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4.2 Multiply and Divide Fractions

Removing common factors to simplify, multiplying straight across, finding a reciprocal, and dividing by multiplying by that reciprocal.

Prealgebra 2e, 4.2 Multiply and Divide Fractions

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82 exercises

4.2 Exercise 1

Before you get started, take this readiness quiz.

Find the prime factorization of 48.48 .
If you missed this problem, review the reference.

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4.2 Exercise 3

Find two fractions equivalent to 56.\frac{5}{6} .
If you missed this problem, review the reference.

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4.2 Exercise 5

Simplify: 812\frac{8}{12}.

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4.2 Exercise 6

Simplify: 1216\frac{12}{16}.

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4.2 Exercise 8

Simplify: −2128.- \frac{21}{28} .

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4.2 Exercise 9

Simplify: −1624.- \frac{16}{24} .

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4.2 Exercise 11

Simplify: −5442.- \frac{54}{42} .

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4.2 Exercise 12

Simplify: −8145.- \frac{81}{45} .

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4.2 Exercise 14

Simplify: 69120.\frac{69}{120} .

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4.2 Exercise 15

Simplify: 120192.\frac{120}{192} .

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4.2 Exercise 16

Simplify: 5xy15x.\frac{5 x y}{15 x} .

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4.2 Exercise 17

Simplify: 7x7y.\frac{7 x}{7 y} .

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4.2 Exercise 18

Simplify: 9a9b.\frac{9 a}{9 b} .

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4.2 Exercise 22

Multiply, and write the answer in simplified form: 34·15.\frac{3}{4} \cdot \frac{1}{5} .

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4.2 Exercise 23

Multiply, and write the answer in simplified form: 13·25.\frac{1}{3} \cdot \frac{2}{5} .

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4.2 Exercise 24

Multiply, and write the answer in simplified form: 35·78.\frac{3}{5} \cdot \frac{7}{8} .

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4.2 Exercise 26

Multiply, and write the answer in simplified form: −47(−58).- \frac{4}{7} \left(- \frac{5}{8}\right) .

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4.2 Exercise 27

Multiply, and write the answer in simplified form: −712(−89).- \frac{7}{12} \left(- \frac{8}{9}\right) .

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4.2 Exercise 29

Multiply, and write the answer in simplified form: −1028·815.- \frac{10}{28} \cdot \frac{8}{15} .

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4.2 Exercise 30

Multiply, and write the answer in simplified form: −920·512.- \frac{9}{20} \cdot \frac{5}{12} .

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4.2 Exercise 32

Multiply, and write the answer in simplified form:

  1. ⓐ 18·72\frac{1}{8} \cdot 72
  2. ⓑ 113(−9a)\frac{11}{3} \left(−9 a\right)

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4.2 Exercise 33

Multiply, and write the answer in simplified form:

  1. ⓐ 38·64\frac{3}{8} \cdot 64
  2. ⓑ 16x·111216 x \cdot \frac{11}{12}

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4.2 Exercise 34

Find the reciprocal of each number. Then check that the product of each number and its reciprocal is 1.1 .

  1. ⓐ 49\frac{4}{9}
  2. ⓑ −16- \frac{1}{6}
  3. ⓒ −145- \frac{14}{5}
  4. ⓓ 77
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4.2 Exercise 35

Find the reciprocal:

  1. ⓐ 57\frac{5}{7}
  2. ⓑ −18- \frac{1}{8}
  3. ⓒ −114- \frac{11}{4}
  4. ⓓ 1414

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4.2 Exercise 36

Find the reciprocal:

  1. ⓐ 37\frac{3}{7}
  2. ⓑ −112- \frac{1}{12}
  3. ⓒ −149- \frac{14}{9}
  4. ⓓ 2121

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4.2 Exercise 37

Fill in the chart for each fraction in the left column:

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4.2 Exercise 46

Divide, and write the answer in simplified form: 25÷(−37).\frac{2}{5} \div \left(- \frac{3}{7}\right) .

