Solutions to Questions on Fractions and Percentages

The solutions, with detailed explanations, to fractions and percentages questions are presented.

Solutions


  1. Solution
    1/3 of 300 is mathematically translated as
    1/3 300
    Simplify
    = 300 / 3 = 100

  2. 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. 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. 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. 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. 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 correct
    6 + 8 + 3 = 17
    Percentage of correct questions that Peter got correct is
    17 / 25 = 0.68 = 68%

  7. 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. 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. Solution
    One out of 5 may be written as a fraction equal to
    1/5
    and in percent as
    20%
    The total number of students in percent is 100%. Since 20% took math and 28% took science, the percent of those who took history is
    100% - 20% - 28% = 52%

  10. Solution
    "one fifth of y + 1 is equal to 2" is mathematically translated as
    (1/5)(y + 1) = 2
    Multiply both sides by 5 and simplify
    y + 1 = 10
    Add 1 to each side of the above equation
    y + 1 + 1 = 10 + 1
    Simplify
    y + 2 = 11

More References and Links

Fractions .
Percent Maths Questions