AI Tutor
Back to Prealgebra 2e

4.3 Multiply and Divide Mixed Numbers and Complex Fractions

Rewriting mixed numbers as improper fractions before multiplying or dividing, plus fractions stacked inside fractions and a fraction bar acting as grouping.

Prealgebra 2e, 4.3 Multiply and Divide Mixed Numbers and Complex Fractions

Status
FlagsLoading your progress…

87 exercises

4.3 Exercise 1

Before you get started, take this readiness quiz.

Divide and reduce, if possible: (4+5)÷(10−7).\left(4 + 5\right) \div \left(10 - 7\right) .
If you missed this problem, review the reference.

2.5

4.3 Exercise 2

Multiply and write the answer in simplified form: 18·23\frac{1}{8} \cdot \frac{2}{3}.
If you missed this problem, review the reference.

2.5

4.3 Exercise 3

Convert 2352 \frac{3}{5} into an improper fraction.
If you missed this problem, review the reference.

2.5

4.3 Exercise 4

Multiply: 313·583 \frac{1}{3} \cdot \frac{5}{8}

2.5

4.3 Exercise 5

Multiply, and write your answer in simplified form: 523·617.5 \frac{2}{3} \cdot \frac{6}{17} .

2.5

4.3 Exercise 6

Multiply, and write your answer in simplified form: 37·514.\frac{3}{7} \cdot 5 \frac{1}{4} .

2.5

4.3 Exercise 7

Multiply, and write your answer in simplified form: 245(−178).2 \frac{4}{5} \left(- 1 \frac{7}{8}\right) .

2.5

4.3 Exercise 8

Multiply, and write your answer in simplified form. 557(−258).5 \frac{5}{7} \left(- 2 \frac{5}{8}\right) .

2.5

4.3 Exercise 9

Multiply, and write your answer in simplified form. −325·416.−3 \frac{2}{5} \cdot 4 \frac{1}{6} .

2.5

4.3 Exercise 10

Divide, and write your answer in simplified form: 347÷5.3 \frac{4}{7} \div 5 .

2.5

4.3 Exercise 11

Divide, and write your answer in simplified form: 438÷7.4 \frac{3}{8} \div 7 .

2.5

4.3 Exercise 12

Divide, and write your answer in simplified form: 258÷3.2 \frac{5}{8} \div 3 .

2.5

4.3 Exercise 13

Divide: 212÷114.2 \frac{1}{2} \div 1 \frac{1}{4} .

2.5

4.3 Exercise 14

Divide, and write your answer in simplified form: 223÷113.2 \frac{2}{3} \div 1 \frac{1}{3} .

2.5

4.3 Exercise 15

Divide, and write your answer in simplified form: 334÷112.3 \frac{3}{4} \div 1 \frac{1}{2} .

2.5

4.3 Exercise 16

Translate the phrase into an algebraic expression: “the quotient of 3x3 x and 8.”8 .”

2.5

4.3 Exercise 17

Translate the phrase into an algebraic expression: the quotient of 9s9 s and 14.14 .

2.5

4.3 Exercise 18

Translate the phrase into an algebraic expression: the quotient of 5y5 y and 6.6 .

2.5

4.3 Exercise 19

Translate the phrase into an algebraic expression: the quotient of the difference of mm and n,n , and p.p .

2.5

4.3 Exercise 20

Translate the phrase into an algebraic expression: the quotient of the difference of aa and b,b , and cd.c d .

2.5

4.3 Exercise 21

Translate the phrase into an algebraic expression: the quotient of the sum of pp and q,q , and r.r .

2.5

4.3 Exercise 22

Simplify: 3458.\frac{ \frac{3}{4} }{ \frac{5}{8} } .

2.5

4.3 Exercise 23

Simplify: 2356.\frac{ \frac{2}{3} }{ \frac{5}{6} } .

2.5

4.3 Exercise 24

Simplify: 37611.\frac{ \frac{3}{7} }{ \frac{6}{11} } .

2.5

4.3 Exercise 25

Simplify: −673.\frac{- \frac{6}{7}}{3} .

2.5

4.3 Exercise 26

Simplify: −874.\frac{- \frac{8}{7}}{4} .

2.5

4.3 Exercise 27

Simplify: −3910.- \frac{ 3 }{ \frac{9}{10} } .

2.5

4.3 Exercise 28

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

2.5

4.3 Exercise 29

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

2.5

4.3 Exercise 30

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

2.5

4.3 Exercise 31

Simplify: 23418.\frac{2 \frac{3}{4}}{\frac{1}{8}} .

