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Proficiency Exam

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 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.

Exercise 1

((Reference)) 316+18316+18 size 12{ { {3} over {"16"} } + { {1} over {8} } } {}

Solution

516516 size 12{ { {5} over {"16"} } } {}

Exercise 2

((Reference)) 223+516223+516 size 12{2 { {2} over {3} } +5 { {1} over {6} } } {}

Solution

756756 size 12{7 { {5} over {6} } } {}

Exercise 3

((Reference)) 715⋅2021+59715⋅2021+59 size 12{ { {7} over {"15"} } cdot { {"20"} over {"21"} } + { {5} over {9} } } {}

Solution

1

Exercise 4

((Reference)) 311+511311+511 size 12{ { {3} over {"11"} } + { {5} over {"11"} } } {}

Solution

811811 size 12{ { {8} over {"11"} } } {}

Exercise 5

((Reference)) 629⋅11728−3417−2117629⋅11728−3417−2117 size 12{6 { {2} over {9} } cdot 1 { {"17"} over {"28"} } - left (3 { {4} over {"17"} } - { {"21"} over {"17"} } right )} {}

Solution

8

Exercise 6

((Reference)) 518−245518−245 size 12{5 { {1} over {8} } - 2 { {4} over {5} } } {}

Solution

2134021340 size 12{2 { {"13"} over {"40"} } } {}

Exercise 7

((Reference)) 712821712821 size 12{ { { { {7} over {"12"} } } over { { {8} over {"21"} } } } } {}

Solution

49324932 size 12{ { {"49"} over {"32"} } } {} or 17321732 size 12{ { {"17"} over {"32"} } } {}

Exercise 8

((Reference)) 18+3417818+34178 size 12{ { { { {1} over {8} } + { {3} over {4} } } over {1 { {7} over {8} } } } } {}

Solution

715715 size 12{ { {7} over {"15"} } } {}

Exercise 9

((Reference)) 4516+113−25244516+113−2524 size 12{4 { {5} over {"16"} } +1 { {1} over {3} } - 2 { {5} over {"24"} } } {}

Solution

37163716 size 12{3 { {7} over {"16"} } } {}

Exercise 10

((Reference)) 518⋅1516−38518⋅1516−38 size 12{ { {5} over {"18"} } cdot left ( { {"15"} over {"16"} } - { {3} over {8} } right )} {}

Solution

532532 size 12{ { {5} over {"32"} } } {}

Exercise 11

((Reference)) 4+2134+213 size 12{4+2 { {1} over {3} } } {}

Solution

613613 size 12{6 { {1} over {3} } } {} or 193193 size 12{ { {"19"} over {3} } } {}

Exercise 12

((Reference)) 837−5837−5 size 12{8 { {3} over {7} } - 5} {}

Solution

337337 size 12{3 { {3} over {7} } } {}

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

Exercise 13

((Reference)) 4545 size 12{ { {4} over {5} } } {}, 12151215 size 12{ { {"12"} over {"15"} } } {}

Solution

equivalent

Exercise 14

((Reference)) 5858 size 12{ { {5} over {8} } } {}, 24402440 size 12{ { {"24"} over {"40"} } } {}

Solution

not equivalent

Exercise 15

((Reference)) 512512 size 12{ { {5} over {"12"} } } {}, 8019280192 size 12{ { {"80"} over {"192"} } } {}

Solution

equivalent

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

Exercise 16

((Reference)) 8989 size 12{ { {8} over {9} } } {}, 6767 size 12{ { {6} over {7} } } {}

Solution

6767 size 12{ { {6} over {7} } } {}, 8989 size 12{ { {8} over {9} } } {}

Exercise 17

((Reference)) 5858 size 12{ { {5} over {8} } } {}, 7979 size 12{ { {7} over {9} } } {}

Solution

5858 size 12{ { {5} over {8} } } {}, 7979 size 12{ { {7} over {9} } } {}

Exercise 18

((Reference)) 1151611516 size 12{"11" { {5} over {"16"} } } {}, 1151211512 size 12{"11" { {5} over {"12"} } } {}

Solution

1151611516 size 12{"11" { {5} over {"16"} } } {}, 1151211512 size 12{"11" { {5} over {"12"} } } {}

Exercise 19

((Reference)) 215215 size 12{ { {2} over {"15"} } } {}, 310310 size 12{ { {3} over {"10"} } } {}, 1616 size 12{ { {1} over {6} } } {}

Solution

215215 size 12{ { {2} over {"15"} } } {}, 1616 size 12{ { {1} over {6} } } {}, 310310 size 12{ { {3} over {"10"} } } {}

Exercise 20

((Reference)) 19321932 size 12{ { {"19"} over {"32"} } } {}, 916916 size 12{ { {9} over {"16"} } } {}, 5858 size 12{ { {5} over {8} } } {}

Solution

916916 size 12{ { {9} over {"16"} } } {}, 19321932 size 12{ { {"19"} over {"32"} } } {}, 5858 size 12{ { {5} over {8} } } {}

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