillings, and
2. ⓑ by multiplying $5(0.20)(80).$
3. ⓒ 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.

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

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?

In the number 63,407,218, find the place value of each digit:

• ⓐ 7
• ⓑ 0
• ⓒ 1
• ⓓ 6
• ⓔ 3

For the number 27,493,615, find the place value of each digit:

ⓐ 2 ⓑ 1 ⓒ 4 ⓓ 7 ⓔ 5

For the number 519,711,641,328, find the place value of each digit:

ⓐ 9 ⓑ 4 ⓒ 2 ⓓ 6 ⓔ 7

Name the number 8,165,432,098,710 using words.

Name the number $9,258,137,904,061$ using words.

Name the number $17,864,325,619,004$ using words.

Write nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-nine as a whole number using digits.