2.5

4.3 Exercise 32

Simplify: 57125.\frac{\frac{5}{7}}{1 \frac{2}{5}} .

2.5

4.3 Exercise 33

Simplify: 85315.\frac{\frac{8}{5}}{3 \frac{1}{5}} .

2.5

4.3 Exercise 34

Which of the following fractions are equivalent to 7−8?\frac{7}{−8} ?

−7−8,−78,78,−78\frac{−7}{−8} , \frac{−7}{8} , \frac{7}{8} , - \frac{7}{8}
2.5

4.3 Exercise 35

Which of the following fractions are equivalent to −35?\frac{−3}{ 5} ?

−3−5,35,−35,3−5\frac{−3}{−5} , \frac{3}{5} , - \frac{3}{5} , \frac{ 3}{−5}

2.5

4.3 Exercise 36

Which of the following fractions are equivalent to −27?- \frac{2}{7} ?

−2−7,−27,27,2−7\frac{−2}{−7} , \frac{−2}{7} , \frac{2}{7} , \frac{2}{−7}

2.5

4.3 Exercise 37

Simplify: 4+85−3.\frac{4 + 8}{5 - 3} .

2.5

4.3 Exercise 38

Simplify: 4+611−2.\frac{4 + 6}{11 - 2} .

2.5

4.3 Exercise 39

Simplify: 3+518−2.\frac{3 + 5}{18 - 2} .

2.5

4.3 Exercise 40

Simplify: 4−2(3)22+2.\frac{4 - 2 \left(3\right)}{2^{2} + 2} .

2.5

4.3 Exercise 41

Simplify: 6−3(5)32+3.\frac{6 - 3 \left(5\right)}{3^{2} + 3} .

2.5

4.3 Exercise 42

Simplify: 4−4(6)33+3.\frac{4 - 4 \left(6\right)}{3^{3} + 3} .

2.5

4.3 Exercise 43

Simplify: (8−4)282−42.\frac{\left(8 - 4\right)^{2}}{8^{2} - 4^{2}} .

2.5

4.3 Exercise 44

Simplify: (11−7)2112−72.\frac{\left(11 - 7\right)^{2}}{11^{2} - 7^{2}} .

2.5

4.3 Exercise 45

Simplify: (6+2)262+22.\frac{\left(6 + 2\right)^{2}}{6^{2} + 2^{2}} .

2.5

4.3 Exercise 46

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

2.5

4.3 Exercise 47

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

2.5

4.3 Exercise 48

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

2.5

4.3 Exercise 50

Multiply and write the answer in simplified form.

249·672 \frac{4}{9} \cdot \frac{6}{7}

2.5

4.3 Exercise 52

Multiply and write the answer in simplified form.

2536·6310\frac{25}{36} \cdot 6 \frac{3}{10}

2.5

4.3 Exercise 54

Multiply and write the answer in simplified form.

225(−229)2 \frac{2}{5} \left(−2 \frac{2}{9}\right)

2.5

4.3 Exercise 56

Multiply and write the answer in simplified form.

−1720·21112−1 \frac{7}{20} \cdot 2 \frac{11}{12}

2.5

4.3 Exercise 58

Divide, and write your answer in simplified form.

1312÷913 \frac{1}{2} \div 9

2.5

4.3 Exercise 60

Divide, and write your answer in simplified form.

−7÷514−7 \div 5 \frac{1}{4}

2.5

4.3 Exercise 62

Divide, and write your answer in simplified form.

215÷11102 \frac{1}{5} \div 1 \frac{1}{10}

2.5

4.3 Exercise 64

Divide, and write your answer in simplified form.

−1834÷(−334)−18 \frac{3}{4} \div \left(−3 \frac{3}{4}\right)

2.5

4.3 Exercise 66

Translate each English phrase into an algebraic expression.

the quotient of 7v7 v and 1313

2.5

4.3 Exercise 68

Translate each English phrase into an algebraic expression.

the quotient of aa and bb

2.5

4.3 Exercise 70

Translate each English phrase into an algebraic expression.

the quotient of AA and the difference of 33 and BB

2.5

4.3 Exercise 72

Simplify the complex fraction.

45815\frac{ \frac{4}{5} }{ \frac{8}{15} }

2.5

4.3 Exercise 74

Simplify the complex fraction.

