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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 "Addition and Subtraction of Fractions, Comparing Fractions, and Complex 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

For problems 1-12, perform each indicated operation and write the result in simplest form.

( [link] ) 3 16 + 1 8 size 12{ { {3} over {"16"} } + { {1} over {8} } } {}

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

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( [link] ) 2 2 3 + 5 1 6 size 12{2 { {2} over {3} } +5 { {1} over {6} } } {}

7 5 6 size 12{7 { {5} over {6} } } {}

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( [link] ) 7 15 20 21 + 5 9 size 12{ { {7} over {"15"} } cdot { {"20"} over {"21"} } + { {5} over {9} } } {}

1

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( [link] ) 3 11 + 5 11 size 12{ { {3} over {"11"} } + { {5} over {"11"} } } {}

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

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( [link] ) 6 2 9 1 17 28 3 4 17 21 17 size 12{6 { {2} over {9} } cdot 1 { {"17"} over {"28"} } - left (3 { {4} over {"17"} } - { {"21"} over {"17"} } right )} {}

8

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( [link] ) 5 1 8 2 4 5 size 12{5 { {1} over {8} } - 2 { {4} over {5} } } {}

2 13 40 size 12{2 { {"13"} over {"40"} } } {}

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( [link] ) 7 12 8 21 size 12{ { { { {7} over {"12"} } } over { { {8} over {"21"} } } } } {}

49 32 size 12{ { {"49"} over {"32"} } } {} or 17 32 size 12{ { {"17"} over {"32"} } } {}

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( [link] ) 1 8 + 3 4 1 7 8 size 12{ { { { {1} over {8} } + { {3} over {4} } } over {1 { {7} over {8} } } } } {}

7 15 size 12{ { {7} over {"15"} } } {}

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( [link] ) 4 5 16 + 1 1 3 2 5 24 size 12{4 { {5} over {"16"} } +1 { {1} over {3} } - 2 { {5} over {"24"} } } {}

3 7 16 size 12{3 { {7} over {"16"} } } {}

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( [link] ) 5 18 15 16 3 8 size 12{ { {5} over {"18"} } cdot left ( { {"15"} over {"16"} } - { {3} over {8} } right )} {}

5 32 size 12{ { {5} over {"32"} } } {}

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( [link] ) 4 + 2 1 3 size 12{4+2 { {1} over {3} } } {}

6 1 3 size 12{6 { {1} over {3} } } {} or 19 3 size 12{ { {"19"} over {3} } } {}

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( [link] ) 8 3 7 5 size 12{8 { {3} over {7} } - 5} {}

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

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For problems 13-15, specify the fractions that are equivalent.

( [link] ) 4 5 size 12{ { {4} over {5} } } {} , 12 15 size 12{ { {"12"} over {"15"} } } {}

equivalent

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( [link] ) 5 8 size 12{ { {5} over {8} } } {} , 24 40 size 12{ { {"24"} over {"40"} } } {}

not equivalent

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( [link] ) 5 12 size 12{ { {5} over {"12"} } } {} , 80 192 size 12{ { {"80"} over {"192"} } } {}

equivalent

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For problems 16-20, place each collection of fractions in order from smallest to largest.

( [link] ) 8 9 size 12{ { {8} over {9} } } {} , 6 7 size 12{ { {6} over {7} } } {}

6 7 size 12{ { {6} over {7} } } {} , 8 9 size 12{ { {8} over {9} } } {}

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( [link] ) 5 8 size 12{ { {5} over {8} } } {} , 7 9 size 12{ { {7} over {9} } } {}

5 8 size 12{ { {5} over {8} } } {} , 7 9 size 12{ { {7} over {9} } } {}

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( [link] ) 11 5 16 size 12{"11" { {5} over {"16"} } } {} , 11 5 12 size 12{"11" { {5} over {"12"} } } {}

11 5 16 size 12{"11" { {5} over {"16"} } } {} , 11 5 12 size 12{"11" { {5} over {"12"} } } {}

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( [link] ) 2 15 size 12{ { {2} over {"15"} } } {} , 3 10 size 12{ { {3} over {"10"} } } {} , 1 6 size 12{ { {1} over {6} } } {}

2 15 size 12{ { {2} over {"15"} } } {} , 1 6 size 12{ { {1} over {6} } } {} , 3 10 size 12{ { {3} over {"10"} } } {}

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( [link] ) 19 32 size 12{ { {"19"} over {"32"} } } {} , 9 16 size 12{ { {9} over {"16"} } } {} , 5 8 size 12{ { {5} over {8} } } {}

9 16 size 12{ { {9} over {"16"} } } {} , 19 32 size 12{ { {"19"} over {"32"} } } {} , 5 8 size 12{ { {5} over {8} } } {}

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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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