What is percent decrease?
Percent decrease is how much a quantity went down, written as a percent of its original value. Subtract the new value from the original, divide by the original, and multiply by 100. A price that drops from 80 dollars to 60 dollars has a decrease of 20 dollars, and 2080 = 25%.
Percent Decrease in a picture
Formal definition and notation
If a quantity changes from an original value O > 0 to a smaller new value N, the percent decrease is O − NO × 100%. It is the percent change N − OO × 100% when that change is negative, stated without the minus sign. A decrease of p% multiplies the original by 1 − p100.
| Symbol | Read it as | Meaning |
|---|---|---|
| 25% | twenty-five percent | 25 per 100, or 0.25 |
| × 0.75 | times zero point seven five | the multiplier for a 25% decrease: 100% minus 25% |
Key facts
- Always divide by the original (the old value), never by the new one.
- A percent decrease is between 0% and 100%. A 100% decrease means the quantity dropped to 0.
- Decrease by p% = multiply by 1 − p100: 30% off means pay 70%, so multiply by 0.70.
- A decrease and an increase of the same percent do not cancel: 100 down 20% is 80, and 80 up 20% is 96.
- Two decreases multiply: 10% off and then 20% off is 0.9 × 0.8 = 0.72, a 28% decrease, not 30%.
Percent decrease formula
- original
- the starting value, before the decrease (always the denominator)
- new
- the value after the decrease
- original − new
- the amount of decrease
To find the new value instead, multiply: new = original × (1 − rate). A 15% decrease multiplies by 0.85.
Percent Decrease examples, step by step
Example 1: Find the percent decrease
A jacket’s price drops from 50 dollars to 42 dollars. What is the percent decrease?
- Amount of decrease: 50 − 42 = 8 dollars.
- Divide by the original price: 850 = 0.16.
- Change to a percent: 0.16 × 100% = 16%.
Answer: The price decreased by 16%.
Example 2: Find the new value
A town of 2,400 people shrinks by 15%. What is the new population?
- A 15% decrease keeps 100% − 15% = 85% of the original.
- Multiply: 2400 × 0.85 = 2040.
- Check with the decrease: 15% of 2,400 is 360, and 2400 − 360 = 2040.
Answer: The new population is 2,040 people.
Example 3: Down 20%, then up 20%
A stock worth 150 dollars falls 20%, then rises 20%. What is the overall percent change from 150 dollars?
- After the 20% fall: 150 × 0.8 = 120 dollars.
- After the 20% rise: 120 × 1.2 = 144 dollars. The rise is 20% of 120, which is smaller than 20% of 150.
- Overall decrease: 150 − 144 = 6 dollars.
- Percent decrease: 6150 = 0.04 = 4%.
Answer: Overall the stock shows a 4% decrease (150 dollars to 144 dollars), not 0%.
Common mistakes
Percent change is always measured against the original (starting) value. Dividing by the new value gives the wrong base.
Multiplying by 0.25 finds the part removed. To find what is left, multiply by 1 minus the rate, or subtract the 20 from 80.
The amount has units like dollars; the percent compares that amount to the original.
Not to be confused with
Percent increase uses new minus original, for a value that went up. From 60 to 80 is a 33.3% increase, but from 80 to 60 is a 25% decrease: the base changes.
Percent change covers both directions and keeps the sign: −25% means a 25% decrease. Percent decrease is the size of a drop, stated as a positive percent.
A rate that falls from 40% to 30% drops 10 percentage points, which is a 25% decrease relative to 40%.
Quick check: 3 questions
A phone price drops from 400 dollars to 340 dollars. What is the percent decrease?
Answer: C. Decrease = 400 − 340 = 60, and 60400 = 0.15 = 15%. 60% treats the dollar amount as a percent, 17.6% divides by the new price 340, and 85% is the part that remains.Show answer and explanation
What is 90 decreased by 30%?
Answer: C. Keep 70%: 90 × 0.7 = 63. 27 is the amount removed, 60 subtracts 30 instead of 30%, and 87 subtracts 3.Show answer and explanation
After a 20% discount, a game costs 48 dollars. What was the original price?
Answer: D. 48 dollars is 80% of the original, so original = 48 ÷ 0.8 = 60 dollars. 57.60 adds 20% of 48, which uses the wrong base; 38.40 takes another 20% off.Show answer and explanation
Percent Decrease: frequently asked questions
What is the formula for percent decrease?
Percent decrease = original − neworiginal × 100%. Subtract to find the amount of decrease, divide by the original value, then multiply by 100. From 250 to 200: 50250 = 0.2, so the percent decrease is 20%. Always divide by the starting value.
Can a percent decrease be more than 100%?
Not for an amount that cannot go below zero. A 100% decrease already takes the quantity all the way to 0, like a 50 dollar item that becomes free. Quantities that can go negative, such as a profit that turns into a loss, can change by more than 100%, but then people usually report a percent change instead.
How do I find the original price before a percent decrease?
Divide the new price by what is left as a decimal. If a 25% decrease left 36 dollars, then 36 dollars is 75% of the original, so the original is 36 ÷ 0.75 = 48 dollars. Do not add 25% of 36 back on, because the 25% was taken from the original, not from 36.
Practice and tools
Sources
- Common Core State Standards, Grade 7 Ratios and Proportional Relationships (7.RP.A.3)
- OpenStax, Prealgebra 2e, 6.2 Solve General Applications of Percent
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.RP.A.3
Cite this entry
Effortless Math Team. “Percent Decrease.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/percent-decrease/
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