4.10.1: Review Exercises

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Review Exercises

Visualize Fractions

In the following exercises, name the fraction of each figure that is shaded.

574.

$A circle is shown. It is divided into 8 equal pieces. 5 pieces are shaded.$

575.

$A square is shown. It is divided into 9 equal pieces. 5 pieces are shaded.$

In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.

576.

$Two squares are shown. Both are divided into four equal pieces. The square on the left has all 4 pieces shaded. The square on the right has one piece shaded.$

577.

$Two circles are shown. Both are divided into two equal pieces. The circle on the left has both pieces shaded. The circle on the right has one piece shaded.$

In the following exercises, convert the improper fraction to a mixed number.

578.

$\frac{58}{15}$

579.

$\frac{63}{11}$

In the following exercises, convert the mixed number to an improper fraction.

580.

$12 \frac{1}{4}$

581.

$9 \frac{4}{5}$

582.

Find three fractions equivalent to $\frac{2}{5} .$ Show your work, using figures or algebra.

583.

Find three fractions equivalent to $- \frac{4}{3} .$ Show your work, using figures or algebra.

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

584.

$\frac{5}{8}, \frac{4}{3}, 3 \frac{3}{4}, 4$

585.

$\frac{1}{4}, - \frac{1}{4}, 1 \frac{1}{3}, −1 \frac{1}{3}, \frac{7}{2}, - \frac{7}{2}$

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

586.

$−1___- \frac{2}{5}$

587.

$−2 \frac{1}{2}___−3$

Multiply and Divide Fractions

In the following exercises, simplify.

588.

$- \frac{63}{84}$

589.

$- \frac{90}{120}$

590.

$- \frac{14 a}{14 b}$

591.

$- \frac{8 x}{8 y}$

In the following exercises, multiply.

592.

$\frac{2}{5} \cdot \frac{8}{13}$

593.

$- \frac{1}{3} \cdot \frac{12}{7}$

594.

$\frac{2}{9} \cdot (- \frac{45}{32})$

595.

$6 m \cdot \frac{4}{11}$

596.

$- \frac{1}{4} (−32)$

597.

$\frac{16}{5} \cdot \frac{15}{8}$

In the following exercises, find the reciprocal.

598.

$\frac{2}{9}$

599.

$\frac{15}{4}$

600.

$3$

601.

$- \frac{1}{4}$

602.

Fill in the chart.

	Opposite	Absolute Value	Reciprocal
$- \frac{5}{13}$
$\frac{3}{10}$
$\frac{9}{4}$
$−12$

In the following exercises, divide.

603.

$\frac{2}{3} \div \frac{1}{6}$

604.

$(- \frac{3 x}{5}) \div (- \frac{2 y}{3})$

605.

$\frac{4}{5} \div 3$

606.

$8 \div \frac{8}{3}$

607.

$\frac{5}{18} \div (- \frac{b}{9})$

Multiply and Divide Mixed Numbers and Complex Fractions

In the following exercises, perform the indicated operation.

608.

$3 \frac{1}{5} \cdot 1 \frac{7}{8}$

609.

$−5 \frac{7}{12} \cdot 4 \frac{4}{11}$

610.

$8 \div 2 \frac{2}{3}$

611.

$8 \frac{2}{3} \div 1 \frac{1}{12}$

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

612.

the quotient of $8$ and $y$

613.

the quotient of $V$ and the difference of $h$ and $6$

In the following exercises, simplify the complex fraction

614.

$\frac{\frac{5}{8}}{\frac{4}{5}}$

615.

$\frac{\frac{8}{9}}{−4}$

616.

$\frac{\frac{n}{4}}{\frac{3}{8}}$

617.

$\frac{−1 \frac{5}{6}}{- \frac{1}{12}}$

In the following exercises, simplify.

618.

$\frac{5 + 16}{5}$

619.

$\frac{8 \cdot 4 - 5^{2}}{3 \cdot 12}$

620.

$\frac{8 \cdot 7 + 5 (8 - 10)}{9 \cdot 3 - 6 \cdot 4}$

Add and Subtract Fractions with Common Denominators

In the following exercises, add.

621.

$\frac{3}{8} + \frac{2}{8}$

622.

$\frac{4}{5} + \frac{1}{5}$

623.

$\frac{2}{5} + \frac{1}{5}$

624.

