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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 "Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions" and contains many exercise problems. Odd problems are accompanied by solutions.

Exercise supplement

Addition and subtractions of fractions with like and unlike denominators, and addition and subtraction of mixed numbers ( [link] , [link] , [link] )

For problems 1-53, perform each indicated operation and write the result in simplest form.

3 4 + 5 8 size 12{ { {3} over {4} } + { {5} over {8} } } {}

11 8 size 12{ { {"11"} over {8} } } {} or 1 3 8 size 12{1 { {3} over {8} } } {}

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9 16 + 1 4 size 12{ { {9} over {"16"} } + { {1} over {4} } } {}

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1 8 + 3 8 size 12{ { {1} over {8} } + { {3} over {8} } } {}

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

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5 7 + 1 14 + 5 21 size 12{ { {5} over {7} } + { {1} over {"14"} } + { {5} over {"21"} } } {}

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5 6 + 1 3 + 5 21 size 12{ { {5} over {6} } + { {1} over {3} } + { {5} over {"21"} } } {}

59 42 = 1 17 42 size 12{ { {"59"} over {"42"} } =1 { {"17"} over {"42"} } } {}

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2 5 + 1 8 size 12{ { {2} over {5} } + { {1} over {8} } } {}

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1 4 + 1 8 + 1 4 size 12{ { {1} over {4} } + { {1} over {8} } + { {1} over {4} } } {}

5 8 size 12{ { {5} over {8} } } {}

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1 16 + 1 10 size 12{ { {1} over {"16"} } + { {1} over {"10"} } } {}

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

13 21 size 12{ { {"13"} over {"21"} } } {}

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

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3 11 16 + 3 4 size 12{3 { {"11"} over {"16"} } + { {3} over {4} } } {}

4 7 16 size 12{4 { {7} over {"16"} } } {}

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5 1 12 + 3 1 8 size 12{5 { {1} over {"12"} } +3 { {1} over {8} } } {}

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16 2 5 + 8 1 4 size 12{"16" { {2} over {5} } +8 { {1} over {4} } } {}

8 3 20 size 12{8 { {3} over {"20"} } } {}

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1 1 7 + 2 4 7 size 12{1 { {1} over {7} } +2 { {4} over {7} } } {}

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1 3 8 + 0 size 12{1 { {3} over {8} } +0} {}

1 3 8 size 12{1 { {3} over {8} } } {}

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3 1 10 + 4 size 12{3 { {1} over {"10"} } +4} {}

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18 2 3 + 6 size 12{"18" { {2} over {3} } +6} {}

24 2 3 size 12{"24" { {2} over {3} } } {}

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1 4 3 + 5 5 4 size 12{1 { {4} over {3} } +5 { {5} over {4} } } {}

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21 4 + 2 3 size 12{ { {"21"} over {4} } + { {2} over {3} } } {}

71 12 = 5 11 12 size 12{ { {"71"} over {"12"} } =5 { {"11"} over {"12"} } } {}

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15 16 1 8 size 12{ { {"15"} over {"16"} } - { {1} over {8} } } {}

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9 11 5 22 size 12{ { {9} over {"11"} } - { {5} over {"22"} } } {}

13 22 size 12{ { {"13"} over {"22"} } } {}

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

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5 2 3 + 8 1 5 2 1 4 size 12{5 { {2} over {3} } +8 { {1} over {5} } - 2 { {1} over {4} } } {}

11 37 60 size 12{"11" { {"37"} over {"60"} } } {}

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8 3 10 4 5 6 3 1 15 size 12{8 { {3} over {"10"} } - 4 { {5} over {6} } - 3 { {1} over {"15"} } } {}

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11 12 + 1 9 1 16 size 12{ { {"11"} over {"12"} } + { {1} over {9} } - { {1} over {"16"} } } {}

139 144 size 12{ { {"139"} over {"144"} } } {}

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7 2 9 5 5 6 1 1 3 size 12{7 { {2} over {9} } - 5 { {5} over {6} } - 1 { {1} over {3} } } {}

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16 2 5 8 1 6 3 2 15 size 12{16 { {2} over {5} } - 8 { {1} over {6} } - 3 { {2} over {15} } } {}

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

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4 1 8 + 0 32 8 size 12{4 { {1} over {8} } +0 - { {"32"} over {8} } } {}

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4 1 8 + 0 32 8 size 12{4 { {1} over {8} } +0 - { {"32"} over {8} } } {}

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

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8 2 1 3 size 12{8 - 2 { {1} over {3} } } {}

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4 3 5 16 size 12{4 - 3 { {5} over {"16"} } } {}

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

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6 3 7 + 4 size 12{6 { {3} over {7} } +4} {}

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11 2 11 3 size 12{"11" { {2} over {"11"} } - 3} {}

8 2 11 size 12{8 { {2} over {"11"} } } {}

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21 5 8 5 8 size 12{"21" { {5} over {8} } - { {5} over {8} } } {}

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3 4 + 5 16 4 5 size 12{ { {3} over {4} } + { {5} over {"16"} } cdot { {4} over {5} } } {}

1

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11 12 + 15 16 ÷ 2 1 2 size 12{ { {"11"} over {"12"} } + { {"15"} over {"16"} } div 2 { {1} over {2} } } {}

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1 3 10 + 2 2 3 ÷ 4 9 size 12{1 { {3} over {"10"} } +2 { {2} over {3} } div { {4} over {9} } } {}

7 3 10 size 12{7 { {3} over {"10"} } } {}

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8 3 5 1 1 14 3 7 size 12{8 { {3} over {5} } - 1 { {1} over {"14"} } cdot { {3} over {7} } } {}

