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1.6 Add and Subtract Fractions

Common denominators and the LCD, sums and differences of unlike fractions, complex fractions, and evaluating variable expressions with them.

Elementary Algebra 2e, 1.6 Add and Subtract Fractions

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87 exercises

1.6 Exercise 1

Find the sum: x3+23.\frac{x}{3} + \frac{2}{3} .

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1.6 Exercise 2

Find the sum: x4+34.\frac{x}{4} + \frac{3}{4} .

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1.6 Exercise 3

Find the sum: y8+58.\frac{y}{8} + \frac{5}{8} .

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1.6 Exercise 4

Find the difference: −2324−1324.- \frac{23}{24} - \frac{13}{24} .

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1.6 Exercise 5

Find the difference: −1928−728.- \frac{19}{28} - \frac{7}{28} .

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1.6 Exercise 6

Find the difference: −2732−132.- \frac{27}{32} - \frac{1}{32} .

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1.6 Exercise 7

Simplify: −10x−4x.- \frac{10}{x} - \frac{4}{x} .

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1.6 Exercise 8

Find the difference: −9x−7x.- \frac{9}{x} - \frac{7}{x} .

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1.6 Exercise 9

Find the difference: −17a−5a.- \frac{17}{a} - \frac{5}{a} .

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1.6 Exercise 10

Simplify: 38+(−58)−18.\frac{3}{8} + \left(- \frac{5}{8}\right) - \frac{1}{8} .

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1.6 Exercise 11

Simplify: −29+(−49)−79.- \frac{2}{9} + \left(- \frac{4}{9}\right) - \frac{7}{9} .

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1.6 Exercise 12

Simplify: 59+(−49)−79.\frac{5}{9} + \left(- \frac{4}{9}\right) - \frac{7}{9} .

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1.6 Exercise 14

Add: 712+1115.\frac{7}{12} + \frac{11}{15} .

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1.6 Exercise 15

Add: 1315+1720.\frac{13}{15} + \frac{17}{20} .

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1.6 Exercise 17

Subtract: 1324−1732.\frac{13}{24} - \frac{17}{32} .

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1.6 Exercise 18

Subtract: 2132−928.\frac{21}{32} - \frac{9}{28} .

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1.6 Exercise 20

Add: y6+79.\frac{y}{6} + \frac{7}{9} .

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1.6 Exercise 21

Add: x6+715.\frac{x}{6} + \frac{7}{15} .

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1.6 Exercise 22

Simplify: ⓐ 5x6−310\frac{5 x}{6} - \frac{3}{10} ⓑ 5x6·310.\frac{5 x}{6} \cdot \frac{3}{10} .

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1.6 Exercise 23

Simplify: ⓐ 3a4−89\frac{3 a}{4} - \frac{8}{9} ⓑ 3a4·89.\frac{3 a}{4} \cdot \frac{8}{9} .

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1.6 Exercise 24

Simplify: ⓐ 4k5−16\frac{4 k}{5} - \frac{1}{6} ⓑ 4k5·16.\frac{4 k}{5} \cdot \frac{1}{6} .

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1.6 Exercise 26

Simplify: (13)223+2.\frac{\left(\frac{1}{3}\right)^{2}}{2^{3} + 2} .

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1.6 Exercise 27

Simplify: 1+42(14)2.\frac{1 + 4^{2}}{\left(\frac{1}{4}\right)^{2}} .

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1.6 Exercise 28

Simplify: 12+2334−16.\frac{\frac{1}{2} + \frac{2}{3}}{\frac{3}{4} - \frac{1}{6}} .

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1.6 Exercise 29

Simplify: 13+1234−13.\frac{\frac{1}{3} + \frac{1}{2}}{\frac{3}{4} - \frac{1}{3}} .

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1.6 Exercise 30

Simplify: 23−1214+13.\frac{\frac{2}{3} - \frac{1}{2}}{\frac{1}{4} + \frac{1}{3}} .

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1.6 Exercise 32

Evaluate x+34x + \frac{3}{4} when ⓐ x=−74x = - \frac{7}{4} ⓑ x=−54.x = - \frac{5}{4} .

