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Addition and Subtraction of Fractions, Comparing Fractions, and Complex Fractions: Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: 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 ((Reference), (Reference), (Reference))

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

Exercise 1

34+5834+58 size 12{ { {3} over {4} } + { {5} over {8} } } {}

Solution

118118 size 12{ { {"11"} over {8} } } {} or 138138 size 12{1 { {3} over {8} } } {}

Exercise 2

916+14916+14 size 12{ { {9} over {"16"} } + { {1} over {4} } } {}

Exercise 3

18+3818+38 size 12{ { {1} over {8} } + { {3} over {8} } } {}

Solution

1212 size 12{ { {1} over {2} } } {}

Exercise 4

57+114+52157+114+521 size 12{ { {5} over {7} } + { {1} over {"14"} } + { {5} over {"21"} } } {}

Exercise 5

56+13+52156+13+521 size 12{ { {5} over {6} } + { {1} over {3} } + { {5} over {"21"} } } {}

Solution

5942=117425942=11742 size 12{ { {"59"} over {"42"} } =1 { {"17"} over {"42"} } } {}

Exercise 6

25+1825+18 size 12{ { {2} over {5} } + { {1} over {8} } } {}

Exercise 7

14+18+1414+18+14 size 12{ { {1} over {4} } + { {1} over {8} } + { {1} over {4} } } {}

Solution

5858 size 12{ { {5} over {8} } } {}

Exercise 8

116+110116+110 size 12{ { {1} over {"16"} } + { {1} over {"10"} } } {}

Exercise 9

27+1327+13 size 12{ { {2} over {7} } + { {1} over {3} } } {}

Solution

13211321 size 12{ { {"13"} over {"21"} } } {}

Exercise 10

213+16213+16 size 12{2 { {1} over {3} } + { {1} over {6} } } {}

Exercise 11

31116+3431116+34 size 12{3 { {"11"} over {"16"} } + { {3} over {4} } } {}

Solution

47164716 size 12{4 { {7} over {"16"} } } {}

Exercise 12

5112+3185112+318 size 12{5 { {1} over {"12"} } +3 { {1} over {8} } } {}

Exercise 13

1625+8141625+814 size 12{"16" { {2} over {5} } +8 { {1} over {4} } } {}

Solution

83208320 size 12{8 { {3} over {"20"} } } {}

Exercise 14

117+247117+247 size 12{1 { {1} over {7} } +2 { {4} over {7} } } {}

Exercise 15

138+0138+0 size 12{1 { {3} over {8} } +0} {}

Solution

138138 size 12{1 { {3} over {8} } } {}

Exercise 16

3110+43110+4 size 12{3 { {1} over {"10"} } +4} {}

Exercise 17

1823+61823+6 size 12{"18" { {2} over {3} } +6} {}

Solution

24232423 size 12{"24" { {2} over {3} } } {}

Exercise 18

143+554143+554 size 12{1 { {4} over {3} } +5 { {5} over {4} } } {}

Exercise 19

214+23214+23 size 12{ { {"21"} over {4} } + { {2} over {3} } } {}

Solution

7112=511127112=51112 size 12{ { {"71"} over {"12"} } =5 { {"11"} over {"12"} } } {}

Exercise 20

1516−181516−18 size 12{ { {"15"} over {"16"} } - { {1} over {8} } } {}

Exercise 21

911−522911−522 size 12{ { {9} over {"11"} } - { {5} over {"22"} } } {}

Solution

13221322 size 12{ { {"13"} over {"22"} } } {}

Exercise 22

6215−13106215−1310 size 12{6 { {2} over {"15"} } - 1 { {3} over {"10"} } } {}

Exercise 23

523+815−214523+815−214 size 12{5 { {2} over {3} } +8 { {1} over {5} } - 2 { {1} over {4} } } {}

Solution

113760113760 size 12{"11" { {"37"} over {"60"} } } {}

Exercise 24

8310−456−31158310−456−3115 size 12{8 { {3} over {"10"} } - 4 { {5} over {6} } - 3 { {1} over {"15"} } } {}

Exercise 25

1112+19−1161112+19−116 size 12{ { {"11"} over {"12"} } + { {1} over {9} } - { {1} over {"16"} } } {}

