Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 7th grade percent change? Then this Grade 7 lesson on Calculating Percent Change and Percent Error explains each idea step by step, with worked examples.
Quick answer: Percent change equals the change divided by the original amount, written as a percent: (new − old) ÷ old × 100%. A positive result is a percent increase and a negative result is a decrease. Percent error uses the same idea, dividing the absolute error by the actual value.
Standards: 7.RP.A.3 · Level: Grade 7
How do you find a percent increase or decrease?
Percent change compares the amount of change with the starting amount. Subtract to get the change, divide by the old value, and write the result as a percent. A positive result is an increase; a negative result is a decrease.
percent change = new − oldold × 100%
The starting (old) value is always the denominator, even when the quantity goes down.
A museum had 480 visitors per day in March and 396 per day in April. Change: 396 − 480 = −84. Then 84 ÷ 480 = 0.175. The visitors decreased by 17.5%.
How do you find the original amount?
After an increase of r, the new amount is 100% + r of the original, so divide the new amount by 1 + r. After a decrease, divide by 1 − r. If a price is $54 after a 20% increase, the original is 54 ÷ 1.20 = $45.
What is percent error?
Percent error tells how far a measurement or estimate is from the true value, compared with that true value.
percent error = |measured − actual|actual × 100%
Use the absolute value, so the error is never negative. Divide by the actual (true) value.
- Identify the old (or actual) value.
- Subtract to find the change or error.
- Divide by the old (or actual) value.
- Multiply by 100 and label the answer increase, decrease or error.
Dividing by the new value. A drop from 80 to 60 is 20 ÷ 80 = 25%, not 20 ÷ 60. And a 25% rise after a 25% drop does not return to the start: 0.75 × 1.25 = 0.9375.
Always circle the starting value first. Whatever you circle is the number you divide by.
- Percent change = (new − old) ÷ old × 100%.
- Always divide by the starting amount, even for a decrease.
- To find the original amount, divide the new amount by 1 + r (increase) or 1 − r (decrease).
- Percent error = |measured − actual| ÷ actual × 100%.
- An increase and a decrease of the same percent do not cancel.
Calculating Percent Change and Percent Error: frequently asked questions
How do I calculate percent increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. A price that rises from $12 to $15.60 changes by $3.60, and 3.60 ÷ 12 = 30%.
Why do we divide by the old value?
Percent change measures the change relative to where you started. The starting amount is the base of the comparison, so it is the denominator.
How do I find the original price after a discount?
Divide the sale price by the remaining percent as a decimal. If a 30% discount leaves $84, the original is 84 ÷ 0.70 = $120.
What is percent error?
Percent error compares the size of a mistake in a measurement or estimate with the true value. It equals the absolute error divided by the actual value, times 100%.
Why does a 25% increase followed by a 25% decrease not return to the start?
The two percents apply to different amounts. The increase is 25% of the smaller start, while the decrease is 25% of the larger result, so the final amount is 0.9375 of the start.
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