$\frac{15}{32} + \frac{9}{32}$

625.

$\frac{x}{10} + \frac{7}{10}$

In the following exercises, subtract.

626.

$\frac{8}{11} - \frac{6}{11}$

627.

$\frac{11}{12} - \frac{5}{12}$

628.

$\frac{4}{5} - \frac{y}{5}$

629.

$- \frac{31}{30} - \frac{7}{30}$

630.

$\frac{3}{2} - (\frac{3}{2})$

631.

$\frac{11}{15} - \frac{5}{15} - (- \frac{2}{15})$

Add and Subtract Fractions with Different Denominators

In the following exercises, find the least common denominator.

632.

$\frac{1}{3}$ and $\frac{1}{12}$

633.

$\frac{1}{3}$ and $\frac{4}{5}$

634.

$\frac{8}{15}$ and $\frac{11}{20}$

635.

$\frac{3}{4}, \frac{1}{6},$ and $\frac{5}{10}$

In the following exercises, change to equivalent fractions using the given LCD.

636.

$\frac{1}{3}$ and $\frac{1}{5},$ LCD $= 15$

637.

$\frac{3}{8}$ and $\frac{5}{6},$ LCD $= 24$

638.

$- \frac{9}{16}$ and $\frac{5}{12},$ LCD $= 48$

639.

$\frac{1}{3}, \frac{3}{4}$ and $\frac{4}{5},$ LCD $= 60$

In the following exercises, perform the indicated operations and simplify.

640.

$\frac{1}{5} + \frac{2}{3}$

641.

$\frac{11}{12} - \frac{2}{3}$

642.

$- \frac{9}{10} - \frac{3}{4}$

643.

$- \frac{11}{36} - \frac{11}{20}$

644.

$- \frac{22}{25} + \frac{9}{40}$

645.

$\frac{y}{10} - \frac{1}{3}$

646.

$\frac{2}{5} + (- \frac{5}{9})$

647.

$\frac{4}{11} \div \frac{2}{7 d}$

648.

$\frac{2}{5} + (- \frac{3 n}{8}) (- \frac{2}{9 n})$

649.

$\frac{{(\frac{2}{3})}^{2}}{{(\frac{5}{8})}^{2}}$

650.

$(\frac{11}{12} + \frac{3}{8}) \div (\frac{5}{6} - \frac{1}{10})$

In the following exercises, evaluate.

651.

$y - \frac{4}{5}$ when

ⓐ $y = - \frac{4}{5}$
ⓑ $y = \frac{1}{4}$

652.

$6 m n^{2}$ when $m = \frac{3}{4}$ and $n = - \frac{1}{3}$

Add and Subtract Mixed Numbers

In the following exercises, perform the indicated operation.

653.

$4 \frac{1}{3} + 9 \frac{1}{3}$

654.

$6 \frac{2}{5} + 7 \frac{3}{5}$

655.

$5 \frac{8}{11} + 2 \frac{4}{11}$

656.

$3 \frac{5}{8} + 3 \frac{7}{8}$

657.

$9 \frac{13}{20} - 4 \frac{11}{20}$

658.

$2 \frac{3}{10} - 1 \frac{9}{10}$

659.

$2 \frac{11}{12} - 1 \frac{7}{12}$

660.

$8 \frac{6}{11} - 2 \frac{9}{11}$

Solve Equations with Fractions

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

661.

$x - \frac{1}{2} = \frac{1}{6}$ :

ⓐ $x = 1$
ⓑ $x = \frac{2}{3}$

662.

$y + \frac{3}{5} = \frac{5}{9}$ :

ⓐ $y = \frac{1}{2}$
ⓑ $y = \frac{52}{45}$

In the following exercises, solve the equation.

663.

$n + \frac{9}{11} = \frac{4}{11}$

664.

$x - \frac{1}{6} = \frac{7}{6}$

665.

$h - (- \frac{7}{8}) = - \frac{2}{5}$

666.

$\frac{x}{5} = −10$

667.

$- z = 23$

In the following exercises, translate and solve.

668.

The sum of two-thirds and $n$ is $- \frac{3}{5} .$

669.

The difference of $q$ and one-tenth is $\frac{1}{2} .$

670.

The quotient of $p$ and $−4$ is $−8 .$

671.

Three-eighths of $y$ is $24 .$

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Review Exercises

Visualize Fractions