Percent Math Questions

Eight worked examples covering percent of a number, percent change, and visual percent problems

Overview

Eight percent questions with fully worked, step-by-step solutions. Each problem covers a different percent operation — from reading a percent off a diagram to computing percent change — so that you can see the whole toolbox in action.

Question 1 — Percent shaded in a 10×10 grid

What percentage of the large square is coloured red in each figure below?

10×10 grid with 1 square shaded red
Figure A
10×10 grid with 41 squares shaded red
Figure B
10×10 grid with 50 squares shaded red
Figure C
10×10 grid fully shaded red
Figure D
Solution

Each grid contains \(10 \times 10 = 100\) small squares, so a percentage is just the count of red squares out of \(100\).

Figure A: 1 of 100 red

\[ \frac{1}{100} = 1\% \]

Figure B: 41 of 100 red

\[ \frac{41}{100} = 41\% \]

Figure C: 50 of 100 red

\[ \frac{50}{100} = 50\% = \frac{1}{2} \]

Figure D: all 100 red

\[ \frac{100}{100} = 100\% = 1 \]

Question 2 — Percent of balls that are red

What percent of the balls in the figure below are red?

Nine balls, of which five are red
Figure 1. 5 of the 9 balls are red.
Solution

Fraction of balls that are red:

\[ \frac{5}{9} \]

Convert to a percentage:

\[ \frac{5}{9} \approx 0.5556 \times 100 \approx 55.56\% \]

Answer: approximately 55.56% (about 55.6%) of the balls are red.

Question 3 — What is 12% of 250?

What is 12% of 250?

Solution

Let \(y\) be the answer. "Of" means multiply and "is" means equals:

\[ y = 12\% \times 250 \]

Replace the percent with a fraction:

\[ y = \frac{12}{100} \times 250 = \frac{3000}{100} = 30 \]

Answer: 30.

Question 4 — 4 is what percent of 32?

4 is what percent of 32?

Solution

Let the unknown percent be \(y\%\):

\[ 4 = y\% \times 32 \]

Divide both sides by 32:

\[ y\% = \frac{4}{32} = \frac{1}{8} = 0.125 \]

Convert to a percentage:

\[ y\% = 0.125 \times 100 = 12.5\% \]

Check: 12.5% of 32 is \(0.125 \times 32 = 4\) ✓

Question 5 — 6 is 80% of what number?

6 is 80% of what number?

Solution

Let \(x\) be the unknown:

\[ 6 = 80\% \times x \]

Solve for \(x\):

\[ x = \frac{6}{0.8} = 7.5 \]

Check: 80% of 7.5 is \(0.8 \times 7.5 = 6\) ✓

Question 6 — Percent increase from 120 to 150

A number increases from 120 to 150. By what percent of its original value did it increase?

Solution

Absolute increase:

\[ 150 - 120 = 30 \]

Percent increase = increase / original:

\[ \frac{30}{120} = 0.25 = 25\% \]

Answer: a 25% increase.

Question 7 — Percent decrease from 80 to 50

A number decreases from 80 to 50. By what percent of its original value did it decrease?

Solution

Absolute decrease:

\[ 80 - 50 = 30 \]

Percent decrease = decrease / original:

\[ \frac{30}{80} = 0.375 = 37.5\% \]

Answer: a 37.5% decrease.

Question 8 — Comparing two percentages

Which is greater: 15% of 380 or 25% of 210?

Solution

First value:

\[ 0.15 \times 380 = 57 \]

Second value:

\[ 0.25 \times 210 = 52.5 \]

Since \(57 > 52.5\), 15% of 380 is greater than 25% of 210.

Frequently Asked Questions

How do you find a percent of a number?

Convert the percent to a decimal or fraction, then multiply. For example, \(12\% \times 250 = 0.12 \times 250 = 30\).

How do you find what percent one number is of another?

Divide the part by the whole and multiply by \(100\). For example, \(4/32 \times 100 = 12.5\%\).

How do you calculate percent increase or decrease?

Percent change \(= \dfrac{\text{new} - \text{original}}{\text{original}} \times 100\). A positive result is an increase; a negative result is a decrease. For example, \(120 \to 150\) gives \(+25\%\), and \(80 \to 50\) gives \(-37.5\%\).

How do you find the whole when you know a percent of it?

Divide the part by the percent as a decimal. For example, if 6 is 80% of \(x\), then \(x = 6/0.8 = 7.5\).

More References and Links

Last updated: October 17, 2026