# 1.7E: Exercises

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• OpenStax
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## 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?

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