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1.3 Fractions

Reducing, multiplying, dividing, adding, and subtracting fractional quantities, then applying order of operations to expressions built from them.

Intermediate Algebra 2e, 1.3 Fractions

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72 exercises

1.3 Exercise 2

Simplify: −69120.- \frac{69}{120} .

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1.3 Exercise 3

Simplify: −120192.- \frac{120}{192} .

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1.3 Exercise 5

Multiply: 113(−9a).\frac{11}{3} \left(−9 a\right) .

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1.3 Exercise 6

Multiply: 137(−14b).\frac{13}{7} \left(−14 b\right) .

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1.3 Exercise 8

Divide: −727÷(−3536).- \frac{7}{27} \div \left(- \frac{35}{36}\right) .

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1.3 Exercise 9

Divide: −514÷(−1528).- \frac{5}{14} \div \left(- \frac{15}{28}\right) .

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1.3 Exercise 10

Simplify: x2xy6.\frac{\frac{x}{2}}{\frac{x y}{6}} .

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1.3 Exercise 11

Simplify: a8ab6.\frac{\frac{a}{8}}{\frac{a b}{6}} .

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1.3 Exercise 12

Simplify: p2pq8.\frac{\frac{p}{2}}{\frac{p q}{8}} .

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1.3 Exercise 14

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

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1.3 Exercise 15

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

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1.3 Exercise 16

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

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1.3 Exercise 17

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

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1.3 Exercise 18

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

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1.3 Exercise 19

Simplify: 4(−3)+6(−2)−3(2)−2.\frac{4 \left(- 3\right) + 6 \left(- 2\right)}{- 3 \left(2\right) - 2} .

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1.3 Exercise 20

Simplify: 8(−2)+4(−3)−5(2)+3.\frac{8 \left(- 2\right) + 4 \left(- 3\right)}{- 5 \left(2\right) + 3} .

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1.3 Exercise 21

Simplify: 7(−1)+9(−3)−5(3)−2.\frac{7 \left(- 1\right) + 9 \left(- 3\right)}{- 5 \left(3\right) - 2} .

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1.3 Exercise 23

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

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1.3 Exercise 24

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

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1.3 Exercise 25

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

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1.3 Exercise 26

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

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1.3 Exercise 27

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

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1.3 Exercise 29

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

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1.3 Exercise 30

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

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1.3 Exercise 31

Simplify.

−10863- \frac{108}{63}

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1.3 Exercise 33

Simplify.

120252\frac{120}{252}

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1.3 Exercise 35

Simplify.

14x221y\frac{14 x^{2}}{21 y}

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1.3 Exercise 37

Simplify.

−210a2110b2- \frac{210 a^{2}}{110 b^{2}}

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1.3 Exercise 39

Perform the indicated operation.

−34(−49)- \frac{3}{4} \left(- \frac{4}{9}\right)

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1.3 Exercise 41

Perform the indicated operation.

(−1415)(920)\left(- \frac{14}{15}\right) \left(\frac{9}{20}\right)

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1.3 Exercise 43

Perform the indicated operation.

(−6384)(−4490)\left(- \frac{63}{84}\right) \left(- \frac{44}{90}\right)

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1.3 Exercise 45

Perform the indicated operation.

37·21n\frac{3}{7} \cdot 21 n

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1.3 Exercise 47

Perform the indicated operation.

34÷x11\frac{3}{4} \div \frac{x}{11}

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1.3 Exercise 49

Perform the indicated operation.

518÷(−1524)\frac{5}{18} \div \left(- \frac{15}{24}\right)

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1.3 Exercise 51

Perform the indicated operation.

8u15÷12v25\frac{8 u}{15} \div \frac{12 v}{25}

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1.3 Exercise 53

Perform the indicated operation.

34÷(−12)\frac{3}{4} \div \left(−12\right)

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1.3 Exercise 55

Simplify.

−8211235\frac{- \frac{8}{21}}{ \frac{12}{35}}

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1.3 Exercise 57

Simplify.

−452\frac{- \frac{4}{5}}{ 2}

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1.3 Exercise 59

Simplify.

m3n2\frac{\frac{m}{3}}{\frac{n}{2}}

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1.3 Exercise 61

Add or subtract.

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

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1.3 Exercise 63

Add or subtract.

712−916\frac{7}{12} - \frac{9}{16}

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1.3 Exercise 65

Add or subtract.

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

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1.3 Exercise 67

Add or subtract.

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

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1.3 Exercise 69

Add or subtract.

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

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1.3 Exercise 71

Add or subtract.

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

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1.3 Exercise 73

Add or subtract.


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

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1.3 Exercise 75

Add or subtract.


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

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1.3 Exercise 77

Add or subtract.


ⓐ −4x9−56- \frac{4 x}{9} - \frac{5}{6}
ⓑ −4k9·56- \frac{4 k}{9} \cdot \frac{5}{6}

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1.3 Exercise 79

Add or subtract.


ⓐ −5a3+(−106)- \frac{5 a}{3} + \left(- \frac{10}{6}\right)
ⓑ −5a3÷(−106)- \frac{5 a}{3} \div \left(- \frac{10}{6}\right)

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1.3 Exercise 81

Simplify.

5·6−3·44·5−2·3\frac{5 \cdot 6 - 3 \cdot 4}{4 \cdot 5 - 2 \cdot 3}

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1.3 Exercise 83

Simplify.

52−323−5\frac{5^{2} - 3^{2}}{3 - 5}

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1.3 Exercise 85

Simplify.

7·4−2(8−5)9·3−3·5\frac{7 \cdot 4 - 2 \left(8 - 5\right)}{9 \cdot 3 - 3 \cdot 5}

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1.3 Exercise 87

Simplify.

9(8−2)−3(15−7)6(7−1)−3(17−9)\frac{9 \left(8 - 2\right) - 3 \left(15 - 7\right)}{6 \left(7 - 1\right) - 3 \left(17 - 9\right)}

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1.3 Exercise 89

Simplify.

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

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1.3 Exercise 91

Simplify.

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

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1.3 Exercise 93

Simplify.

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

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1.3 Exercise 95

Simplify.

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

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1.3 Exercise 97

Simplify.

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

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1.3 Exercise 99

Simplify.

−38+512- \frac{3}{8} + \frac{5}{12}

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1.3 Exercise 101

Simplify.

−715−y4- \frac{7}{15} - \frac{y}{4}

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1.3 Exercise 103

Simplify.

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

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1.3 Exercise 105

Simplify.

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

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1.3 Exercise 107

Simplify.

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

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1.3 Exercise 109

Simplify.

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

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1.3 Exercise 111

Simplify.

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

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1.3 Exercise 113

Simplify.

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

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1.3 Exercise 115

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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1.3 Exercise 117

Evaluate.

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

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1.3 Exercise 119

Evaluate.

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

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1.3 Exercise 121

Evaluate.

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

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1.3 Exercise 123

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

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1.3 Exercise 125

Explain how you find the reciprocal of a fraction.

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