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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 "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

Exercise 1

((Reference)) Shade a portion that corresponds to the fraction 5858 size 12{ { {5} over {8} } } {}.
A rectangle divided into eight parts.

Solution

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

Exercise 2

((Reference)) Specify the numerator and denominator of the fraction 5959 size 12{ { {5} over {9} } } {}.

Solution

Numerator, 5; denominator, 9

Exercise 3

((Reference)) Write the fraction five elevenths.

Solution

511511 size 12{ { {5} over {"11"} } } {}

Exercise 4

((Reference)) Write, in words, 4545 size 12{ { {4} over {5} } } {}.

Solution

Four fifths

Exercise 5

((Reference)) Which of the fractions is a proper fraction? 41124112 size 12{4 { {1} over {"12"} } } {}, 512512 size 12{ { {5} over {"12"} } } {}, 125125 size 12{ { {"12"} over {5} } } {}

Solution

512512 size 12{ { {5} over {"12"} } } {}

Exercise 6

((Reference)) Convert 347347 size 12{3 { {4} over {7} } } {} to an improper fraction.

Solution

257257 size 12{ { {"25"} over {7} } } {}

Exercise 7

((Reference)) Convert 165165 size 12{ { {"16"} over {5} } } {} to a mixed number.

Solution

315315 size 12{3 { {1} over {5} } } {}

Exercise 8

((Reference)) Determine if 512512 size 12{ { {5} over {"12"} } } {} and 20482048 size 12{ { {"20"} over {"48"} } } {} are equivalent fractions.

Solution

yes

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

Exercise 9

((Reference)) 21352135 size 12{ { {"21"} over {"35"} } } {}

Solution

3535 size 12{ { {3} over {5} } } {}

Exercise 10

((Reference)) 15511551 size 12{ { {"15"} over {"51"} } } {}

Solution

517517 size 12{ { {5} over {"17"} } } {}

Exercise 11

((Reference)) 104480104480 size 12{ { {"104"} over {"480"} } } {}

Solution

13601360 size 12{ { {"13"} over {"60"} } } {}

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

Exercise 12

((Reference)) 59=?3659=?36 size 12{ { {5} over {9} } = { {?} over {"36"} } } {}

Solution

20

Exercise 13

((Reference)) 43=32?43=32? size 12{ { {4} over {3} } = { {"32"} over {?} } } {}

Solution

24

For problems 14-25, find each value.

Exercise 14

((Reference)) 1516⋅4251516⋅425 size 12{ { {"15"} over {"16"} } cdot { {4} over {"25"} } } {}

Solution

320320 size 12{ { {3} over {"20"} } } {}

Exercise 15

((Reference)) 334⋅229⋅635334⋅229⋅635 size 12{3 { {3} over {4} } cdot 2 { {2} over {9} } cdot 6 { {3} over {5} } } {}

Solution

55

Exercise 16

((Reference)) 25362536 size 12{ sqrt { { {"25"} over {"36"} } } } {}

Solution

5656 size 12{ { {5} over {6} } } {}

Exercise 17

((Reference)) 49⋅816449⋅8164 size 12{ sqrt { { {4} over {9} } } cdot sqrt { { {"81"} over {"64"} } } } {}

Solution

3434 size 12{ { {3} over {4} } } {}

Exercise 18

((Reference)) 1130⋅2251211130⋅225121 size 12{ { {"11"} over {"30"} } cdot sqrt { { {"225"} over {"121"} } } } {}

Solution

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

Exercise 19

((Reference)) 415÷8415÷8 size 12{ { {4} over {"15"} } div 8} {}

Solution

130130 size 12{ { {1} over {"30"} } } {}

Exercise 20

((Reference)) 815⋅512÷249815⋅512÷249 size 12{ { {8} over {"15"} } cdot { {5} over {"12"} } div 2 { {4} over {9} } } {}

Solution

111111 size 12{ { {1} over {"11"} } } {}

Exercise 21

((Reference)) 653÷11125653÷11125 size 12{ left ( { {6} over {5} } right ) rSup { size 8{3} } div sqrt {1 { {"11"} over {"25"} } } } {}

Solution

3625=111253625=11125 size 12{ { {"36"} over {"25"} } =1 { {"11"} over {"25"} } } {}

Exercise 22

((Reference)) Find 512512 size 12{ { {5} over {"12"} } } {} of 24252425 size 12{ { {"24"} over {"25"} } } {}.

Solution

2525 size 12{ { {2} over {5} } } {}

Exercise 23

((Reference)) 2929 size 12{ { {2} over {9} } } {} of what number is 118118 size 12{ { {1} over {"18"} } } {}?

Solution

1414 size 12{ { {1} over {4} } } {}

Exercise 24

((Reference)) 157157 size 12{1 { {5} over {7} } } {} of 21202120 size 12{ { {"21"} over {"20"} } } {} is what number?

Solution

95=14595=145 size 12{ { {9} over {5} } =1 { {4} over {5} } } {}

Exercise 25

((Reference)) What part of 914914 size 12{ { {9} over {"14"} } } {} is 6767 size 12{ { {6} over {7} } } {}?

Solution

43or 11343or 113 size 12{ { {4} over {3} } `"or "1 { {1} over {3} } } {}

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