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4.2 Exercise 47

Divide, and write the answer in simplified form: 37÷(−23).\frac{3}{7} \div \left(- \frac{2}{3}\right) .

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4.2 Exercise 48

Divide, and write the answer in simplified form: 23÷(−75).\frac{2}{3} \div \left(- \frac{7}{5}\right) .

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4.2 Exercise 49

Divide, and write the answer in simplified form: 23÷n5.\frac{2}{3} \div \frac{n}{5} .

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4.2 Exercise 50

Divide, and write the answer in simplified form: 35÷p7.\frac{3}{5} \div \frac{p}{7} .

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4.2 Exercise 51

Divide, and write the answer in simplified form: 58÷q3.\frac{5}{8} \div \frac{q}{3} .

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4.2 Exercise 52

Divide, and write the answer in simplified form: −34÷(−78).- \frac{3}{4} \div \left(- \frac{7}{8}\right) .

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4.2 Exercise 53

Divide, and write the answer in simplified form: −23÷(−56).- \frac{2}{3} \div \left(- \frac{5}{6}\right) .

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4.2 Exercise 54

Divide, and write the answer in simplified form: −56÷(−23).- \frac{5}{6} \div \left(- \frac{2}{3}\right) .

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4.2 Exercise 56

Divide, and write the answer in simplified form: 727÷3536.\frac{7}{27} \div \frac{35}{36} .

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4.2 Exercise 57

Divide, and write the answer in simplified form: 514÷1528.\frac{5}{14} \div \frac{15}{28} .

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4.2 Exercise 58

Simplify each fraction. Do not convert any improper fractions to mixed numbers.

721\frac{7}{21}

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4.2 Exercise 60

Simplify each fraction. Do not convert any improper fractions to mixed numbers.

1520\frac{15}{20}

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4.2 Exercise 62

Simplify each fraction. Do not convert any improper fractions to mixed numbers.

−4088- \frac{40}{88}

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4.2 Exercise 64

Simplify each fraction. Do not convert any improper fractions to mixed numbers.

−10863- \frac{108}{63}

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4.2 Exercise 66

Simplify each fraction. Do not convert any improper fractions to mixed numbers.

120252\frac{120}{252}

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4.2 Exercise 68

Simplify each fraction. Do not convert any improper fractions to mixed numbers.

−168192- \frac{168}{192}

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4.2 Exercise 70

Simplify each fraction. Do not convert any improper fractions to mixed numbers.

11x11y\frac{11 x}{11 y}

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4.2 Exercise 72

Simplify each fraction. Do not convert any improper fractions to mixed numbers.

−3x12y- \frac{3 x}{12 y}

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4.2 Exercise 74

Simplify each fraction. Do not convert any improper fractions to mixed numbers.

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

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4.2 Exercise 80

Multiply, and write the answer in simplified form.

25·13\frac{2}{5} \cdot \frac{1}{3}

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4.2 Exercise 82

Multiply, and write the answer in simplified form.

34·910\frac{3}{4} \cdot \frac{9}{10}

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4.2 Exercise 84

Multiply, and write the answer in simplified form.

−23(−38)- \frac{2}{3} \left(- \frac{3}{8}\right)

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4.2 Exercise 86

Multiply, and write the answer in simplified form.

−59·310- \frac{5}{9} \cdot \frac{3}{10}

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4.2 Exercise 88

Multiply, and write the answer in simplified form.

712(−821)\frac{7}{12} \left(- \frac{8}{21}\right)

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4.2 Exercise 90

Multiply, and write the answer in simplified form.

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

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4.2 Exercise 92

Multiply, and write the answer in simplified form.

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

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4.2 Exercise 94

Multiply, and write the answer in simplified form.

4·5114 \cdot \frac{5}{11}

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4.2 Exercise 96

Multiply, and write the answer in simplified form.

37·21n\frac{3}{7} \cdot 21 n

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4.2 Exercise 98

Multiply, and write the answer in simplified form.

