A price rises from $60 to $75
- Change = 75 − 60 = $15.
- 15 ÷ 60 × 100% = 25% increase.
- The new price is 125% of the original.
Percent increase & decrease
Measure change against the original amount.
The original amount is the reference
Percent change = (new − original) ÷ original × 100%. A positive result is an increase and a negative result is a decrease. To report a decrease, state its positive size and the word decrease. The original must be nonzero for this calculation.
Compare with where you started.
Predict first. Change one value, then explain what stays the same and what changes. All bars use the same scale within a model.
Percent of original is not percent change
If attendance rises from 80 to 100, the new attendance is 125% of the original, but the increase is 25%. Dividing new by original includes the original 100%. Subtracting 100 percentage points gives the percent increase.
Percentages and percentage points differ
If participation rises from 40% to 50%, that is an increase of 10 percentage points. Relative to the original 40%, it is a 25% increase: 10 ÷ 40 × 100%. State which comparison you mean so the report does not mislead.
Worked examples
A quantity falls from 200 to 150
- Decrease = 200 − 150 = 50.
- 50 ÷ 200 × 100% = 25% decrease.
- The new amount is 75% of the original.
Guided Practice
A price rises from $40 to $50, then falls to $40. Find each percent change.
A first hint
Use $40 as the first base and $50 as the second.
Compare your reasoning
The rise is 10/40 = 25%. The fall is 10/50 = 20%. Equal dollar changes can have different percent changes.
Practice
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Connections
A team reports that success rose from 20% to 30%. Explain the difference between 10 percentage points and a 50% relative increase.
Use it in Extreme Couponing
Record the whole, the percent multiplier and the result with units. For each coupon, use the eligible amount at that step. State whether a resale percentage means percent of cost or markup on cost.