Solution

139144139144 size 12{ { {"139"} over {"144"} } } {}

Exercise 26

729−556−113729−556−113 size 12{7 { {2} over {9} } - 5 { {5} over {6} } - 1 { {1} over {3} } } {}

Exercise 27

1625−816−32151625−816−3215 size 12{16 { {2} over {5} } - 8 { {1} over {6} } - 3 { {2} over {15} } } {}

Solution

51105110 size 12{5 { {1} over {"10"} } } {}

Exercise 28

418+0−328418+0−328 size 12{4 { {1} over {8} } +0 - { {"32"} over {8} } } {}

Exercise 29

418+0−328418+0−328 size 12{4 { {1} over {8} } +0 - { {"32"} over {8} } } {}

Solution

1818 size 12{ { {1} over {8} } } {}

Exercise 30

8−2138−213 size 12{8 - 2 { {1} over {3} } } {}

Exercise 31

4−35164−3516 size 12{4 - 3 { {5} over {"16"} } } {}

Solution

11161116 size 12{ { {"11"} over {"16"} } } {}

Exercise 32

637+4637+4 size 12{6 { {3} over {7} } +4} {}

Exercise 33

11211−311211−3 size 12{"11" { {2} over {"11"} } - 3} {}

Solution

82118211 size 12{8 { {2} over {"11"} } } {}

Exercise 34

2158−582158−58 size 12{"21" { {5} over {8} } - { {5} over {8} } } {}

Exercise 35

34+516⋅4534+516⋅45 size 12{ { {3} over {4} } + { {5} over {"16"} } cdot { {4} over {5} } } {}

Solution

1

Exercise 36

1112+1516÷2121112+1516÷212 size 12{ { {"11"} over {"12"} } + { {"15"} over {"16"} } div 2 { {1} over {2} } } {}

Exercise 37

1310+223÷491310+223÷49 size 12{1 { {3} over {"10"} } +2 { {2} over {3} } div { {4} over {9} } } {}

Solution

73107310 size 12{7 { {3} over {"10"} } } {}

Exercise 38

835−1114⋅37835−1114⋅37 size 12{8 { {3} over {5} } - 1 { {1} over {"14"} } cdot { {3} over {7} } } {}

Exercise 39

238÷3916−19238÷3916−19 size 12{2 { {3} over {8} } div 3 { {9} over {"16"} } - { {1} over {9} } } {}

Solution

5959 size 12{ { {5} over {9} } } {}

Exercise 40

1525÷50−1101525÷50−110 size 12{"15" { {2} over {5} } div "50" - { {1} over {"10"} } } {}

Complex Fractions and Combinations of Operations with Fractions ((Reference),(Reference))

Exercise 41

91621329162132 size 12{ { { { {9} over {"16"} } } over { { {"21"} over {"32"} } } } } {}

Solution

6767 size 12{ { {6} over {7} } } {}

Exercise 42

1021111410211114 size 12{ { { { {"10"} over {"21"} } } over { { {"11"} over {"14"} } } } } {}

Exercise 43

17915271791527 size 12{ { {1 { {7} over {9} } } over {1 { {5} over {"27"} } } } } {}

Solution

3232 size 12{ { {3} over {2} } } {} or 112112 size 12{1 { {1} over {2} } } {}

Exercise 44

1517505115175051 size 12{ { { { {"15"} over {"17"} } } over { { {"50"} over {"51"} } } } } {}

Exercise 45

191621112191621112 size 12{ { {1 { {9} over {"16"} } } over {2 { {"11"} over {"12"} } } } } {}

Solution

15281528 size 12{ { {"15"} over {"28"} } } {}

Exercise 46

8415384153 size 12{ { {8 { {4} over {"15"} } } over {3} } } {}

Exercise 47

9118691186 size 12{ { {9 { {1} over {"18"} } } over {6} } } {}

Solution

163108163108 size 12{ { {"163"} over {"108"} } } {} or 155108155108 size 12{1 { {"55"} over {"108"} } } {}

Exercise 48

314+218516314+218516 size 12{ { {3 { {1} over {4} } +2 { {1} over {8} } } over {5 { {1} over {6} } } } } {}

