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Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Introduction to Fractions and Multiplication and Division of Fractions" and contains many exercise problems. Odd problems are accompanied by solutions.

Exercise Supplement

Fractions of Whole Numbers ((Reference))

For Problems 1 and 2, name the suggested fraction.

Exercise 1

A circle divided into six equal parts. Two parts are shaded.

Solution

2626 size 12{ { {2} over {6} } } {} or 1313 size 12{ { {1} over {3} } } {}

Exercise 2

A rectangle divided into eight parts. Four parts are shaded.

For problems 3-5, specify the numerator and denominator.

Exercise 3

4545 size 12{ { {4} over {5} } } {}

Solution

numerator, 4; denominator, 5

Exercise 4

512512 size 12{ { {5} over {"12"} } } {}

Exercise 5

1313 size 12{ { {1} over {3} } } {}

Solution

numerator, 1; denominator, 3

For problems 6-10, write each fraction using digits.

Exercise 6

Three fifths

Exercise 7

Eight elevenths

Solution

811811 size 12{ { {8} over {"11"} } } {}

Exercise 8

Sixty-one forty firsts

Exercise 9

Two hundred six-thousandths

Solution

2006,0002006,000 size 12{ { {"200"} over {6,"000"} } } {}

Exercise 10

zero tenths

For problems 11-15, write each fraction using words.

Exercise 11

10171017 size 12{ { {"10"} over {"17"} } } {}

Solution

ten seventeenths

Exercise 12

21382138 size 12{ { {"21"} over {"38"} } } {}

Exercise 13

60614316061431 size 12{ { {"606"} over {"1431"} } } {}

Solution

six hundred six, one thousand four hundred thirty-firsts

Exercise 14

0808 size 12{ { {0} over {8} } } {}

Exercise 15

116116 size 12{ { {1} over {"16"} } } {}

Solution

one sixteenth

For problems 16-18, state each numerator and denominator and write each fraction using digits.

Exercise 16

One minute is one sixtieth of an hour.

Exercise 17

In a box that contains forty-five electronic components, eight are known to be defective. If three components are chosen at random from the box, the probability that all three are defective is fifty-six fourteen thousand one hundred ninetieths.

Solution

numerator, 56; denominator, 14,190

Exercise 18

About three fifths of the students in a college algebra class received a “B” in the course.

For problems 19 and 20, shade the region corresponding to the given fraction.

Exercise 19

1414 size 12{ { {1} over {4} } } {}

A rectangle divided into four parts.

Solution

A rectangle divided into four parts. One part is shaded.

Exercise 20

3737 size 12{ { {3} over {7} } } {}

A rectangle divided into seven parts.

Proper Fraction, Improper Fraction, and Mixed Numbers ((Reference))

For problems 21-29, convert each improper fraction to a mixed number.

Exercise 21

114114 size 12{ { {"11"} over {4} } } {}

Solution

234234 size 12{2 { {3} over {4} } } {}

Exercise 22

152152 size 12{ { {"15"} over {2} } } {}

Exercise 23

518518 size 12{ { {"51"} over {8} } } {}

Solution

638638 size 12{6 { {3} over {8} } } {}

Exercise 24

1211512115 size 12{ { {"121"} over {"15"} } } {}

Exercise 25

35633563 size 12{ { {"356"} over {3} } } {}

Solution

1182311823 size 12{"118" { {2} over {3} } } {}

Exercise 26

3232 size 12{ { {3} over {2} } } {}

Exercise 27

5454 size 12{ { {5} over {4} } } {}

Solution

114114 size 12{1 { {1} over {4} } } {}

Exercise 28

205205 size 12{ { {"20"} over {5} } } {}

Exercise 29

9393 size 12{ { {9} over {3} } } {}

Solution

3

For problems 30-40, convert each mixed number to an improper fraction.

Exercise 30

523523 size 12{5 { {2} over {3} } } {}

Exercise 31

16181618 size 12{"16" { {1} over {8} } } {}

Solution

12981298 size 12{ { {"129"} over {8} } } {}

Exercise 32

18131813 size 12{"18" { {1} over {3} } } {}

Exercise 33

315315 size 12{3 { {1} over {5} } } {}

Solution

165165 size 12{ { {"16"} over {5} } } {}

Exercise 34

29162916 size 12{2 { {9} over {"16"} } } {}

Exercise 35

172021172021 size 12{"17" { {"20"} over {"21"} } } {}

Solution

3772137721 size 12{ { {"377"} over {"21"} } } {}

Exercise 36

178178 size 12{1 { {7} over {8} } } {}

Exercise 37

112112 size 12{1 { {1} over {2} } } {}

Solution

3232 size 12{ { {3} over {2} } } {}

Exercise 38

212212 size 12{2 { {1} over {2} } } {}

Exercise 39

867867 size 12{8 { {6} over {7} } } {}

Solution

627627 size 12{ { {"62"} over {7} } } {}

Exercise 40

292292 size 12{2 { {9} over {2} } } {}

Exercise 41

Why does 01120112 size 12{0 { {1} over {"12"} } } {} not qualify as a mixed number?

