5.10.1: Review Exercises

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Review Exercises

Decimals

Name Decimals

In the following exercises, name each decimal.

534.

$0.8$

535.

$0.375$

536.

$0.007$

537.

$5.24$

538.

$−12.5632$

539.

$−4.09$

Write Decimals

In the following exercises, write as a decimal.

540.

three tenths

541.

nine hundredths

542.

twenty-seven hundredths

543.

ten and thirty-five thousandths

544.

negative twenty and three tenths

545.

negative five hundredths

Convert Decimals to Fractions or Mixed Numbers

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

546.

$0.43$

547.

$0.825$

548.

$9.7$

549.

$3.64$

Locate Decimals on the Number Line

550.

ⓐ $0.6$

ⓑ $−0.9$

ⓓ $−1.3$

Order Decimals

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

551.

$0.6___0.8$

552.

$0.2___0.15$

553.

$0.803____0.83$

554.

$−0.56____−0.562$

Round Decimals

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

555.

$12.529$

556.

$4.8447$

557.

$5.897$

Decimal Operations

Add and Subtract Decimals

In the following exercises, add or subtract.

558.

$5.75 + 8.46$

559.

$32.89 - 8.22$

560.

$24 - 19.31$

561.

$10.2 + 14.631$

562.

$−6.4 + (−2.9)$

563.

$1.83 - 4.2$

Multiply Decimals

In the following exercises, multiply.

564.

$(0.3) (0.7)$

565.

$(−6.4) (0.25)$

566.

$(−3.35) (−12.7)$

567.

$(15.4) (1000)$

Divide Decimals

In the following exercises, divide.

568.

$0.48 \div 6$

569.

$4.32 \div 24$

570.

$$6.29 \div 12$

571.

$(−0.8) \div (−0.2)$

572.

$1.65 \div 0.15$

573.

$9 \div 0.045$

Use Decimals in Money Applications

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

574.

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

575.

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

576.

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

577.

Alice bought a roll of paper towels that cost $$2.49.$ She had a coupon for $$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.

578.

$\frac{3}{5}$

579.

$\frac{7}{8}$

580.

$- \frac{19}{20}$

581.

$- \frac{21}{4}$

582.

$\frac{1}{3}$

583.

$\frac{6}{11}$

Order Decimals and Fractions

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

584.

$\frac{1}{2}___0.2$

585.

$\frac{3}{5}___0 .$

586.

$- \frac{7}{8}___−0.84$

587.

$- \frac{5}{12}___−0.42$

588.

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

589.

$0.33___\frac{5}{16}$

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

590.

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

591.

$\frac{7}{9}, 0.75, \frac{11}{15}$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify

592.

$4 (10.3 - 5.8)$

593.

$\frac{3}{4} (15.44 - 7.4)$

594.

$30 \div (0.45 + 0.15)$

595.

$1.6 + \frac{3}{8}$

596.

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

597.

$- \frac{2}{5} \cdot \frac{9}{10} + 0.14$

Find the Circumference and Area of Circles

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

598.

$radius = 6 in.$

599.

$radius = 3.5 ft.$

600.

$radius = \frac{7}{33} m$

601.

$diameter = 11 cm$

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.

602.

$x - 0.4 = 2.1$
ⓐ $x = 1.7$ ⓑ $x = 2.5$

603.

$y + 3.2 = −1.5$
ⓐ $y = 1.7$ ⓑ $y = −4.7$

604.

$\frac{u}{2.5} = −12.5$
ⓐ $u = −5$ ⓑ $u = −31.25$

605.

$0.45 v = −40.5$
ⓐ $v = −18.225$ ⓑ $v = −90$

Solve Equations with Decimals

In the following exercises, solve.

606.

$m + 3.8 = 7.5$

607.

$h + 5.91 = 2.4$

608.

$a + 2.26 = −1.1$

609.

$p - 4.3 = −1.65$

610.

$x - 0.24 = −8.6$

611.

$j - 7.42 = −3.7$

612.

$0.6 p = 13.2$

613.

$−8.6 x = 34.4$

614.

