1.7E: Exercises
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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
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\(\frac{x+3}{4}\)
Exercise \(\PageIndex{4}\)
\(\dfrac{ 8}{q}+ \dfrac{6}{q}\)
Exercise \(\PageIndex{5}\)
\(-\dfrac{ 3}{16}+\left(− \dfrac{ 7}{16}\right)\)
- Answer
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\(-\frac{5}{8}\)
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
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\(-\frac{16}{13}\)
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
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\(\frac{5y-7}{8}\)
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
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\(-\frac{1}{4}\)
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
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\(-frac{5}{24}\)
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
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\(-\frac{53}{40}\)
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 \(\PageIndex{57}\)
- \(\frac{2}{3}+\frac{1}{6}\)
- \(\frac{2}{3} \div \frac{1}{6}\)
- Answer
-
- \(\frac{5}{6}\)
- \(4\)
Exercise \(\PageIndex{58}\)
- \(-\frac{2}{5}-\frac{1}{8}\)
- \(-\frac{2}{5} \cdot \frac{1}{8}\)
Exercise \(\PageIndex{59}\)
- \(\frac{5 n}{6} \div \frac{8}{15}\)
- \(\frac{5 n}{6}-\frac{8}{15}\)
- Answer
-
- \(\frac{25n}{16}\)
- \(\frac{25n-16}{30}\)
Exercise \(\PageIndex{60}\)
- \(\frac{3 a}{8} \div \frac{7}{12}\)
- \(\frac{3 a}{8}-\frac{7}{12}\)
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
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\(\frac{-28-15y}{60}\)
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
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\(\frac{7}{9}\)
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 \(\PageIndex{93}\)
\(x+\left(-\frac{5}{6}\right) \text { when }\)
- \(x = \frac{1}{3}\)
- \(x=-\frac{1}{6}\)
- Answer
-
- \(-\frac{1}{2}\)
- \(-1\)
Exercise \(\PageIndex{94}\)
\(x+\left(-\frac{11}{12}\right) \text { when }\)
- \(x = \frac{11}{12}\)
- \(x=-\frac{3}{4}\)
Exercise \(\PageIndex{95}\)
\(x - \frac{2}{5} \text { when }\)
- \(x = \frac{3}{5}\)
- \(x=-\frac{3}{5}\)
- Answer
-
- \(\frac{1}{5}\)
- \(-1\)
Exercise \(\PageIndex{96}\)
\(x-\frac{1}{3} \text { when }\)
- \(x=\frac{2}{3}\)
- \(x=-\frac{2}{3}\)
Exercise \(\PageIndex{97}\)
\(\frac{7}{10}-w \text { when }\)
- \(w=\frac{1}{2}\)
- \(w=-\frac{1}{2}\)
- Answer
-
- \(\frac{1}{5}\)
- \(\frac{6}{5}\)
Exercise \(\PageIndex{98}\)
\(\frac{5}{12}-w \text { when }\)
- \(w=\frac{1}{4}\)
- \(w=-\frac{1}{4}\)
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?