1.7E: Exercises
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Practice Makes Perfect
Add and Subtract Fractions with a Common Denominator
In the following exercises, add.
613+513
- Answer
-
1113
415+715
x4+34
- Answer
-
x+34
8q+6q
−316+(−716)
- Answer
-
−58
−516+(−916)
−817+1517
- Answer
-
717
−919+1719
613+(−1013)+(−1213)
- Answer
-
−1613
512+(−712)+(−1112)
In the following exercises, subtract.
1115−715
- Answer
-
415
913−413
1112−512
- Answer
-
12
712−512
1921−421
- Answer
-
57
1721−821
5y8−78
- Answer
-
5y−78
11z13−813
−23u−15u
- Answer
-
−38u
−29v−26v
−35−(−45)
- Answer
-
15
−37−(−57)
−79−(−59)
- Answer
-
−29
−811−(−511)
Mixed Practice
In the following exercises, simplify.
−518·910
- Answer
-
−14
−314·712
n5−45
- Answer
-
n−45
611−s11
−724+224
- Answer
-
−frac524
−518+118
815÷125
- Answer
-
29
712÷928
Add or Subtract Fractions with Different Denominators
In the following exercises, add or subtract.
12+17
- Answer
-
914
13+18
13−(−19)
- Answer
-
49
14−(−18)
712+512
- Answer
-
2924
512+38
712−916
- Answer
-
148
716−512
23−38
- Answer
-
724
56−34
−1130+2740
- Answer
-
37120
−920+1730
−1330+2542
- Answer
-
17105
−2330+548
−3956−2235
- Answer
-
−5340
−3349−1835
−23−(−34)
- Answer
-
112
−34−(−45)
1+78
- Answer
-
158
1−310
x3+14
- Answer
-
4x+312
y2+23
y4−35
- Answer
-
5y−1220
x5−14
Mixed Practice
In the following exercises, simplify.
- 23+16
- 23÷16
- Answer
-
- 56
- 4
- −25−18
- −25⋅18
- 5n6÷815
- 5n6−815
- Answer
-
- 25n16
- 25n−1630
- 3a8÷712
- 3a8−712
−38÷(−310)
- Answer
-
54
−512÷(−59)
−38+512
- Answer
-
124
−18+712
\frac{5}{6}−\frac{1}{9}
- Answer
-
\frac{13}{18}
\frac{5}{9}−\frac{1}{6}
−\frac{7}{15}−\frac{y}{4}
- Answer
-
\frac{-28-15y}{60}
−\frac{3}{8}−\frac{x}{11}
\frac{11}{12a} \cdot \frac{9a}{16}
- Answer
-
\frac{33}{64}
\frac{10y}{13} \cdot \frac{8}{15y}
Use the Order of Operations to Simplify Complex Fractions
In the following exercises, simplify.
\frac{2^{3}+4^{2}}{\left(\frac{2}{3}\right)^{2}}
- Answer
-
54
\frac{3^{3}-3^{2}}{\left(\frac{3}{4}\right)^{2}}
\frac{\left(\frac{3}{5}\right)^{2}}{\left(\frac{3}{7}\right)^{2}}
- Answer
-
\frac{49}{25}
\frac{\left(\frac{3}{4}\right)^{2}}{\left(\frac{5}{8}\right)^{2}}
\frac{2}{\frac{1}{3}+\frac{1}{5}}
- Answer
-
\frac{15}{4}
\frac{5}{\frac{1}{4}+\frac{1}{3}}
\frac{\frac{7}{8}-\frac{2}{3}}{\frac{1}{2}+\frac{3}{8}}
- Answer
-
\frac{5}{21}
\frac{\frac{3}{4}-\frac{3}{5}}{\frac{1}{4}+\frac{2}{5}}
\frac{1}{2}+\frac{2}{3} \cdot \frac{5}{12}
- Answer
-
\frac{7}{9}
\frac{1}{3}+\frac{2}{5} \cdot \frac{3}{4}
1-\frac{3}{5} \div \frac{1}{10}
- Answer
-
-5
1-\frac{5}{6} \div \frac{1}{12}
\frac{2}{3}+\frac{1}{6}+\frac{3}{4}
- Answer
-
\frac{19}{12}
\frac{2}{3}+\frac{1}{4}+\frac{3}{5}
\frac{3}{8}−\frac{1}{6}+\frac{3}{4}
- Answer
-
\frac{23}{24}
\frac{2}{5}+\frac{5}{8}−\frac{3}{4}
12\left(\frac{9}{20}-\frac{4}{15}\right)
- Answer
-
\frac{11}{5}
8\left(\frac{15}{16}-\frac{5}{6}\right)
\frac{\frac{5}{8}+\frac{1}{6}}{\frac{19}{24}}
- Answer
-
1
\frac{\frac{1}{6}+\frac{3}{10}}{\frac{14}{30}}
\left(\frac{5}{9}+\frac{1}{6}\right) \div\left(\frac{2}{3}-\frac{1}{2}\right)
- Answer
-
\frac{13}{3}
\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.
x+\left(-\frac{5}{6}\right) \text { when }
- x = \frac{1}{3}
- x=-\frac{1}{6}
- Answer
-
- -\frac{1}{2}
- -1
x+\left(-\frac{11}{12}\right) \text { when }
- x = \frac{11}{12}
- x=-\frac{3}{4}
x - \frac{2}{5} \text { when }
- x = \frac{3}{5}
- x=-\frac{3}{5}
- Answer
-
- \frac{1}{5}
- -1
x-\frac{1}{3} \text { when }
- x=\frac{2}{3}
- x=-\frac{2}{3}
\frac{7}{10}-w \text { when }
- w=\frac{1}{2}
- w=-\frac{1}{2}
- Answer
-
- \frac{1}{5}
- \frac{6}{5}
\frac{5}{12}-w \text { when }
- w=\frac{1}{4}
- w=-\frac{1}{4}
2 x^{2} y^{3} \text { when } x=-\frac{2}{3} \text { and } y=-\frac{1}{2}
- Answer
- -\frac{1}{9}
8 u^{2} v^{3} \text { when } u=-\frac{3}{4} \text { and } v=-\frac{1}{2}
\frac{a+b}{a-b} \text { when } a=-3, b=8
- Answer
- -\frac{5}{11}
\frac{r-s}{r+s} \text { when } r=10, s=-5
Everyday Math
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
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
Why do you need a common denominator to add or subtract fractions? Explain.
- Answer
-
Answers may vary
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?