$−22.32 = −2.4 z$

615.

$\frac{a}{0.3} = −24$

616.

$\frac{p}{−7} = −4.2$

617.

$\frac{s}{−2.5} = −10$

Translate to an Equation and Solve

In the following exercises, translate and solve.

618.

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

619.

The product of $−5.9$ and $x$ is $−3.54 .$

620.

The quotient of $y$ and $−1.8$ is $−9 .$

621.

The sum of $m$ and $(−4.03)$ is $6.8 .$

Averages and Probability

Find the Mean of a Set of Numbers

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

622.

$2, 4, 1, 0, 1, and 1$

623.

$$270$ , $$310.50$ , $$243.75$ , and $$252.15$

624.

Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited $3, 0, 8, 1, and 8$ minutes. Find the mean.

625.

In the last three months, Raul’s water bills were $$31.45, $48.76, and $42.60 .$ Find the mean.

Find the Median of a Set of Numbers

In the following exercises, find the median.

626.

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

627.

$25$ , $23$ , $24$ , $26$ , $29$ , $19$ , $18$ , $32$

628.

The ages of the eight men in Jerry’s model train club are $52, 63, 45, 51, 55, 75, 60, and 59 .$ Find the median age.

629.

The number of clients at Miranda’s beauty salon each weekday last week were $18, 7, 12, 16, and 20 .$ Find the median number of clients.

Find the Mode of a Set of Numbers

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

630.

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

631.

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.)

632.

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.

633.

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.

634.

$28$ to $40$

635.

$56$ to $32$

636.

$3.5$ to $0.5$

637.

$1.2$ to $1.8$

638.

$1 \frac{3}{4} to 1 \frac{5}{8}$

639.

$2 \frac{1}{3} to 5 \frac{1}{4}$

640.

$64$ ounces to $30$ ounces

641.

$28$ inches to $3$ feet

Write a Rate as a Fraction

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

642.

$180$ calories per $8$ ounces

643.

$90$ pounds per $7.5$ square inches

644.

$126$ miles in $4$ hours

645.

$$612.50$ for $35$ hours

Find Unit Rates

In the following exercises, find the unit rate.

646.

$180$ calories per $8$ ounces

647.

$90$ pounds per $7.5$ square inches

648.

$126$ miles in $4$ hours

649.

$$612.50$ for $35$ hours

Find Unit Price

In the following exercises, find the unit price.

650.

t-shirts: $3$ for $$8.97$

651.

Highlighters: $6$ for $$2.52$

652.

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

653.

Anna bought a pack of $8$ kitchen towels for $$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.

654.

Shampoo: $12$ ounces for $$4.29$ or $22$ ounces for $$7.29 ?$

655.

Vitamins: $60$ tablets for $$6.49$ or $100$ for $$11.99 ?$

Translate Phrases to Expressions with Fractions

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

656.

$535$ miles per $h hours$

657.

$a$ adults to $45$ children

658.

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

659.

the ratio of $19$ and the sum of $3$ and $n$

Simplify and Use Square Roots

Simplify Expressions with Square Roots

In the following exercises, simplify.

660.

$\sqrt{64}$

661.

$\sqrt{144}$

662.

$- \sqrt{25}$

663.

$- \sqrt{81}$

664.

$\sqrt{−9}$

665.

$\sqrt{−36}$

666.

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

667.

$\sqrt{64 + 225}$

Estimate Square Roots

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

668.

$\sqrt{28}$

669.

$\sqrt{155}$

Approximate Square Roots

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

670.

$\sqrt{15}$

671.

$\sqrt{57}$

Simplify Variable Expressions with Square Roots

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

672.

$\sqrt{q^{2}}$

673.

$\sqrt{64 b^{2}}$

674.

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

675.

$\sqrt{225 m^{2} n^{2}}$

676.

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

677.

$\sqrt{49 y^{2}}$

678.

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

679.

$\sqrt{121 c^{2} d^{2}}$

Use Square Roots in Applications

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

680.

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?

681.

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?

682.

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?

683.

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?

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