Percent Change Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Percent Change.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The ratio of the change in a quantity to the original value, expressed as a percentage.

If a price goes from \50 to \60, the change is \10. Compared to the original \50, that's \frac{10}{50} = 20\% increase.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Percent change measures how much something grew or shrank relative to where it started.

Common stuck point: A 50% increase followed by a 50% decrease does NOT return to the original value.

Sense of Study hint: Write down the original value first and underline it -- that number always goes in the denominator of the fraction.

Worked Examples

Example 1

easy
A jacket originally costs \60 and is on sale for \45. What is the percent decrease?

Solution

  1. 1
    Find the change: 60 - 45 = 15.
  2. 2
    Divide by the original value: \frac{15}{60} = 0.25.
  3. 3
    Convert to a percentage: 0.25 \times 100 = 25\%.

Answer

25\% \text{ decrease}
Percent change is calculated as \frac{\text{change}}{\text{original}} \times 100\%. A decrease means the new value is less than the original.

Example 2

medium
A town's population grew from 12{,}000 to 15{,}000. What is the percent increase?

Example 3

hard
A stock price rises by 20\% one year and falls by 20\% the next year. If it started at \100$, what is the final price and the overall percent change?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A shirt's price increases from \25 to \30. What is the percent increase?

Example 2

medium
After a 15\% discount, a laptop costs \680$. What was the original price?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

percentagessubtractiondivision