Key takeaway: A percent decrease is the amount a quantity fell, expressed as a percent of its original value, found by dividing the drop by the starting amount and multiplying by 100.
Grade 77.RP.A.3Ratios, Rates and Percents
Definition of Percent Decrease
A percent decrease describes a drop. When a quantity falls from a larger starting value to a smaller new value, the percent decrease says what part of the starting value disappeared, written out of 100.
If the original amount and the rate are known, the new amount comes from taking the lost part away from the original, or from multiplying the original by \(1\) minus the rate written as a decimal.
Formula and notation
When both values are known:
\[\text{percent decrease} = \frac{\text{original} – \text{new}}{\text{original}} \times 100\%\]
When the rate \(r\) (as a decimal) is known: \(\text{new} = \text{original} \times (1 – r)\).
Key facts
- A percent decrease can never exceed 100%, because a quantity cannot lose more than all of itself.
- Multiplying by 0.85 lowers an amount by 15% in a single step.
- The divisor is the original value, which is the larger of the two numbers.
- A 100% decrease leaves exactly zero.
Percent Decrease example
A shipping box weighed 250 pounds before Camila removed some books. Afterward it weighed 190 pounds. Find the percent decrease in weight.
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Weight removed: \(250 – 190 = 60\) pounds.
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Divide by the original weight: \(\frac{60}{250} = 0.24\).
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Convert: \(0.24 \times 100\% = 24\%\).
The weight fell by 24%. Check: keeping 76% of the box gives \(250 \times 0.76 = 190\), the weight Camila measured on the shipping scale. Subtracting first and dividing second is the order that works for every drop.
Common mistake
Watch out
Nolan says that if a stock drops 40% and then rises 40%, it is back where it began.
Why it is wrong
The two percents use different starting values, so they do not cancel. From \$100, a 40% drop leaves \$60. A 40% rise is then \(0.40 \times 60 = \$24\), giving \$84, not \$100. To undo a 40% drop, the amount must grow by about 66.7%.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Ratios, Rates and Percents