1.5E: Exercises

Practice Makes Perfect

Add and Subtract Fractions with a Common Denominator

In the following exercises, add.

Exercise $\PageIndex{1}$

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

Answer

$\frac{11}{13}$

Exercise $\PageIndex{2}$

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

Exercise $\PageIndex{3}$

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

Answer

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

Exercise $\PageIndex{4}$

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

Exercise $\PageIndex{5}$

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

Answer

$-\frac{5}{8}$

Exercise $\PageIndex{6}$

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

Exercise $\PageIndex{7}$

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

Answer

$\frac{7}{17}$

Exercise $\PageIndex{8}$

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

Exercise $\PageIndex{9}$

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

Answer

$-\frac{16}{13}$

Exercise $\PageIndex{10}$

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

In the following exercises, subtract.

Exercise $\PageIndex{11}$

$\dfrac{ 11}{15}− \dfrac{ 7}{15}$

Answer

$\frac{4}{15}$

Exercise $\PageIndex{12}$

$\dfrac{ 9}{13}− \dfrac{ 4}{13}$

Exercise $\PageIndex{13}$

$\dfrac{ 11}{12}− \dfrac{ 5}{12}$

Answer

$\frac{1}{2}$

Exercise $\PageIndex{14}$

$\dfrac{ 7}{12}− \dfrac{ 5}{12}$

Exercise $\PageIndex{15}$

$\dfrac{ 19}{21}− \dfrac{ 4}{21}$

Answer

$\frac{5}{7}$

Exercise $\PageIndex{16}$

$\dfrac{ 17}{21}− \dfrac{ 8}{21}$

Exercise $\PageIndex{17}$

$\dfrac{ 5y}{8}− \dfrac{ 7}{8}$

Answer

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

Exercise $\PageIndex{18}$

$\dfrac{ 11z}{13}− \dfrac{ 8}{13}$

Exercise $\PageIndex{19}$

$-\dfrac{ 23}{u}− \dfrac{ 15}{u}$

Answer

$-\frac{38}{u}$

Exercise $\PageIndex{20}$

$-\dfrac{ 29}{v}− \dfrac{ 26}{v}$

Exercise $\PageIndex{21}$

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

Answer

$\frac{1}{5}$

Exercise $\PageIndex{22}$

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

Exercise $\PageIndex{23}$

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

Answer

$-\frac{2}{9}$

Exercise $\PageIndex{24}$

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

Mixed Practice

In the following exercises, simplify.

Exercise $\PageIndex{25}$

$−\dfrac{5}{18}·\dfrac{9}{10}$

Answer

$-\frac{1}{4}$

Exercise $\PageIndex{26}$

$−\dfrac{3}{14}·\dfrac{7}{12}$

Exercise $\PageIndex{27}$

$\dfrac{n}{5}−\dfrac{4}{5}$

Answer

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

Exercise $\PageIndex{28}$

$\dfrac{6}{11}− \dfrac{s}{11}$

Exercise $\PageIndex{29}$

$−\dfrac{7}{24}+\dfrac{2}{24}$

Answer

$-frac{5}{24}$

Exercise $\PageIndex{30}$

$−\dfrac{5}{18}+\dfrac{1}{18}$

Exercise $\PageIndex{31}$

$\dfrac{8}{15}÷\dfrac{12}{5}$

Answer

$\frac{2}{9}$

Exercise $\PageIndex{32}$

$\dfrac{7}{12}÷\dfrac{9}{28}$

Add or Subtract Fractions with Different Denominators

In the following exercises, add or subtract.