−9163340\frac{- \frac{9}{16}}{\frac{33}{40}}

2.5

4.3 Exercise 76

Simplify the complex fraction.

−9103\frac{- \frac{9}{10}}{3}

2.5

4.3 Exercise 78

Simplify the complex fraction.

5310\frac{ \frac{5}{3} }{ 10 }

2.5

4.3 Exercise 80

Simplify the complex fraction.

r5s3\frac{ \frac{r}{5} }{ \frac{s}{3} }

2.5

4.3 Exercise 82

Simplify the complex fraction.

−38−y12\frac{- \frac{3}{8}}{- \frac{y}{12}}

2.5

4.3 Exercise 84

Simplify the complex fraction.

42316\frac{4 \frac{2}{3}}{\frac{1}{6}}

2.5

4.3 Exercise 86

Simplify the complex fraction.

38−634\frac{\frac{3}{8}}{−6 \frac{3}{4}}

2.5

4.3 Exercise 88

Identify the equivalent fractions.

Which of the following fractions are equivalent to −49?\frac{−4}{9} ?
−4−9,−49,49,−49\frac{−4}{−9} , \frac{−4}{9} , \frac{4}{9} , - \frac{4}{9}

2.5

4.3 Exercise 90

Identify the equivalent fractions.

Which of the following fractions are equivalent to −136?- \frac{13}{6} ?
136,13−6,−13−6,−136\frac{13}{6} , \frac{13}{−6} , \frac{−13}{−6} , \frac{−13}{6}

2.5

4.3 Exercise 92

Simplify.

9+37\frac{9 + 3}{7}

2.5

4.3 Exercise 94

Simplify.

19−46\frac{19 - 4}{6}

2.5

4.3 Exercise 96

Simplify.

464+4\frac{46}{4 + 4}

2.5

4.3 Exercise 98

Simplify.

−6+317−8\frac{−6 + 3}{17 - 8}

2.5

4.3 Exercise 100

Simplify.

15+918+12\frac{15 + 9}{18 + 12}

2.5

4.3 Exercise 102

Simplify.

3⋅4−24\frac{3 \cdot 4}{−24}

2.5

4.3 Exercise 104

Simplify.

6⋅69⋅2\frac{6 \cdot 6}{9 \cdot 2}

2.5

4.3 Exercise 106

Simplify.

72+160\frac{7^{2} + 1}{60}

2.5

4.3 Exercise 108

Simplify.

9⋅6−4⋅722+3\frac{9 \cdot 6 - 4 \cdot 7}{22 + 3}

2.5

4.3 Exercise 110

Simplify.

12⋅9−323⋅18\frac{12 \cdot 9 - 3^{2}}{3 \cdot 18}

2.5

4.3 Exercise 112

Simplify.

8⋅9−7⋅65⋅6−9⋅2\frac{8 \cdot 9 - 7 \cdot 6}{5 \cdot 6 - 9 \cdot 2}

2.5

4.3 Exercise 114

Simplify.

62−424−6\frac{6^{2} - 4^{2}}{4 - 6}

2.5

4.3 Exercise 116

Simplify.

7+3(5)−2−32\frac{7 + 3 \left(5\right)}{−2 - 3^{2}}

2.5

4.3 Exercise 118

Simplify.

9⋅7−3(12−8)8⋅7−6⋅6\frac{9 \cdot 7 - 3 \left(12 - 8\right)}{8 \cdot 7 - 6 \cdot 6}

2.5

4.3 Exercise 120

Simplify.

8(9−2)−4(14−9)7(8−3)−3(16−9)\frac{8 \left(9 - 2\right) −4 \left(14 - 9\right)}{7 \left(8 - 3\right) −3 \left(16 - 9\right)}

2.5

4.3 Exercise 122

Baking A booth at the county fair sells fudge by the pound. Their award winning “Chocolate Overdose” fudge contains 2232 \frac{2}{3} cups of chocolate chips per pound.

  1. ⓐ How many cups of chocolate chips are in a half-pound of the fudge?
  2. ⓑ The owners of the booth make the fudge in 1010-pound batches. How many chocolate chips do they need to make a 1010-pound batch? Write your results as improper fractions and as a mixe…

2.5

4.3 Exercise 124

Explain how to multiply mixed numbers.

2.5

4.3 Exercise 126

Explain why −12,−12,- \frac{1}{2} , \frac{−1}{2} , and 1−2\frac{1}{−2} are equivalent.

2.5

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