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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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