Key takeaway: A percent increase is the amount a quantity grew, expressed as a percent of its original value, found by dividing the gain by the starting amount and multiplying by 100.
Grade 77.RP.A.3Ratios, Rates and Percents
Definition of Percent Increase
A percent increase describes growth. When a quantity goes from a smaller starting value to a larger new value, the percent increase tells what fraction of the starting value was added, written out of 100. Growth of a school club, a savings balance or a city’s population can all be reported this way.
It can also run in reverse. If you know the original amount and the percent increase, you can find the new amount by adding the extra part to the original, or by multiplying the original by \(1\) plus the rate written as a decimal.
Formula and notation
To find the rate when both values are known:
\[\text{percent increase} = \frac{\text{new} – \text{original}}{\text{original}} \times 100\%\]
To find the new value from a rate \(r\) (as a decimal): \(\text{new} = \text{original} \times (1 + r)\).
Key facts
- The new value is always larger than the original when growth has occurred.
- A percent increase can be more than 100%, which means the amount more than doubled.
- Multiplying by 1.25 raises an amount by 25% in a single step.
- The divisor is always the original value, not the new value.
Percent Increase example
The Westside Chess Club had 40 members in September and 52 members in January. What was the percent increase in membership?
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Members gained: \(52 – 40 = 12\).
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Compare with the starting count: \(\frac{12}{40} = 0.30\).
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Write as a percent: \(0.30 = 30\%\).
Membership grew by 30%. Check: \(40 \times 1.30 = 52\).
Common mistake
Watch out
Marcus has a \$60 allowance and gets a 25% raise. He adds 25 to get \$85.
Why it is wrong
A percent is a part of the original amount, not a number of dollars. A 25% raise adds \(0.25 \times 60 = 15\), so the new allowance is \$75. Marcus treated the percent sign as if it were a plain 25. Whenever a problem gives a rate, first turn it into a decimal and multiply by the starting amount; only then add the result to that amount.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Ratios, Rates and Percents