### Review Exercises

## Decimals

**Name Decimals**

In the following exercises, name each decimal.

$0.8$

$0.007$

$\mathrm{-12.5632}$

**Write Decimals**

In the following exercises, write as a decimal.

three tenths

twenty-seven hundredths

negative twenty and three tenths

**Convert Decimals to Fractions or Mixed Numbers**

In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.

$0.43$

$9.7$

**Locate Decimals on the Number Line**

ⓐ $\phantom{\rule{0.2em}{0ex}}0.6$

ⓑ $\phantom{\rule{0.2em}{0ex}}\mathrm{-0.9}$

ⓒ $\phantom{\rule{0.2em}{0ex}}2.2$

ⓓ $\phantom{\rule{0.2em}{0ex}}\mathrm{-1.3}$

**Order Decimals**

In the following exercises, order each of the following pairs of numbers, using $<$ or $\text{>.}$

$0.2\_\_\_0.15$

$\mathrm{-0.56}\_\_\_\_\mathrm{-0.562}$

**Round Decimals**

In the following exercises, round each number to the nearest: ⓐ hundredth ⓑ tenth ⓒ whole number.

$4.8447$

## Decimal Operations

**Add and Subtract Decimals**

In the following exercises, add or subtract.

$5.75+8.46$

$24-19.31$

$\mathrm{-6.4}+(\mathrm{-2.9})$

**Multiply Decimals**

In the following exercises, multiply.

$(0.3)(0.7)$

$(\mathrm{-3.35})(\mathrm{-12.7})$

**Divide Decimals**

In the following exercises, divide.

$0.48\xf76$

$\text{\$6.29}\xf712$

$1.65\xf70.15$

**Use Decimals in Money Applications**

In the following exercises, use the strategy for applications to solve.

Miranda got $\text{\$40}$ from her ATM. She spent $\text{\$9.32}$ on lunch and $\text{\$16.99}$ on a book. How much money did she have left? Round to the nearest cent if necessary.

Jessie put $8$ gallons of gas in her car. One gallon of gas costs $\text{\$3.528.}$ How much did Jessie owe for all the gas?

A pack of $16$ water bottles cost $\text{\$6.72.}$ How much did each bottle cost?

Alice bought a roll of paper towels that cost $\text{\$2.49.}$ She had a coupon for $\text{\$0.35}$ off, and the store doubled the coupon. How much did Alice pay for the paper towels?

## Decimals and Fractions

**Convert Fractions to Decimals**

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

$\frac{3}{5}$

$-\frac{19}{20}$

$\frac{1}{3}$

**Order Decimals and Fractions**

In the following exercises, order each pair of numbers, using $<$ or $\text{>.}$

$\frac{1}{2}\_\_\_0.2$

$-\frac{7}{8}\_\_\_\mathrm{-0.84}$

$0.625\_\_\_\frac{13}{20}$

In the following exercises, write each set of numbers in order from least to greatest.

$\frac{2}{3},\frac{17}{20},0.65$

**Simplify Expressions Using the Order of Operations**

In the following exercises, simplify

$4(10.3-5.8)$

$30\xf7(0.45+0.15)$

$52(0.5)+{(0.4)}^{2}$

**Find the Circumference and Area of Circles**

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle.

$\text{radius}=\text{6 in.}$

$\text{radius}=\frac{7}{33}\phantom{\rule{0.2em}{0ex}}\text{m}$

## Solve Equations with Decimals

**Determine Whether a Decimal is a Solution of an Equation**

In the following exercises, determine whether the each number is a solution of the given equation.

$x-0.4=2.1\phantom{\rule{1em}{0ex}}$

ⓐ $\phantom{\rule{0.2em}{0ex}}x=1.7\phantom{\rule{0.2em}{0ex}}$ ⓑ $\phantom{\rule{0.2em}{0ex}}x=2.5$

$y+3.2=\mathrm{-1.5}\phantom{\rule{1em}{0ex}}$

ⓐ $\phantom{\rule{0.2em}{0ex}}y=1.7\phantom{\rule{0.2em}{0ex}}$ⓑ $\phantom{\rule{0.2em}{0ex}}y=\mathrm{-4.7}$

$\frac{u}{2.5}=\mathrm{-12.5}\phantom{\rule{1em}{0ex}}$

ⓐ $\phantom{\rule{0.2em}{0ex}}u=\mathrm{-5}\phantom{\rule{0.2em}{0ex}}$ⓑ $\phantom{\rule{0.2em}{0ex}}u=\mathrm{-31.25}$

$0.45v=\mathrm{-40.5}\phantom{\rule{1em}{0ex}}$

ⓐ $\phantom{\rule{0.2em}{0ex}}v=\mathrm{-18.225}\phantom{\rule{0.2em}{0ex}}$ⓑ $\phantom{\rule{0.2em}{0ex}}v=\mathrm{-90}$

**Solve Equations with Decimals**

In the following exercises, solve.