Solution

because the whole number part is zero

Exercise 42

Why does 8 qualify as a mixed number?

Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Term ((Reference))

For problems 43-47, determine if the pairs of fractions are equivalent.

Exercise 43

1212 size 12{ { {1} over {2} } } {}, 15301530 size 12{ { {"15"} over {"30"} } } {}

Solution

equivalent

Exercise 44

8989 size 12{ { {8} over {9} } } {}, 32363236 size 12{ { {"32"} over {"36"} } } {}

Exercise 45

314314 size 12{ { {3} over {"14"} } } {}, 2411024110 size 12{ { {"24"} over {"110"} } } {}

Solution

not equivalent

Exercise 46

238238 size 12{2 { {3} over {8} } } {}, 38163816 size 12{ { {"38"} over {"16"} } } {}

Exercise 47

1087710877 size 12{ { {"108"} over {"77"} } } {}, 15131513 size 12{1 { {5} over {"13"} } } {}

Solution

not equivalent

For problems 48-60, reduce, if possible, each fraction.

Exercise 48

10251025 size 12{ { {"10"} over {"25"} } } {}

Exercise 49

32443244 size 12{ { {"32"} over {"44"} } } {}

Solution

811811 size 12{ { {8} over {"11"} } } {}

Exercise 50

102266102266 size 12{ { {"102"} over {"266"} } } {}

Exercise 51

15331533 size 12{ { {"15"} over {"33"} } } {}

Solution

511511 size 12{ { {5} over {"11"} } } {}

Exercise 52

18251825 size 12{ { {"18"} over {"25"} } } {}

Exercise 53

21352135 size 12{ { {"21"} over {"35"} } } {}

Solution

3535 size 12{ { {3} over {5} } } {}

Exercise 54

916916 size 12{ { {9} over {"16"} } } {}

Exercise 55

45854585 size 12{ { {"45"} over {"85"} } } {}

Solution

917917 size 12{ { {9} over {"17"} } } {}

Exercise 56

24422442 size 12{ { {"24"} over {"42"} } } {}

Exercise 57

7013670136 size 12{ { {"70"} over {"136"} } } {}

Solution

35683568 size 12{ { {"35"} over {"68"} } } {}

Exercise 58

182580182580 size 12{ { {"182"} over {"580"} } } {}

Exercise 59

325810325810 size 12{ { {"325"} over {"810"} } } {}

Solution

6516265162 size 12{ { {"65"} over {"162"} } } {}

Exercise 60

25010002501000 size 12{ { {"250"} over {"1000"} } } {}

For problems 61-72, determine the missing numerator or denominator.

Exercise 61

37=?3537=?35 size 12{ { {3} over {7} } = { {?} over {"35"} } } {}

Solution

15

Exercise 62

411=?99411=?99 size 12{ { {4} over {"11"} } = { {?} over {"99"} } } {}

Exercise 63

112=?72112=?72 size 12{ { {1} over {"12"} } = { {?} over {"72"} } } {}

Solution

6

Exercise 64

58=25?58=25? size 12{ { {5} over {8} } = { {"25"} over {?} } } {}

Exercise 65

119=33?119=33? size 12{ { {"11"} over {9} } = { {"33"} over {?} } } {}

Solution

27

Exercise 66

415=24?415=24? size 12{ { {4} over {"15"} } = { {"24"} over {?} } } {}

Exercise 67

1415=?451415=?45 size 12{ { {"14"} over {"15"} } = { {?} over {"45"} } } {}

Solution

42

Exercise 68

0 5 = ? 20 0 5 = ? 20

Exercise 69

1221=96?1221=96? size 12{ { {"12"} over {"21"} } = { {"96"} over {?} } } {}

Solution

168

Exercise 70

1423=?2531423=?253 size 12{ { {"14"} over {"23"} } = { {?} over {"253"} } } {}

Exercise 71

1516=180?1516=180? size 12{ { {"15"} over {"16"} } = { {"180"} over {?} } } {}

Solution

192

Exercise 72

2122=336?2122=336? size 12{ { {"21"} over {"22"} } = { {"336"} over {?} } } {}

Multiplication and Division of Fractions ((Reference), (Reference))

For problems 73-95, perform each multiplication and division.

