Key takeaway: Percent change is the amount a quantity rose or fell, written as a percent of its starting value, found by dividing the difference between the new and original values by the original.
Grade 77.RP.A.3Ratios, Rates and Percents
Definition of Percent Change
Percent change tells by how much a quantity has grown or shrunk compared with where it started. The answer is stated per hundred of the starting amount, so a \$20 jump on a \$200 item and a \$20 jump on a \$50 item give very different results: 10% and 40%.
A positive result means the quantity went up and a negative result means it went down. The starting value always goes in the denominator, because the change is being compared with that starting value. Prices, populations, test scores and temperatures on a scale with a true zero are all described this way.
Formula and notation
Work out the change first, then compare it with the starting value:
\[\text{percent change} = \frac{\text{ending value} – \text{starting value}}{\text{starting value}} \times 100\%\]
A result of \(+8\%\) means a rise; \(-8\%\) means a fall.
Key facts
- The original (starting) value is always the divisor, never the new value.
- A positive percent change is an increase and a negative one is a decrease.
- Rising 50% and then falling 50% leaves you below where you began.
- The amount of change is the absolute difference between the two values.
Percent Change example
A gas station in Tulsa raised its price from \$3.20 to \$3.68 per gallon after a refinery delay. Find the percent change in the price.
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Find the change: \(3.68 – 3.20 = 0.48\).
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Put that change over the starting price: \(\frac{0.48}{3.20} = 0.15\).
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Convert to a percent: \(0.15 \times 100\% = 15\%\).
The price rose by 15%.
Common mistake
Watch out
Priya divides the change by the new price: \(\frac{0.48}{3.68} \approx 0.13\), so she reports a 13% rise.
Why it is wrong
She compared the change with the wrong number. The question is how big the jump is relative to where the price began, so the divisor is the \$3.20 she started with. Dividing \(0.48\) by \(3.20\) gives the correct 15%. A quick check: 15% of \$3.20 is \$0.48, which matches the raise exactly, while 13% of \$3.20 is only about \$0.42.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Ratios, Rates and Percents