Fractions and Percentages Practice Problems with Solutions

Practice questions on fractions and percentages are presented below. Detailed solutions are included via the collapsible sections.

Note: A percentage is a fraction with a denominator of 100 (e.g., \(20\% = \frac{20}{100}\)).

Practice Questions

Question 1

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

A) 100   B) 900   C) 1   D) 10   E) 9

Show Solution

\[ \frac{1}{3} \times 300 = 100 \]

Question 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

Show Solution

\[ \frac{2}{7}x = 6 \Rightarrow x = 6 \times \frac{7}{2} = 21 \]

Question 3

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

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

Show Solution

\[ 0.15 \times 0.45 \times 1.4 = 0.0945 \]

Question 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

Show Solution

\[ \frac{2}{3} \times \frac{1}{5} \times 12,000 = 1,600 \]

Question 5

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

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

Show Solution

\[ \frac{x}{100} \times 23 = 9.2 \Rightarrow x = 40 \]

Question 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) \(50\%\)

Show Solution

Algebra: 6, Geometry: 8, Trig: 3. Total: 17/25 = 68%

Question 7

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

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

Show Solution

\[ 0.25y = x \Rightarrow \frac{1}{4}y = x \Rightarrow y = 4x \]

Question 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) \(\frac{3}{5}\)

Show Solution

\[ (\frac{1}{2} + \frac{4}{5}) - x = 1 \Rightarrow \frac{13}{10} - x = 1 \Rightarrow x = \frac{3}{10} \]

Question 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) \(50\%\)

Show Solution

Math: 20%. Science: 28%. History: \(100\% - 48\% = 52\%\).

Question 10

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

A) 11   B) 9   C) 8   D) 7   E) 6

Show Solution

\[ \frac{1}{5}(y+1) = 2 \Rightarrow y+1 = 10 \Rightarrow y = 9 \Rightarrow y+2 = 11 \]