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. What is 1/3 of 300? Solution 1/3 of 300 is mathematically translated as 1/3 × 300 Simplify = 300 / 3 = 100 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 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 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 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 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% 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 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 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 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 More Compass practice