Pre-Algebra
Percentage
Percent change
20 practice questions
0 video lessons
Theory + worked examples
Percent Change
California Pre-Algebra • Standard 7.RP.3 • Percentage
Percent Change is a topic in Percentage in the California Common Core State Standards. It is aligned to Standard 7.RP.3, which requires students to solve percent-change problems, including increases, decreases, and discounts.
Percent change compares a change to the original amount; increases and decreases scale the original by \(1\pm r\).
Theory
Percent change is the change divided by the original amount, written as a percent.
Increase: multiply the original by \(1+r\); decrease: by \(1-r\).
Computing percent change.
Increase and decrease.
Percent change:
\[\%\text{ change}=\dfrac{\text{new}-\text{original}}{\text{original}}\times100\%\]
Always divide by the original, not the new value.
How to find percent change
- Subtract to find the change.
- Divide by the original amount.
- Multiply by \(100\%\).
- Positive is an increase, negative a decrease.
Example 1 — Increase
A price rises from \(\$50\) to \(\$65\). Find the percent increase.
Solution
Change over original.
| \(\dfrac{15}{50}\) | \(=\) | \(0.30=30\%\) |
Example 2 — Decrease
A value drops from \(80\) to \(60\). Find the percent decrease.
Solution
Change is \(20\) down.
| \(\dfrac{20}{80}\) | \(=\) | \(0.25=25\%\) |
Example 3 — Discount
Find the sale price of a \(\$40\) item at \(25\%\) off.
Solution
Multiply by \(0.75\).
| \(40\cdot 0.75\) | \(=\) | \(\$30\) |
Example 4 — Markup
A \(\$20\) item has \(10\%\) tax. Find the total.
Solution
Multiply by \(1.10\).
| \(20\cdot 1.10\) | \(=\) | \(\$22\) |
Common pitfalls
Divide by the original, not the new amount.
A discount multiplies by \(1-r\), not \(-r\).
Tax adds: multiply by \(1+r\).
Frequently asked questions
How do I find percent change?
Change divided by the original, times 100%.
What do I divide by?
The original amount.
Sale price of \(\$40\) at \(25\%\) off?
\(\$30\).
\(\$20\) with \(10\%\) tax?
\(\$22\).
More in Percentage