Exercise 49

3+21214+563+21214+56 size 12{ { {3+2 { {1} over {2} } } over { { {1} over {4} } + { {5} over {6} } } } } {}

Solution

66136613 size 12{ { {"66"} over {"13"} } } {} or 51135113 size 12{5 { {1} over {"13"} } } {}

Exercise 50

4+17109−2154+17109−215 size 12{ { {4+1 { {7} over {"10"} } } over {9 - 2 { {1} over {5} } } } } {}

Exercise 51

1259−221259−22 size 12{ { {1 { {2} over {5} } } over {9 - { {2} over {2} } } } } {}

Solution

740740 size 12{ { {7} over {"40"} } } {}

Exercise 52

123⋅14+15112123⋅14+15112 size 12{ { {1 { {2} over {3} } cdot left ( { {1} over {4} } + { {1} over {5} } right )} over {1 { {1} over {2} } } } } {}

Exercise 53

1023⋅56+2891023⋅56+289 size 12{ { { { {"10"} over {"23"} } cdot left ( { {5} over {6} } +2 right )} over { { {8} over {9} } } } } {}

Solution

255184255184 size 12{ { {"255"} over {"184"} } } {} or 171184171184 size 12{1 { {"71"} over {"184"} } } {}

Comparing Fractions ((Reference))

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

Exercise 54

1818 size 12{ { {1} over {8} } } {}, 316316 size 12{ { {3} over {"16"} } } {}

Exercise 55

332332 size 12{ { {3} over {"32"} } } {}, 1818 size 12{ { {1} over {8} } } {}

Solution

332332 size 12{ { {3} over {"32"} } } {}, 1818 size 12{ { {1} over {8} } } {}

Exercise 56

516516 size 12{ { {5} over {"16"} } } {}, 324324 size 12{ { {3} over {"24"} } } {}

Exercise 57

310310 size 12{ { {3} over {"10"} } } {}, 5656 size 12{ { {5} over {6} } } {}

Solution

310310 size 12{ { {3} over {"10"} } } {}, 5656 size 12{ { {5} over {6} } } {}

Exercise 58

2929 size 12{ { {2} over {9} } } {}, 1313 size 12{ { {1} over {3} } } {}, 1616 size 12{ { {1} over {6} } } {}

Exercise 59

3838 size 12{ { {3} over {8} } } {}, 8383 size 12{ { {8} over {3} } } {}, 196196 size 12{ { {"19"} over {6} } } {}

Solution

3838 size 12{ { {3} over {8} } } {}, 8383 size 12{ { {8} over {3} } } {}, 196196 size 12{ { {"19"} over {6} } } {}

Exercise 60

3535 size 12{ { {3} over {5} } } {}, 210210 size 12{ { {2} over {"10"} } } {}, 720720 size 12{ { {7} over {"20"} } } {}

Exercise 61

4747 size 12{ { {4} over {7} } } {}, 5959 size 12{ { {5} over {9} } } {}

Solution

5959 size 12{ { {5} over {9} } } {}, 4747 size 12{ { {4} over {7} } } {}

Exercise 62

4545 size 12{ { {4} over {5} } } {}, 5757 size 12{ { {5} over {7} } } {}

Exercise 63

512512 size 12{ { {5} over {"12"} } } {}, 4949 size 12{ { {4} over {9} } } {}, 715715 size 12{ { {7} over {"15"} } } {}

Solution

512512 size 12{ { {5} over {"12"} } } {}, 4949 size 12{ { {4} over {9} } } {}, 715715 size 12{ { {7} over {"15"} } } {}

Exercise 64

736736 size 12{ { {7} over {"36"} } } {}, 124124 size 12{ { {1} over {"24"} } } {}, 512512 size 12{ { {5} over {"12"} } } {}

Exercise 65

5858 size 12{ { {5} over {8} } } {}, 13161316 size 12{ { {"13"} over {"16"} } } {}, 3434 size 12{ { {3} over {4} } } {}

Solution

5858 size 12{ { {5} over {8} } } {}, 3434 size 12{ { {3} over {4} } } {}, 13161316 size 12{ { {"13"} over {"16"} } } {}

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