−28p(−14)−28 p \left(- \frac{1}{4}\right)

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4.2 Exercise 100

Multiply, and write the answer in simplified form.

−8(174)−8 \left(\frac{17}{4}\right)

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4.2 Exercise 102

Multiply, and write the answer in simplified form.

−1(−38)−1 \left(- \frac{3}{8}\right)

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4.2 Exercise 104

Multiply, and write the answer in simplified form.

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

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4.2 Exercise 106

Multiply, and write the answer in simplified form.

(65)4\left(\frac{6}{5}\right)^{4}

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4.2 Exercise 108

Find the reciprocal.

34\frac{3}{4}

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4.2 Exercise 110

Find the reciprocal.

−517- \frac{5}{17}

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4.2 Exercise 112

Find the reciprocal.

118\frac{11}{8}

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4.2 Exercise 114

Find the reciprocal.

−19−19

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4.2 Exercise 116

Find the reciprocal.

11

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4.2 Exercise 124

Divide, and write the answer in simplified form.

12÷18\frac{1}{2} \div \frac{1}{8}

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4.2 Exercise 126

Divide, and write the answer in simplified form.

45÷34\frac{4}{5} \div \frac{3}{4}

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4.2 Exercise 128

Divide, and write the answer in simplified form.

−34÷35- \frac{3}{4} \div \frac{3}{5}

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4.2 Exercise 130

Divide, and write the answer in simplified form.

−56÷(−56)- \frac{5}{6} \div \left(- \frac{5}{6}\right)

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4.2 Exercise 132

Divide, and write the answer in simplified form.

25÷y9\frac{2}{5} \div \frac{y}{9}

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4.2 Exercise 134

Divide, and write the answer in simplified form.

56÷c15\frac{5}{6} \div \frac{c}{15}

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4.2 Exercise 136

Divide, and write the answer in simplified form.

718÷(−1427)\frac{7}{18} \div \left(- \frac{14}{27}\right)

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4.2 Exercise 138

Divide, and write the answer in simplified form.

5q12÷15q8\frac{5 q}{12} \div \frac{15 q}{8}

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4.2 Exercise 140

Divide, and write the answer in simplified form.

12r25÷18s35\frac{12 r}{25} \div \frac{18 s}{35}

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4.2 Exercise 142

Divide, and write the answer in simplified form.

−3÷14−3 \div \frac{1}{4}

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4.2 Exercise 144

Divide, and write the answer in simplified form.

25÷(−10)\frac{2}{5} \div \left(−10\right)

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4.2 Exercise 146

Divide, and write the answer in simplified form.

−15÷(−53)−15 \div \left(- \frac{5}{3}\right)

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4.2 Exercise 148

Divide, and write the answer in simplified form.

112÷78·211\frac{11}{2} \div \frac{7}{8} \cdot \frac{2}{11}

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4.2 Exercise 150

Baking Nina is making 44 pans of fudge to serve after a music recital. For each pan, she needs 23\frac{2}{3} cup of condensed milk.

  1. ⓐ How much condensed milk will Nina need? Show your calculation. Write your result as an improper fraction and as a mixed number.
  2. ⓑ Measuring cups usually come in sets of 18,14,13,12,\frac{1}{8} , \frac{1}{4} , \frac{1}{3} , \frac{1}{2} , and 11 cup. Draw a diagram to show two different ways that Nina could measure the condensed milk she needs.

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4.2 Exercise 152

Portions Kristen has 34\frac{3}{4} yards of ribbon. She wants to cut it into equal parts to make hair ribbons for her daughter’s 66 dolls. How long will each doll’s hair ribbon be?

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4.2 Exercise 154

Explain how you find the reciprocal of a negative fraction.

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4.2 Exercise 156

Give an example from everyday life that demonstrates how 12·23\frac{1}{2} \cdot \frac{2}{3} is 13.\frac{1}{3} .

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