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2 3 8 ÷ 3 9 16 1 9 size 12{2 { {3} over {8} } div 3 { {9} over {"16"} } - { {1} over {9} } } {}

5 9 size 12{ { {5} over {9} } } {}

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15 2 5 ÷ 50 1 10 size 12{"15" { {2} over {5} } div "50" - { {1} over {"10"} } } {}

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Complex fractions and combinations of operations with fractions ( [link] , [link] )

9 16 21 32 size 12{ { { { {9} over {"16"} } } over { { {"21"} over {"32"} } } } } {}

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

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10 21 11 14 size 12{ { { { {"10"} over {"21"} } } over { { {"11"} over {"14"} } } } } {}

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1 7 9 1 5 27 size 12{ { {1 { {7} over {9} } } over {1 { {5} over {"27"} } } } } {}

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

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15 17 50 51 size 12{ { { { {"15"} over {"17"} } } over { { {"50"} over {"51"} } } } } {}

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1 9 16 2 11 12 size 12{ { {1 { {9} over {"16"} } } over {2 { {"11"} over {"12"} } } } } {}

15 28 size 12{ { {"15"} over {"28"} } } {}

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8 4 15 3 size 12{ { {8 { {4} over {"15"} } } over {3} } } {}

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9 1 18 6 size 12{ { {9 { {1} over {"18"} } } over {6} } } {}

163 108 size 12{ { {"163"} over {"108"} } } {} or 1 55 108 size 12{1 { {"55"} over {"108"} } } {}

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3 1 4 + 2 1 8 5 1 6 size 12{ { {3 { {1} over {4} } +2 { {1} over {8} } } over {5 { {1} over {6} } } } } {}

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3 + 2 1 2 1 4 + 5 6 size 12{ { {3+2 { {1} over {2} } } over { { {1} over {4} } + { {5} over {6} } } } } {}

66 13 size 12{ { {"66"} over {"13"} } } {} or 5 1 13 size 12{5 { {1} over {"13"} } } {}

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4 + 1 7 10 9 2 1 5 size 12{ { {4+1 { {7} over {"10"} } } over {9 - 2 { {1} over {5} } } } } {}

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1 2 5 9 2 2 size 12{ { {1 { {2} over {5} } } over {9 - { {2} over {2} } } } } {}

7 40 size 12{ { {7} over {"40"} } } {}

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1 2 3 1 4 + 1 5 1 1 2 size 12{ { {1 { {2} over {3} } cdot left ( { {1} over {4} } + { {1} over {5} } right )} over {1 { {1} over {2} } } } } {}

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10 23 5 6 + 2 8 9 size 12{ { { { {"10"} over {"23"} } cdot left ( { {5} over {6} } +2 right )} over { { {8} over {9} } } } } {}

255 184 size 12{ { {"255"} over {"184"} } } {} or 1 71 184 size 12{1 { {"71"} over {"184"} } } {}

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Comparing fractions ( [link] )

For problems 54-65, place each collection in order from smallest to largest.

1 8 size 12{ { {1} over {8} } } {} , 3 16 size 12{ { {3} over {"16"} } } {}

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3 32 size 12{ { {3} over {"32"} } } {} , 1 8 size 12{ { {1} over {8} } } {}

3 32 size 12{ { {3} over {"32"} } } {} , 1 8 size 12{ { {1} over {8} } } {}

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5 16 size 12{ { {5} over {"16"} } } {} , 3 24 size 12{ { {3} over {"24"} } } {}

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3 10 size 12{ { {3} over {"10"} } } {} , 5 6 size 12{ { {5} over {6} } } {}

3 10 size 12{ { {3} over {"10"} } } {} , 5 6 size 12{ { {5} over {6} } } {}

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2 9 size 12{ { {2} over {9} } } {} , 1 3 size 12{ { {1} over {3} } } {} , 1 6 size 12{ { {1} over {6} } } {}

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3 8 size 12{ { {3} over {8} } } {} , 8 3 size 12{ { {8} over {3} } } {} , 19 6 size 12{ { {"19"} over {6} } } {}

3 8 size 12{ { {3} over {8} } } {} , 8 3 size 12{ { {8} over {3} } } {} , 19 6 size 12{ { {"19"} over {6} } } {}

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3 5 size 12{ { {3} over {5} } } {} , 2 10 size 12{ { {2} over {"10"} } } {} , 7 20 size 12{ { {7} over {"20"} } } {}

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4 7 size 12{ { {4} over {7} } } {} , 5 9 size 12{ { {5} over {9} } } {}

5 9 size 12{ { {5} over {9} } } {} , 4 7 size 12{ { {4} over {7} } } {}

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4 5 size 12{ { {4} over {5} } } {} , 5 7 size 12{ { {5} over {7} } } {}

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5 12 size 12{ { {5} over {"12"} } } {} , 4 9 size 12{ { {4} over {9} } } {} , 7 15 size 12{ { {7} over {"15"} } } {}

5 12 size 12{ { {5} over {"12"} } } {} , 4 9 size 12{ { {4} over {9} } } {} , 7 15 size 12{ { {7} over {"15"} } } {}

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7 36 size 12{ { {7} over {"36"} } } {} , 1 24 size 12{ { {1} over {"24"} } } {} , 5 12 size 12{ { {5} over {"12"} } } {}

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5 8 size 12{ { {5} over {8} } } {} , 13 16 size 12{ { {"13"} over {"16"} } } {} , 3 4 size 12{ { {3} over {4} } } {}

5 8 size 12{ { {5} over {8} } } {} , 3 4 size 12{ { {3} over {4} } } {} , 13 16 size 12{ { {"13"} over {"16"} } } {}

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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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