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1.6 Exercise 33

Evaluate y+12y + \frac{1}{2} when ⓐ y=23y = \frac{2}{3} ⓑ y=−34.y = - \frac{3}{4} .

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1.6 Exercise 35

Evaluate −12−y- \frac{1}{2} - y when y=−14.y = - \frac{1}{4} .

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1.6 Exercise 36

Evaluate −38−y- \frac{3}{8} - y when y=−52.y = - \frac{5}{2} .

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1.6 Exercise 38

Evaluate 3ab23 a b^{2} when a=−23a = - \frac{2}{3} and b=−12.b = - \frac{1}{2} .

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1.6 Exercise 39

Evaluate 4c3d4 c^{3} d when c=−12c = - \frac{1}{2} and d=−43.d = - \frac{4}{3} .

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1.6 Exercise 41

Evaluate a+bc\frac{a + b}{c} when a=−8,b=−7,andc=6.a = −8 , b = −7 , \text{and} c = 6 .

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1.6 Exercise 42

Evaluate x+yz\frac{x + y}{z} when x=9,y=−18,andz=−6.x = 9 , y = −18 , \text{and} z = −6 .

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1.6 Exercise 43

Add.

613+513\frac{6}{13} + \frac{5}{13}

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1.6 Exercise 45

Add.

x4+34\frac{x}{4} + \frac{3}{4}

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1.6 Exercise 47

Add.

−316+(−716)- \frac{3}{16} + \left(- \frac{7}{16}\right)

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1.6 Exercise 49

Add.

−817+1517- \frac{8}{17} + \frac{15}{17}

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1.6 Exercise 51

Add.

613+(−1013)+(−1213)\frac{6}{13} + \left(- \frac{10}{13}\right) + \left(- \frac{12}{13}\right)

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1.6 Exercise 53

Subtract.

1115−715\frac{11}{15} - \frac{7}{15}

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1.6 Exercise 55

Subtract.

1112−512\frac{11}{12} - \frac{5}{12}

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1.6 Exercise 57

Subtract.

1921−421\frac{19}{21} - \frac{4}{21}

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1.6 Exercise 59

Subtract.

5y8−78\frac{5 y}{8} - \frac{7}{8}

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1.6 Exercise 61

Subtract.

−23u−15u- \frac{23}{u} - \frac{15}{u}

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1.6 Exercise 63

Subtract.

−35−(−45)- \frac{3}{5} - \left(- \frac{4}{5}\right)

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1.6 Exercise 65

Subtract.

−79−(−59)- \frac{7}{9} - \left(- \frac{5}{9}\right)

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1.6 Exercise 67

Simplify.

−518·910- \frac{5}{18} \cdot \frac{9}{10}

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1.6 Exercise 69

Simplify.

n5−45\frac{n}{5} - \frac{4}{5}

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1.6 Exercise 71

Simplify.

−724+224- \frac{7}{24} + \frac{2}{24}

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1.6 Exercise 73

Simplify.

815÷125\frac{8}{15} \div \frac{12}{5}

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1.6 Exercise 75

Add or subtract.

12+17\frac{1}{2} + \frac{1}{7}

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1.6 Exercise 77

Add or subtract.

13−(−19)\frac{1}{3} - \left(- \frac{1}{9}\right)

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1.6 Exercise 79

Add or subtract.

712+58\frac{7}{12} + \frac{5}{8}

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1.6 Exercise 81

Add or subtract.

712−916\frac{7}{12} - \frac{9}{16}

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1.6 Exercise 83

Add or subtract.

23−38\frac{2}{3} - \frac{3}{8}

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1.6 Exercise 85

Add or subtract.

−1130+2740- \frac{11}{30} + \frac{27}{40}

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1.6 Exercise 87

Add or subtract.

−1330+2542- \frac{13}{30} + \frac{25}{42}

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1.6 Exercise 89

Add or subtract.

−3956−2235- \frac{39}{56} - \frac{22}{35}

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1.6 Exercise 91

Add or subtract.

−23−(−34)- \frac{2}{3} - \left(- \frac{3}{4}\right)

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1.6 Exercise 93

Add or subtract.

