Free Compass Math Practice on Fractions
and Percentages with Solutions and Explanations - Sample 12

Solutions with detailed explanations to compass math test practice questions in sample 12.

  1. What is 1/3 of 300?



    Solution

    1/3 of 300 is mathematically translated as

    1/3 300

    Simplify

    = 300 / 3 = 100

  2. If 2/7 of x is equal to 6, then x =

    Solution

    "2/7 of x is equal to 6" is mathematically translated as

    (2/7) x = 6

    Solve for x

    2x = 42

    x = 21

  3. What is 15% of 45% of 1.4?

    Solution

    "15% of 45% of 1.4" is mathematically translated as

    15%(45% 1.4)

    Simplify

    = (15/100) (45 / 100 1.4)

    = (15 45 1.4) / 10,000

    = 945 / 10,000

    = 0.0945


  4. What is 2/3 of 1/5 of 12,000?

    Solution

    "2/3 of 1/5 of 12,000" is mathematically translated as

    (2/3)( 1/5 12,000) =

    Simplify

    (2/3)( 1/5 12,000) =

    = (2/3)(12,000/5)

    = (2/3)(2,400)

    = 2 2,400 / 3

    = 1,600

  5. If x% of 23 is 9.2, then x =

    Solution

    "x% of 23 is 9.2" is mathematically translated as

    (x%) (23) = 9.2

    Solve for x

    (x / 100) 23 = 9.2

    23 x = 9.2 100

    x = 40

  6. On a 25 questions Math test, Peter got 60% of the 10 algebra questions correct, 80% of the 10 geometry questions correct and 60% of the 5 trigonometry questions correct. What percentage of all the questions did Peter get correct

    Solution

    60% of the 10 algebra questions correct

    60% * 10 = 6

    80% of the 10 geometry questions correct

    80% * 10 = 8

    60% of the 5 trigonometry questions correct

    60% * 5 = 3

    Total number of questions

    6 + 8 + 3 = 17

    Percentage of correct questions

    17 / 25 = 0.68 = 68%

  7. If 25% of y is x, then y =

    Solution

    "25% of y is x" is mathematically translated as

    (25 / 100) y = x

    Solve for y

    25 y = 100 x

    y = (100 x) / 25

    y = 4x

  8. What fraction subtracted from 1/2 + 4/5 gives 1?

    Solution

    Let x be the fraction to be subtracted. Hence

    (1/2 + 4/5) - x = 1

    Solve for x

    x = (1/2 + 4/5) - 1

    x = (5/10 + 8/10) - 10/10 = 3/10

  9. One out of 5 of a group of students took a math test, 28% of the same group took a science test and the rest took a history test. What percent of students took a history test?

    Solution

    One out of 5 may be written as a fraction equal to

    1/5

    and in percent as

    20%

    So 20% took math and 28% took science. The percent of those who took history is

    100% - 20% - 28% = 52% of students took history

  10. If one fifth of y + 1 is equal to 2, then y + 2 =

    Solution

    "one fifth of y + 1 is equal to 2" is mathematically translated as

    (1/5)(y + 1) = 2

    Multiply both sides by 5

    y + 1 = 10

    y + 1 + 1 = 10 + 1

    y + 2 = 11

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