# 1.7E: Exercises

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$

## Practice Makes Perfect

Add and Subtract Fractions with a Common Denominator

##### Exercise $$\PageIndex{1}$$

$$\dfrac{6}{13}+\dfrac{5}{13}$$

$$\frac{11}{13}$$

##### Exercise $$\PageIndex{2}$$

$$\dfrac{ 4}{15}+ \dfrac{ 7}{15}$$

##### Exercise $$\PageIndex{3}$$

$$\dfrac{ x}{4}+ \dfrac{3}{4}$$

$$\frac{x+3}{4}$$

##### Exercise $$\PageIndex{4}$$

$$\dfrac{ 8}{q}+ \dfrac{6}{q}$$

##### Exercise $$\PageIndex{5}$$

$$-\dfrac{ 3}{16}+\left(− \dfrac{ 7}{16}\right)$$

$$-\frac{5}{8}$$

##### Exercise $$\PageIndex{6}$$

$$-\dfrac{ 5}{16}+\left(- \dfrac{ 9}{16}\right)$$

##### Exercise $$\PageIndex{7}$$

$$-\dfrac{ 8}{17}+ \dfrac{ 15}{17}$$

$$\frac{7}{17}$$

##### Exercise $$\PageIndex{8}$$

$$-\dfrac{ 9}{19}+ \dfrac{ 17}{19}$$

##### Exercise $$\PageIndex{9}$$

$$\dfrac{ 6}{13}+\left(- \dfrac{ 10}{13}\right)+\left(- \dfrac{ 12}{13}\right)$$

$$-\frac{16}{13}$$

##### Exercise $$\PageIndex{10}$$

$$\dfrac{ 5}{12}+\left(- \dfrac{ 7}{12}\right)+\left(- \dfrac{ 11}{12}\right)$$

In the following exercises, subtract.

##### Exercise $$\PageIndex{11}$$

$$\dfrac{ 11}{15}− \dfrac{ 7}{15}$$

$$\frac{4}{15}$$

##### Exercise $$\PageIndex{12}$$

$$\dfrac{ 9}{13}− \dfrac{ 4}{13}$$

##### Exercise $$\PageIndex{13}$$

$$\dfrac{ 11}{12}− \dfrac{ 5}{12}$$

$$\frac{1}{2}$$

##### Exercise $$\PageIndex{14}$$

$$\dfrac{ 7}{12}− \dfrac{ 5}{12}$$

##### Exercise $$\PageIndex{15}$$

$$\dfrac{ 19}{21}− \dfrac{ 4}{21}$$

$$\frac{5}{7}$$

##### Exercise $$\PageIndex{16}$$

$$\dfrac{ 17}{21}− \dfrac{ 8}{21}$$

##### Exercise $$\PageIndex{17}$$

$$\dfrac{ 5y}{8}− \dfrac{ 7}{8}$$

$$\frac{5y-7}{8}$$

##### Exercise $$\PageIndex{18}$$

$$\dfrac{ 11z}{13}− \dfrac{ 8}{13}$$

##### Exercise $$\PageIndex{19}$$

$$-\dfrac{ 23}{u}− \dfrac{ 15}{u}$$

$$-\frac{38}{u}$$

##### Exercise $$\PageIndex{20}$$

$$-\dfrac{ 29}{v}− \dfrac{ 26}{v}$$

##### Exercise $$\PageIndex{21}$$

$$-\dfrac{ 3}{5}−\left(- \dfrac{ 4}{5}\right)$$

$$\frac{1}{5}$$

##### Exercise $$\PageIndex{22}$$

$$-\dfrac{ 3}{7}−\left(- \dfrac{ 5}{7}\right)$$

##### Exercise $$\PageIndex{23}$$

$$-\dfrac{ 7}{9}−\left(- \dfrac{ 5}{9}\right)$$

$$-\frac{2}{9}$$

##### Exercise $$\PageIndex{24}$$

$$-\dfrac{ 8}{11}−\left(- \dfrac{ 5}{11}\right)$$

Mixed Practice

In the following exercises, simplify.

