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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 ( [link] )

For Problems 1 and 2, name the suggested fraction.

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

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

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

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

numerator, 4; denominator, 5

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

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

numerator, 1; denominator, 3

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

Eight elevenths

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

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Two hundred six-thousandths

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

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

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

ten seventeenths

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

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

six hundred six, one thousand four hundred thirty-firsts

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

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

one sixteenth

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

One minute is one sixtieth of an hour.

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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.

numerator, 56; denominator, 14,190

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

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

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

A rectangle divided into four parts.

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

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

A rectangle divided into seven parts.

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Proper fraction, improper fraction, and mixed numbers ( [link] )

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

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

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

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

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

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

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

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

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

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

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

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

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

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

3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

because the whole number part is zero

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Why does 8 qualify as a mixed number?

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Equivalent fractions, reducing fractions to lowest terms, and raising fractions to higher term ( [link] )

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

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

equivalent

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

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

not equivalent

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

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

not equivalent

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

15

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

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

6

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

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

27

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

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

42

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

168

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

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

192

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

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Multiplication and division of fractions ( [link] , [link] )

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

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

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

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

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

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

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

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

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

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

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

1

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

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

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

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

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

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

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

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

50 7 = 7 1 7 size 12{ { {"50"} over {7} } =7 { {1} over {7} } } {}

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4 1 2 ÷ 2 4 7 size 12{4 { {1} over {2} } div 2 { {4} over {7} } } {}

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

2

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

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

3

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

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5 8 ÷ 1 1 4 size 12{ { {5} over {8} } div 1 { {1} over {4} } } {}

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

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

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

90

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

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

1

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Applications involving fractions ( [link] )

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

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

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

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

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

4

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

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

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

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

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

4

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

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

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

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Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Mueller Reply
7hours 36 min - 4hours 50 min
Tanis Reply

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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