$m+3.8=7.5$

$a+2.26=\mathrm{-1.1}$

$x-0.24=\mathrm{-8.6}$

$0.6p=13.2$

$\mathrm{-22.32}=\mathrm{-2.4}z$

$\frac{p}{\mathrm{-7}}=\mathrm{-4.2}$

**Translate to an Equation and Solve**

In the following exercises, translate and solve.

The difference of $n$ and $15.2$ is $4.4.$

The quotient of $y$ and $\mathrm{-1.8}$ is $\mathrm{-9}.$

## Averages and Probability

**Find the Mean of a Set of Numbers**

In the following exercises, find the mean of the numbers.

$2,4,1,0,1,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}1$

Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited $3,0,8,1,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}8$ minutes. Find the mean.

In the last three months, Raul’s water bills were $\text{\$31.45},\phantom{\rule{0.2em}{0ex}}\text{\$48.76},\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}\text{\$42.60}.$ Find the mean.

**Find the Median of a Set of Numbers**

In the following exercises, find the median.

$41$, $45$, $32$, $60$, $58$

The ages of the eight men in Jerry’s model train club are $52,63,45,51,55,75,60,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}59.$ Find the median age.

The number of clients at Miranda’s beauty salon each weekday last week were $18,7,12,16,\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}20.$ Find the median number of clients.

**Find the Mode of a Set of Numbers**

In the following exercises, identify the mode of the numbers.

$6$, $4$, $4,5$, $6,6$, $4$, $4$, $4$, $3$, $5$

The number of siblings of a group of students: $2$, $0$, $3$, $2$, $4$, $1$, $6$, $5$, $4$, $1$, $2$, $3$

**Use the Basic Definition of Probability**

In the following exercises, solve. (Round decimals to three places.)

The Sustainability Club sells $200$ tickets to a raffle, and Albert buys one ticket. One ticket will be selected at random to win the grand prize. Find the probability Albert will win the grand prize. Express your answer as a fraction and as a decimal.

Luc has to read $3$ novels and $12$ short stories for his literature class. The professor will choose one reading at random for the final exam. Find the probability that the professor will choose a novel for the final exam. Express your answer as a fraction and as a decimal.

## Ratios and Rate

**Write a Ratio as a Fraction**

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

$28$ to $40$

$3.5$ to $0.5$

$1\frac{3}{4}\phantom{\rule{0.2em}{0ex}}\text{to}\phantom{\rule{0.2em}{0ex}}1\frac{5}{8}$

$64$ ounces to $30$ ounces

**Write a Rate as a Fraction**

In the following exercises, write each rate as a fraction. Simplify the answer if possible.

$180$ calories per $8$ ounces

$126$ miles in $4$ hours

**Find Unit Rates**

In the following exercises, find the unit rate.

$180$ calories per $8$ ounces

$126$ miles in $4$ hours

**Find Unit Price**

In the following exercises, find the unit price.

t-shirts: $3$ for $\text{\$8.97}$

An office supply store sells a box of pens for $\text{\$11}.$ The box contains $12$ pens. How much does each pen cost?

Anna bought a pack of $8$ kitchen towels for $\text{\$13.20}.$ How much did each towel cost? Round to the nearest cent if necessary.

In the following exercises, find each unit price and then determine the better buy.

Shampoo: $12$ ounces for $\text{\$4.29}$ or $22$ ounces for $\text{\$7.29}?$

**Translate Phrases to Expressions with Fractions**

In the following exercises, translate the English phrase into an algebraic expression.

$535$ miles per $h\phantom{\rule{0.2em}{0ex}}\text{hours}$

the ratio of $4y$ and the difference of $x$ and $10$

## Simplify and Use Square Roots

**Simplify Expressions with Square Roots**

In the following exercises, simplify.

$\sqrt{64}$

$-\sqrt{25}$

$\sqrt{\mathrm{-9}}$

$\sqrt{64}+\sqrt{225}$

**Estimate Square Roots**

In the following exercises, estimate each square root between two consecutive whole numbers.

$\sqrt{28}$

**Approximate Square Roots**

In the following exercises, approximate each square root and round to two decimal places.

$\sqrt{15}$

**Simplify Variable Expressions with Square Roots**

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{{q}^{2}}$

$-\sqrt{121{a}^{2}}$

$-\sqrt{100{q}^{2}}$

$\sqrt{4{a}^{2}{b}^{2}}$

**Use Square Roots in Applications**

In the following exercises, solve. Round to one decimal place.

**Art** Diego has $225$ square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?

**Landscaping** Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of $30$ square feet. How long can a side of the flower garden be?

**Gravity** A hiker dropped a granola bar from a lookout spot $576$ feet above a valley. How long did it take the granola bar to reach the valley floor?

**Accident investigation** The skid marks of a car involved in an accident were $216$ feet. How fast had the car been going before applying the brakes?