##### Exercise $$\PageIndex{25}$$

$$−\dfrac{5}{18}·\dfrac{9}{10}$$

$$-\frac{1}{4}$$

##### Exercise $$\PageIndex{26}$$

$$−\dfrac{3}{14}·\dfrac{7}{12}$$

##### Exercise $$\PageIndex{27}$$

$$\dfrac{n}{5}−\dfrac{4}{5}$$

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

##### Exercise $$\PageIndex{28}$$

$$\dfrac{6}{11}− \dfrac{s}{11}$$

##### Exercise $$\PageIndex{29}$$

$$−\dfrac{7}{24}+\dfrac{2}{24}$$

$$-frac{5}{24}$$

##### Exercise $$\PageIndex{30}$$

$$−\dfrac{5}{18}+\dfrac{1}{18}$$

##### Exercise $$\PageIndex{31}$$

$$\dfrac{8}{15}÷\dfrac{12}{5}$$

$$\frac{2}{9}$$

##### Exercise $$\PageIndex{32}$$

$$\dfrac{7}{12}÷\dfrac{9}{28}$$

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

##### Exercise $$\PageIndex{33}$$

$$\dfrac{1}{2}+\dfrac{1}{7}$$

$$\frac{9}{14}$$

##### Exercise $$\PageIndex{34}$$

$$\dfrac{1}{3}+\dfrac{1}{8}$$

##### Exercise $$\PageIndex{35}$$

$$\dfrac{1}{3}−\left(−\dfrac{1}{9}\right)$$

$$\frac{4}{9}$$

##### Exercise $$\PageIndex{36}$$

$$\dfrac{1}{4}−\left(−\dfrac{1}{8}\right)$$

##### Exercise $$\PageIndex{37}$$

$$\frac{7}{12} + \frac{5}{12}$$

$$\frac{29}{24}$$

##### Exercise $$\PageIndex{38}$$

$$\frac{5}{12}+\frac{3}{8}$$

##### Exercise $$\PageIndex{39}$$

$$\frac{7}{12}-\frac{9}{16}$$

$$\frac{1}{48}$$

##### Exercise $$\PageIndex{40}$$

$$\frac{7}{16}-\frac{5}{12}$$

##### Exercise $$\PageIndex{41}$$

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

$$\frac{7}{24}$$

##### Exercise $$\PageIndex{42}$$

$$\frac{5}{6}-\frac{3}{4}$$

##### Exercise $$\PageIndex{43}$$

$$−\frac{11}{30}+\frac{27}{40}$$

$$\frac{37}{120}$$

##### Exercise $$\PageIndex{44}$$

$$−\frac{9}{20}+\frac{17}{30}$$

##### Exercise $$\PageIndex{45}$$

$$-\frac{13}{30}+\frac{25}{42}$$

$$\frac{17}{105}$$

##### Exercise $$\PageIndex{46}$$

$$−\frac{23}{30}+\frac{5}{48}$$

##### Exercise $$\PageIndex{47}$$

$$−\frac{39}{56}−\frac{22}{35}$$

$$-\frac{53}{40}$$

##### Exercise $$\PageIndex{48}$$

$$−\frac{33}{49}−\frac{18}{35}$$

##### Exercise $$\PageIndex{49}$$

$$−\frac{2}{3}−(−\frac{3}{4})$$

$$\frac{1}{12}$$

##### Exercise $$\PageIndex{50}$$

$$−\frac{3}{4}−(−\frac{4}{5})$$

##### Exercise $$\PageIndex{51}$$

$$1+\frac{7}{8}$$

$$\frac{15}{8}$$

##### Exercise $$\PageIndex{52}$$

$$1−\frac{3}{10}$$

##### Exercise $$\PageIndex{53}$$

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

$$\frac{4x+3}{12}$$

##### Exercise $$\PageIndex{54}$$

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

##### Exercise $$\PageIndex{55}$$

$$\frac{y}{4}−\frac{3}{5}$$

$$\frac{5y-12}{20}$$

##### Exercise $$\PageIndex{56}$$

$$\frac{x}{5}−\frac{1}{4}$$

Mixed Practice

In the following exercises, simplify.

