### Review Exercises

##### Use the Language of Algebra

**Identify Multiples and Factors**

Use the divisibility tests to determine whether 180 is divisible by 2, by 3, by 5, by 6, and by 10.

Find the prime factorization of 252.

In the following exercises, simplify each expression.

$24\xf73+4\left(5-2\right)$

**Evaluate an Expression**

In the following exercises, evaluate the following expressions.

When $x=4,$ ⓐ ${x}^{3}$ ⓑ ${5}^{x}$ ⓒ $2{x}^{2}-5x+3$

**Simplify Expressions by Combining Like Terms**

In the following exercises, simplify the following expressions by combining like terms.

$12y+7+2y-5$

**Translate an English Phrase to an Algebraic Expression**

In the following exercises, translate the phrases into algebraic expressions.

ⓐ the sum of $4a{b}^{2}$ and $7{a}^{3}{b}^{2}$

ⓑ the product of $6{y}^{2}$ and $3y$

ⓒ twelve more than $5x$

ⓓ $5y$ less than $8{y}^{2}$

Dushko has nickels and pennies in his pocket. The number of pennies is four less than five times the number of nickels. Let $n$ represent the number of nickels. Write an expression for the number of pennies.

##### Integers

**Simplify Expressions with Absolute Value**

In the following exercise, fill in $<,>,$ or $=$ for each of the following pairs of numbers.

ⓐ $\text{\u2212}\left|7\right|\_\_\_-\left|\mathrm{-7}\right|$

ⓑ $\mathrm{-8}\_\_\_-\left|\mathrm{-8}\right|$

ⓒ $\left|\mathrm{-13}\right|\_\_\_-13$

ⓓ $\left|\mathrm{-12}\right|\_\_\_-\left(\mathrm{-12}\right)$

In the following exercises, simplify.

$9-\left|3\left(4-8\right)\right|$

**Add and Subtract Integers**

In the following exercises, simplify each expression.

$\mathrm{-12}+\left(\mathrm{-8}\right)+7$

$\mathrm{-11}-\left(\mathrm{-12}\right)+5$

$\text{\u2212}\left(7-11\right)-\left(3-5\right)$

**Multiply and Divide Integers**

In the following exercise, multiply or divide.

ⓐ $\mathrm{-27}\xf79$ ⓑ $120\xf7\left(\mathrm{-8}\right)$ ⓒ $4\left(\mathrm{-14}\right)$ ⓓ $\mathrm{-1}\left(\mathrm{-17}\right)$

**Simplify and Evaluate Expressions with Integers**

In the following exercises, simplify each expression.

ⓐ ${\left(\mathrm{-7}\right)}^{3}$ ⓑ $\text{\u2212}{7}^{3}$

$63\xf7\left(\mathrm{-9}\right)+\left(\mathrm{-36}\right)\xf7\left(\mathrm{-4}\right)$

${\left(\mathrm{-2}\right)}^{4}-24\xf7\left(13-5\right)$

For the following exercises, evaluate each expression.

$3{x}^{2}-2xy+4{y}^{2}$ when

$x=\mathrm{-2},y=\mathrm{-3}$

**Translate English Phrases to Algebraic Expressions**

In the following exercises, translate to an algebraic expression and simplify if possible.

ⓐ the difference of 17 and $\mathrm{-8}$ ⓑ subtract 17 from $\mathrm{-25}$

**Use Integers in Applications**

In the following exercise, solve.

**Temperature** On July 10, the high temperature in Phoenix, Arizona, was 109°, and the high temperature in Juneau, Alaska, was 63°. What was the difference between the temperature in Phoenix and the temperature in Juneau?

##### Fractions

**Simplify Fractions**

In the following exercises, simplify.

$\frac{204}{228}$

**Multiply and Divide Fractions**

In the following exercises, perform the indicated operation.

$\left(-\frac{14}{15}\right)\left(\frac{10}{21}\right)$

$\frac{-\frac{4}{9}}{\frac{8}{21}}$

**Add and Subtract Fractions**

In the following exercises, perform the indicated operation.

$\frac{11}{36}-\frac{15}{48}$

ⓐ $-\frac{3y}{10}-\frac{5}{6}$ ⓑ $-\frac{3y}{10}\xb7\frac{5}{6}$

**Use the Order of Operations to Simplify Fractions**

In the following exercises, simplify.

$\frac{4\left(7-3\right)-2\left(4-9\right)}{\mathrm{-3}\left(4+2\right)+7\left(3-6\right)}$

**Evaluate Variable Expressions with Fractions**

In the following exercises, evaluate.

$4{x}^{2}{y}^{2}$ when

$x=\frac{2}{3}$ and $y=-\frac{3}{4}$

##### Decimals

**Round Decimals**

Round $6.738$ to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

**Add and Subtract Decimals**

In the following exercises, perform the indicated operation.

$54.3-100$

**Multiply and Divide Decimals**

In the following exercises, perform the indicated operation.

$\left(\mathrm{-2.8}\right)\left(3.97\right)$

$\left(53.48\right)\left(10\right)$

$\text{\$}118.35\xf72.6$

**Convert Decimals, Fractions and Percents**

In the following exercises, convert each decimal to a fraction.

$0.65$

In the following exercises, convert each fraction to a decimal.

$-\frac{5}{8}$

In the following exercises, convert each decimal to a percent.

$2.43$

**Simplify Expressions with Square Roots**

In the following exercises, simplify.

$\sqrt{289}$

**Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers**

In the following exercise, list the ⓐ whole numbers ⓑ integers ⓒ rational numbers ⓓ irrational numbers ⓔ real numbers for each set of numbers

$\mathrm{-8},0,\mathrm{1.95286...},\frac{12}{5},\sqrt{36},9$

**Locate Fractions and Decimals on the Number Line**

In the following exercises, locate the numbers on a number line.

ⓐ $3.2$ ⓑ $\mathrm{-1.35}$

##### Properties of Real Numbers

**Use the Commutative and Associative Properties**

In the following exercises, simplify.

$\mathrm{-32}\xb79\xb7\frac{5}{8}$

**Use the Properties of Identity, Inverse and Zero**

In the following exercises, simplify.

$\frac{4}{7}+\frac{8}{15}+\left(-\frac{4}{7}\right)$

$\frac{0}{x-3},x\ne 3$

**Simplify Expressions Using the Distributive Property**

In the following exercises, simplify using the Distributive Property.

$8\left(a-4\right)$

$18\xb7\frac{5}{6}\left(2x-5\right)$

$\mathrm{-4}\left(y-3\right)$

$6\left(3x-4\right)-\left(\mathrm{-5}\right)$