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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is a proficiency exam to the chapter "Introduction to Fractions and Multiplication and Division of Fractions." Each problem is accompanied with a reference link pointing back to the module that discusses the type of problem demonstrated in the question. The problems in this exam are accompanied by solutions.

Proficiency exam

( [link] ) Shade a portion that corresponds to the fraction 5 8 size 12{ { {5} over {8} } } {} .
A rectangle divided into eight parts.

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

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( [link] ) Specify the numerator and denominator of the fraction 5 9 size 12{ { {5} over {9} } } {} .

Numerator, 5; denominator, 9

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( [link] ) Write the fraction five elevenths.

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

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( [link] ) Write, in words, 4 5 size 12{ { {4} over {5} } } {} .

Four fifths

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( [link] ) Which of the fractions is a proper fraction? 4 1 12 size 12{4 { {1} over {"12"} } } {} , 5 12 size 12{ { {5} over {"12"} } } {} , 12 5 size 12{ { {"12"} over {5} } } {}

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

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( [link] ) Convert 3 4 7 size 12{3 { {4} over {7} } } {} to an improper fraction.

25 7 size 12{ { {"25"} over {7} } } {}

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( [link] ) Convert 16 5 size 12{ { {"16"} over {5} } } {} to a mixed number.

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

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( [link] ) Determine if 5 12 size 12{ { {5} over {"12"} } } {} and 20 48 size 12{ { {"20"} over {"48"} } } {} are equivalent fractions.

yes

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For problems 9-11, reduce, if possible, each fraction to lowest terms.

( [link] ) 21 35 size 12{ { {"21"} over {"35"} } } {}

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

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( [link] ) 15 51 size 12{ { {"15"} over {"51"} } } {}

5 17 size 12{ { {5} over {"17"} } } {}

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( [link] ) 104 480 size 12{ { {"104"} over {"480"} } } {}

13 60 size 12{ { {"13"} over {"60"} } } {}

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For problems 12 and 13, determine the missing numerator or denominator.

( [link] ) 5 9 = ? 36 size 12{ { {5} over {9} } = { {?} over {"36"} } } {}

20

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( [link] ) 4 3 = 32 ? size 12{ { {4} over {3} } = { {"32"} over {?} } } {}

24

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For problems 14-25, find each value.

( [link] ) 15 16 4 25 size 12{ { {"15"} over {"16"} } cdot { {4} over {"25"} } } {}

3 20 size 12{ { {3} over {"20"} } } {}

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( [link] ) 3 3 4 2 2 9 6 3 5 size 12{3 { {3} over {4} } cdot 2 { {2} over {9} } cdot 6 { {3} over {5} } } {}

55

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( [link] ) 25 36 size 12{ sqrt { { {"25"} over {"36"} } } } {}

5 6 size 12{ { {5} over {6} } } {}

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( [link] ) 4 9 81 64 size 12{ sqrt { { {4} over {9} } } cdot sqrt { { {"81"} over {"64"} } } } {}

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

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( [link] ) 11 30 225 121 size 12{ { {"11"} over {"30"} } cdot sqrt { { {"225"} over {"121"} } } } {}

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

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( [link] ) 4 15 ÷ 8 size 12{ { {4} over {"15"} } div 8} {}

1 30 size 12{ { {1} over {"30"} } } {}

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( [link] ) 8 15 5 12 ÷ 2 4 9 size 12{ { {8} over {"15"} } cdot { {5} over {"12"} } div 2 { {4} over {9} } } {}

1 11 size 12{ { {1} over {"11"} } } {}

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( [link] ) 6 5 3 ÷ 1 11 25 size 12{ left ( { {6} over {5} } right ) rSup { size 8{3} } div sqrt {1 { {"11"} over {"25"} } } } {}

36 25 = 1 11 25 size 12{ { {"36"} over {"25"} } =1 { {"11"} over {"25"} } } {}

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( [link] ) Find 5 12 size 12{ { {5} over {"12"} } } {} of 24 25 size 12{ { {"24"} over {"25"} } } {} .

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

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( [link] ) 2 9 size 12{ { {2} over {9} } } {} of what number is 1 18 size 12{ { {1} over {"18"} } } {} ?

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

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( [link] ) 1 5 7 size 12{1 { {5} over {7} } } {} of 21 20 size 12{ { {"21"} over {"20"} } } {} is what number?

9 5 = 1 4 5 size 12{ { {9} over {5} } =1 { {4} over {5} } } {}

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( [link] ) What part of 9 14 size 12{ { {9} over {"14"} } } {} is 6 7 size 12{ { {6} over {7} } } {} ?

4 3 or 1 1 3 size 12{ { {4} over {3} } `"or "1 { {1} over {3} } } {}

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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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