##### Exercise $$\PageIndex{57}$$
1. $$\frac{2}{3}+\frac{1}{6}$$
2. $$\frac{2}{3} \div \frac{1}{6}$$
1. $$\frac{5}{6}$$
2. $$4$$
##### Exercise $$\PageIndex{58}$$
1. $$-\frac{2}{5}-\frac{1}{8}$$
2. $$-\frac{2}{5} \cdot \frac{1}{8}$$
##### Exercise $$\PageIndex{59}$$
1. $$\frac{5 n}{6} \div \frac{8}{15}$$
2. $$\frac{5 n}{6}-\frac{8}{15}$$
1. $$\frac{25n}{16}$$
2. $$\frac{25n-16}{30}$$
##### Exercise $$\PageIndex{60}$$
1. $$\frac{3 a}{8} \div \frac{7}{12}$$
2. $$\frac{3 a}{8}-\frac{7}{12}$$
##### Exercise $$\PageIndex{61}$$

$$-\frac{3}{8} \div\left(-\frac{3}{10}\right)$$

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

##### Exercise $$\PageIndex{62}$$

$$-\frac{5}{12} \div\left(-\frac{5}{9}\right)$$

##### Exercise $$\PageIndex{63}$$

$$−\frac{3}{8}+\frac{5}{12}$$

$$\frac{1}{24}$$

##### Exercise $$\PageIndex{64}$$

$$−\frac{1}{8}+\frac{7}{12}$$

##### Exercise $$\PageIndex{65}$$

$$\frac{5}{6}−\frac{1}{9}$$

$$\frac{13}{18}$$

##### Exercise $$\PageIndex{66}$$

$$\frac{5}{9}−\frac{1}{6}$$

##### Exercise $$\PageIndex{67}$$

$$−\frac{7}{15}−\frac{y}{4}$$

$$\frac{-28-15y}{60}$$

##### Exercise $$\PageIndex{68}$$

$$−\frac{3}{8}−\frac{x}{11}$$

##### Exercise $$\PageIndex{69}$$

$$\frac{11}{12a} \cdot \frac{9a}{16}$$

$$\frac{33}{64}$$

##### Exercise $$\PageIndex{70}$$

$$\frac{10y}{13} \cdot \frac{8}{15y}$$

Use the Order of Operations to Simplify Complex Fractions

In the following exercises, simplify.

