Fractions and Percentages Practice Problems with Solutions

Practice questions on fractions and percentages are presented below. Detailed solutions are included at the bottom of the page.

Note: A percentage is a fraction with a denominator of 100.

For example: \(20\%\) is a fraction equal to \(\frac{20}{100}\).

Practice Questions

  1. What is \(\frac{1}{3}\) of 300?

    A) 100
    B) 900
    C) 1
    D) 10
    E) 9

  2. If \(\frac{2}{7}\) of \(x\) is equal to 6, then \(x = \)

    A) \(\frac{12}{7}\)
    B) \(\frac{1}{21}\)
    C) 84
    D) 42
    E) 21

  3. What is \(15\%\) of \(45\%\) of 1.4?

    A) 0.945
    B) 0.0945
    C) 9450
    D) 94.5
    E) 9.45

  4. What is \(\frac{2}{3}\) of \(\frac{1}{5}\) of 12,000?

    A) \(1.1 \times 10^{-5}\)
    B) 8000
    C) 1600
    D) 2400
    E) 1.6

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

    A) 211.6
    B) 80
    C) 21.16
    D) 40
    E) 4

  6. On a 25-question 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 questions did Peter get correct?

    A) \(200\%\)
    B) \(66.6\%\)
    C) \(68\%\)
    D) \(25\%\)
    E) \(50\%\)

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

    A) \(0.25x\)
    B) \(2x\)
    C) \(8x\)
    D) \(0.50x\)
    E) \(4x\)

  8. What fraction subtracted from \(\frac{1}{2} + \frac{4}{5}\) gives 1?

    A) \(\frac{1}{2}\)
    B) \(\frac{4}{5}\)
    C) \(\frac{3}{10}\)
    D) \(\frac{9}{10}\)
    E) \(\frac{3}{5}\)

  9. One out of 5 students in a group took a math test, \(28\%\) of the same group took a science test, and the rest took a history test. If each student took only one test, what percentage took a history test?

    A) \(80\%\)
    B) \(72\%\)
    C) \(48\%\)
    D) \(52\%\)
    E) \(50\%\)

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

    A) 11
    B) 9
    C) 8
    D) 7
    E) 6

Answers and Solutions

  1. A) 100
    Solution: \(\frac{1}{3} \times 300 = 100\)
  2. E) 21
    Solution: \(\frac{2}{7}x = 6 \Rightarrow x = 6 \times \frac{7}{2} = 21\)
  3. B) 0.0945
    Solution: \(15\% \times 45\% \times 1.4 = 0.15 \times 0.45 \times 1.4 = 0.0945\)
  4. C) 1600
    Solution: \(\frac{2}{3} \times \frac{1}{5} \times 12000 = \frac{2}{15} \times 12000 = 1600\)
  5. D) 40
    Solution: \(\frac{x}{100} \times 23 = 9.2 \Rightarrow x = \frac{9.2 \times 100}{23} = 40\)
  6. C) 68%
    Solution: Algebra correct: \(60\% \times 10 = 6\)
    Geometry correct: \(80\% \times 10 = 8\)
    Trigonometry correct: \(60\% \times 5 = 3\)
    Total correct: \(6+8+3=17\)
    Percentage: \(\frac{17}{25} \times 100 = 68\%\)
  7. E) 4x
    Solution: \(25\% \times y = x \Rightarrow \frac{1}{4}y = x \Rightarrow y = 4x\)
  8. C) \(\frac{3}{10}\)
    Solution: \(\frac{1}{2} + \frac{4}{5} = \frac{5}{10} + \frac{8}{10} = \frac{13}{10}\)
    Let the fraction be \(f\): \(\frac{13}{10} - f = 1 \Rightarrow f = \frac{13}{10} - 1 = \frac{3}{10}\)
  9. D) 52%
    Solution: Math test: \(\frac{1}{5} = 20\%\)
    Science test: \(28\%\)
    History test: \(100\% - (20\% + 28\%) = 52\%\)
  10. A) 11
    Solution: \(\frac{1}{5}(y+1) = 2 \Rightarrow y+1 = 10 \Rightarrow y = 9 \Rightarrow y+2 = 11\)

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