Exercise 73

451516451516 size 12{ { {4} over {5} } cdot { {"15"} over {"16"} } } {}

Solution

3434 size 12{ { {3} over {4} } } {}

Exercise 74

8932489324 size 12{ { {8} over {9} } cdot { {3} over {"24"} } } {}

Exercise 75

110512110512 size 12{ { {1} over {"10"} } cdot { {5} over {"12"} } } {}

Solution

124124 size 12{ { {1} over {"24"} } } {}

Exercise 76

141575141575 size 12{ { {"14"} over {"15"} } cdot { {7} over {5} } } {}

Exercise 77

56132211395613221139 size 12{ { {5} over {6} } cdot { {"13"} over {"22"} } cdot { {"11"} over {"39"} } } {}

Solution

536536 size 12{ { {5} over {"36"} } } {}

Exercise 78

23÷1575623÷15756 size 12{ { {2} over {3} } div { {"15"} over {7} } cdot { {5} over {6} } } {}

Exercise 79

312÷72312÷72 size 12{3 { {1} over {2} } div { {7} over {2} } } {}

Solution

1

Exercise 80

249÷1145249÷1145 size 12{2 { {4} over {9} } div { {"11"} over {"45"} } } {}

Exercise 81

815316524815316524 size 12{ { {8} over {"15"} } cdot { {3} over {"16"} } cdot { {5} over {"24"} } } {}

Solution

148148 size 12{ { {1} over {"48"} } } {}

Exercise 82

815÷335916815÷335916 size 12{ { {8} over {"15"} } div 3 { {3} over {5} } cdot { {9} over {"16"} } } {}

Exercise 83

1415÷38910211415÷3891021 size 12{ { {"14"} over {"15"} } div 3 { {8} over {9} } cdot { {"10"} over {"21"} } } {}

Solution

435435 size 12{ { {4} over {"35"} } } {}

Exercise 84

1853418534 size 12{"18" cdot 5 { {3} over {4} } } {}

Exercise 85

33721123372112 size 12{3 { {3} over {7} } cdot 2 { {1} over {"12"} } } {}

Solution

507=717507=717 size 12{ { {"50"} over {7} } =7 { {1} over {7} } } {}

Exercise 86

412÷247412÷247 size 12{4 { {1} over {2} } div 2 { {4} over {7} } } {}

Exercise 87

612÷314612÷314 size 12{6 { {1} over {2} } div 3 { {1} over {4} } } {}

Solution

2

Exercise 88

3516÷27183516÷2718 size 12{3 { {5} over {"16"} } div 2 { {7} over {"18"} } } {}

Exercise 89

7÷2137÷213 size 12{7 div 2 { {1} over {3} } } {}

Solution

3

Exercise 90

17÷41417÷414 size 12{"17" div 4 { {1} over {4} } } {}

Exercise 91

58÷11458÷114 size 12{ { {5} over {8} } div 1 { {1} over {4} } } {}

Solution

1212 size 12{ { {1} over {2} } } {}

Exercise 92

223334223334 size 12{2 { {2} over {3} } cdot 3 { {3} over {4} } } {}

Exercise 93

2018420184 size 12{"20" cdot { {"18"} over {4} } } {}

Solution

90

Exercise 94

0÷4180÷418 size 12{0 div 4 { {1} over {8} } } {}

Exercise 95

1÷6142541÷614254 size 12{1 div 6 { {1} over {4} } cdot { {"25"} over {4} } } {}

Solution

1

Applications Involving Fractions ((Reference))

Exercise 96

Find 8989 size 12{ { {8} over {9} } } {} of 272272 size 12{ { {"27"} over {2} } } {}.

Exercise 97

What part of 3838 size 12{ { {3} over {8} } } {} is 21162116 size 12{ { {"21"} over {"16"} } } {}?

Solution

7272 size 12{ { {7} over {2} } } {} or 312312 size 12{3 { {1} over {2} } } {}

Exercise 98

What part of 315315 size 12{3 { {1} over {5} } } {} is 17251725 size 12{1 { {7} over {"25"} } } {}?

Exercise 99

Find 623623 size 12{6 { {2} over {3} } } {} of 915915 size 12{ { {9} over {"15"} } } {}.

Solution

4

Exercise 100

720720 size 12{ { {7} over {"20"} } } {} of what number is 14351435 size 12{ { {"14"} over {"35"} } } {}?

Exercise 101

What part of 41164116 size 12{4 { {1} over {"16"} } } {} is 334334 size 12{3 { {3} over {4} } } {}?

Solution

12131213 size 12{ { {"12"} over {"13"} } } {}

Exercise 102

Find 83108310 size 12{8 { {3} over {"10"} } } {} of 16231623 size 12{"16" { {2} over {3} } } {}.

Exercise 103

320320 size 12{ { {3} over {"20"} } } {} of what number is 18301830 size 12{ { {"18"} over {"30"} } } {}?

Solution

4

Exercise 104

Find 1313 size 12{ { {1} over {3} } } {} of 0.

Exercise 105

Find 11121112 size 12{ { {"11"} over {"12"} } } {} of 1.

Solution

11121112 size 12{ { {"11"} over {"12"} } } {}

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