##### Exercise $$\PageIndex{71}$$

$$\frac{2^{3}+4^{2}}{\left(\frac{2}{3}\right)^{2}}$$

$$54$$

##### Exercise $$\PageIndex{72}$$

$$\frac{3^{3}-3^{2}}{\left(\frac{3}{4}\right)^{2}}$$

##### Exercise $$\PageIndex{73}$$

$$\frac{\left(\frac{3}{5}\right)^{2}}{\left(\frac{3}{7}\right)^{2}}$$

$$\frac{49}{25}$$

##### Exercise $$\PageIndex{74}$$

$$\frac{\left(\frac{3}{4}\right)^{2}}{\left(\frac{5}{8}\right)^{2}}$$

##### Exercise $$\PageIndex{75}$$

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

$$\frac{15}{4}$$

##### Exercise $$\PageIndex{76}$$

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

##### Exercise $$\PageIndex{77}$$

$$\frac{\frac{7}{8}-\frac{2}{3}}{\frac{1}{2}+\frac{3}{8}}$$

$$\frac{5}{21}$$

##### Exercise $$\PageIndex{78}$$

$$\frac{\frac{3}{4}-\frac{3}{5}}{\frac{1}{4}+\frac{2}{5}}$$

##### Exercise $$\PageIndex{79}$$

$$\frac{1}{2}+\frac{2}{3} \cdot \frac{5}{12}$$

$$\frac{7}{9}$$

##### Exercise $$\PageIndex{80}$$

$$\frac{1}{3}+\frac{2}{5} \cdot \frac{3}{4}$$

##### Exercise $$\PageIndex{81}$$

$$1-\frac{3}{5} \div \frac{1}{10}$$

$$-5$$

##### Exercise $$\PageIndex{82}$$

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

##### Exercise $$\PageIndex{83}$$

$$\frac{2}{3}+\frac{1}{6}+\frac{3}{4}$$

$$\frac{19}{12}$$

##### Exercise $$\PageIndex{84}$$

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

##### Exercise $$\PageIndex{85}$$

$$\frac{3}{8}−\frac{1}{6}+\frac{3}{4}$$

$$\frac{23}{24}$$

##### Exercise $$\PageIndex{86}$$

$$\frac{2}{5}+\frac{5}{8}−\frac{3}{4}$$

##### Exercise $$\PageIndex{87}$$

$$12\left(\frac{9}{20}-\frac{4}{15}\right)$$

$$\frac{11}{5}$$

##### Exercise $$\PageIndex{88}$$

$$8\left(\frac{15}{16}-\frac{5}{6}\right)$$

##### Exercise $$\PageIndex{89}$$

$$\frac{\frac{5}{8}+\frac{1}{6}}{\frac{19}{24}}$$

$$1$$

##### Exercise $$\PageIndex{90}$$

$$\frac{\frac{1}{6}+\frac{3}{10}}{\frac{14}{30}}$$

##### Exercise $$\PageIndex{91}$$

$$\left(\frac{5}{9}+\frac{1}{6}\right) \div\left(\frac{2}{3}-\frac{1}{2}\right)$$

$$\frac{13}{3}$$

##### Exercise $$\PageIndex{92}$$

$$\left(\frac{3}{4}+\frac{1}{6}\right) \div\left(\frac{5}{8}-\frac{1}{3}\right)$$

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

##### Exercise $$\PageIndex{93}$$

$$x+\left(-\frac{5}{6}\right) \text { when }$$

1. $$x = \frac{1}{3}$$
2. $$x=-\frac{1}{6}$$
1. $$-\frac{1}{2}$$
2. $$-1$$
##### Exercise $$\PageIndex{94}$$

$$x+\left(-\frac{11}{12}\right) \text { when }$$

1. $$x = \frac{11}{12}$$
2. $$x=-\frac{3}{4}$$
##### Exercise $$\PageIndex{95}$$

$$x - \frac{2}{5} \text { when }$$

1. $$x = \frac{3}{5}$$
2. $$x=-\frac{3}{5}$$
1. $$\frac{1}{5}$$
2. $$-1$$
##### Exercise $$\PageIndex{96}$$

$$x-\frac{1}{3} \text { when }$$

1. $$x=\frac{2}{3}$$
2. $$x=-\frac{2}{3}$$
##### Exercise $$\PageIndex{97}$$

$$\frac{7}{10}-w \text { when }$$

1. $$w=\frac{1}{2}$$
2. $$w=-\frac{1}{2}$$
1. $$\frac{1}{5}$$
2. $$\frac{6}{5}$$
##### Exercise $$\PageIndex{98}$$

$$\frac{5}{12}-w \text { when }$$

1. $$w=\frac{1}{4}$$
2. $$w=-\frac{1}{4}$$
##### Exercise $$\PageIndex{99}$$

$$2 x^{2} y^{3} \text { when } x=-\frac{2}{3} \text { and } y=-\frac{1}{2}$$

$$-\frac{1}{9}$$
##### Exercise $$\PageIndex{100}$$

$$8 u^{2} v^{3} \text { when } u=-\frac{3}{4} \text { and } v=-\frac{1}{2}$$

##### Exercise $$\PageIndex{101}$$

$$\frac{a+b}{a-b} \text { when } a=-3, b=8$$

$$-\frac{5}{11}$$
##### Exercise $$\PageIndex{102}$$

$$\frac{r-s}{r+s} \text { when } r=10, s=-5$$

## Everyday Math

##### Exercise $$\PageIndex{103}$$

Decorating Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs $$\frac{1}{2}$$ yard of print fabric and \frac{3}{8}\) yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?

$$\frac{7}{8}$$ yard

##### Exercise $$\PageIndex{104}$$

Baking Vanessa is baking chocolate chip cookies and oatmeal cookies. She needs $$\frac{1}{2}$$ cup of sugar for the chocolate chip cookies and $$\frac{1}{4}$$ of sugar for the oatmeal cookies. How much sugar does she need altogether?

## Writing Exercises

##### Exercise $$\PageIndex{105}$$

Why do you need a common denominator to add or subtract fractions? Explain.

##### Exercise $$\PageIndex{106}$$

How do you find the LCD of 2 fractions?

## Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After looking at the checklist, do you think you are well-prepared for the next chapter? Why or why not?

1.7E: Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.