1+781 + \frac{7}{8}

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1.6 Exercise 95

Add or subtract.

x3+14\frac{x}{3} + \frac{1}{4}

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1.6 Exercise 97

Add or subtract.

y4−35\frac{y}{4} - \frac{3}{5}

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1.6 Exercise 99

Simplify.

ⓐ 23+16\frac{2}{3} + \frac{1}{6} ⓑ 23÷16\frac{2}{3} \div \frac{1}{6}

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1.6 Exercise 101

Simplify.

ⓐ 5n6÷815\frac{5 n}{6} \div \frac{8}{15} ⓑ 5n6−815\frac{5 n}{6} - \frac{8}{15}

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1.6 Exercise 103

Simplify.

−38÷(−310)- \frac{3}{8} \div \left(- \frac{3}{10}\right)

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1.6 Exercise 105

Simplify.

−38+512- \frac{3}{8} + \frac{5}{12}

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1.6 Exercise 107

Simplify.

56−19\frac{5}{6} - \frac{1}{9}

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1.6 Exercise 109

Simplify.

−715−y4- \frac{7}{15} - \frac{y}{4}

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1.6 Exercise 111

Simplify.

1112a·9a16\frac{11}{12 a} \cdot \frac{9 a}{16}

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1.6 Exercise 113

Simplify.

23+42(23)2\frac{2^{3} + 4^{2}}{\left(\frac{2}{3}\right)^{2}}

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1.6 Exercise 115

Simplify.

(35)2(37)2\frac{\left(\frac{3}{5}\right)^{2}}{\left(\frac{3}{7}\right)^{2}}

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1.6 Exercise 117

Simplify.

213+15\frac{2}{\frac{1}{3} + \frac{1}{5}}

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1.6 Exercise 119

Simplify.

78−2312+38\frac{\frac{7}{8} - \frac{2}{3}}{\frac{1}{2} + \frac{3}{8}}

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1.6 Exercise 121

Simplify.

12+23·512\frac{1}{2} + \frac{2}{3} \cdot \frac{5}{12}

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1.6 Exercise 123

Simplify.

1−35÷1101 - \frac{3}{5} \div \frac{1}{10}

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1.6 Exercise 125

Simplify.

23+16+34\frac{2}{3} + \frac{1}{6} + \frac{3}{4}

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1.6 Exercise 127

Simplify.

38−16+34\frac{3}{8} - \frac{1}{6} + \frac{3}{4}

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1.6 Exercise 129

Simplify.

12(920−415)12 \left(\frac{9}{20} - \frac{4}{15}\right)

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1.6 Exercise 131

Simplify.

58+161924\frac{\frac{5}{8} + \frac{1}{6}}{\frac{19}{24}}

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1.6 Exercise 133

Simplify.

(59+16)÷(23−12)\left(\frac{5}{9} + \frac{1}{6}\right) \div \left(\frac{2}{3} - \frac{1}{2}\right)

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1.6 Exercise 135

Evaluate.

x+(−56)x + \left(- \frac{5}{6}\right) when
ⓐ x=13x = \frac{1}{3}
ⓑ x=−16x = - \frac{1}{6}

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1.6 Exercise 137

Evaluate.

x−25x - \frac{2}{5} when ⓐ x=35x = \frac{3}{5} ⓑ x=−35x = - \frac{3}{5}

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1.6 Exercise 139

Evaluate.

710−w\frac{7}{10} - w when ⓐ w=12w = \frac{1}{2} ⓑ w=−12w = - \frac{1}{2}

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1.6 Exercise 141

Evaluate.

2x2y32 x^{2} y^{3} when x=−23x = - \frac{2}{3} and y=−12y = - \frac{1}{2}

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1.6 Exercise 143

Evaluate.

a+ba−b\frac{a + b}{a - b} when a=−3,b=8a = −3 , b = 8

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1.6 Exercise 145

Decorating Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs 12\frac{1}{2} yard of print fabric and 38\frac{3}{8} yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?

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1.6 Exercise 147

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

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Adapted from Elementary Algebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Elementary Algebra 2e. Imported at revision 77a933c.