Exercise $\PageIndex{33}$

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

Answer

$\frac{9}{14}$

Exercise $\PageIndex{34}$

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

Exercise $\PageIndex{35}$

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

Answer

$\frac{4}{9}$

Exercise $\PageIndex{36}$

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

Exercise $\PageIndex{37}$

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

Answer

$\frac{29}{24}$

Exercise $\PageIndex{38}$

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

Exercise $\PageIndex{39}$

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

Answer

$\frac{1}{48}$

Exercise $\PageIndex{40}$

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

Exercise $\PageIndex{41}$

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

Answer

$\frac{7}{24}$

Exercise $\PageIndex{42}$

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

Exercise $\PageIndex{43}$

$−\frac{11}{30}+\frac{27}{40}$

Answer

$\frac{37}{120}$

Exercise $\PageIndex{44}$

$−\frac{9}{20}+\frac{17}{30}$

Exercise $\PageIndex{45}$

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

Answer

$\frac{17}{105}$

Exercise $\PageIndex{46}$

$−\frac{23}{30}+\frac{5}{48}$

Exercise $\PageIndex{47}$

$−\frac{39}{56}−\frac{22}{35}$

Answer

$-\frac{53}{40}$

Exercise $\PageIndex{48}$

$−\frac{33}{49}−\frac{18}{35}$

Exercise $\PageIndex{49}$

$−\frac{2}{3}−(−\frac{3}{4})$

Answer

$\frac{1}{12}$

Exercise $\PageIndex{50}$

$−\frac{3}{4}−(−\frac{4}{5})$

Exercise $\PageIndex{51}$

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

Answer

$\frac{15}{8}$

Exercise $\PageIndex{52}$

$1−\frac{3}{10}$

Exercise $\PageIndex{53}$

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

Answer

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

Exercise $\PageIndex{54}$

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

Exercise $\PageIndex{55}$

$\frac{y}{4}−\frac{3}{5}$

Answer

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

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

Answer

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. $\frac{5 n}{6}-\frac{8}{15}$

Answer

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 $\PageIndex{61}$

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

Answer

$\frac{5}{4}$

Exercise $\PageIndex{62}$

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

Exercise $\PageIndex{63}$

$−\frac{3}{8}+\frac{5}{12}$

Answer

$\frac{1}{24}$

Exercise $\PageIndex{64}$

$−\frac{1}{8}+\frac{7}{12}$

Exercise $\PageIndex{65}$

$\frac{5}{6}−\frac{1}{9}$

Answer

$\frac{13}{18}$

Exercise $\PageIndex{66}$

$\frac{5}{9}−\frac{1}{6}$

Exercise $\PageIndex{67}$

$−\frac{7}{15}−\frac{y}{4}$

Answer

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

Exercise $\PageIndex{68}$

$−\frac{3}{8}−\frac{x}{11}$

Exercise $\PageIndex{69}$

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

Answer

$\frac{33}{64}$

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 $\PageIndex{71}$

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

Answer

$54$

Exercise $\PageIndex{72}$

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

Exercise $\PageIndex{73}$

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

Answer

$\frac{49}{25}$

Exercise $\PageIndex{74}$

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

Exercise $\PageIndex{75}$

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

Answer

$\frac{15}{4}$

Exercise $\PageIndex{76}$

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

Exercise $\PageIndex{77}$

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

Answer

$\frac{5}{21}$

Exercise $\PageIndex{78}$

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

Exercise $\PageIndex{79}$

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

Answer

$\frac{7}{9}$

Exercise $\PageIndex{80}$

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

Exercise $\PageIndex{81}$

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

Answer

$-5$

Exercise $\PageIndex{82}$

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

Exercise $\PageIndex{83}$

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

Answer

$\frac{19}{12}$

Exercise $\PageIndex{84}$

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

Exercise $\PageIndex{85}$

$\frac{3}{8}−\frac{1}{6}+\frac{3}{4}$

Answer

$\frac{23}{24}$

Exercise $\PageIndex{86}$

$\frac{2}{5}+\frac{5}{8}−\frac{3}{4}$

Exercise $\PageIndex{87}$

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

Answer

$\frac{11}{5}$

Exercise $\PageIndex{88}$

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

Exercise $\PageIndex{89}$

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

Answer

$1$

Exercise $\PageIndex{90}$

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

Exercise $\PageIndex{91}$

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

Answer

$\frac{13}{3}$

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

Answer

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. $x=-\frac{3}{5}$

Answer

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. $w=-\frac{1}{2}$

Answer

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 $\PageIndex{99}$

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

Answer

$-\frac{1}{9}$

Exercise $\PageIndex{100}$

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

Exercise $\PageIndex{101}$

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

Answer

$-\frac{5}{11}$

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?

Answer

$\frac{7}{8}$ 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.

Answer

Answers may vary

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?