Percent change measures how much something grew or shrank relative to where it started. Nearly every mark lost in this topic comes from dividing by the wrong number, so the formula is worth writing out before any arithmetic.
Percent change = (change ÷ original) × 100
Find the difference between the new value and the original, divide that difference by the original value, then multiply by 100 to express it as a percentage. The original value is always the denominator, whether the change is an increase or a decrease.
A price falls from $80 to $68. Find the percent decrease.
Answer: 15% decrease
Increase 250 by 12%.
Answer: 280
A $100 item rises 20%, then falls 20%. What is the final price?
Answer: $96
Work through these in order. Each answer opens to show the full method, so you can check your reasoning rather than just your final number.
Increase 200 by 10%.
Answer: 220
10% of 200 is 20, so 200 + 20 = 220.
Decrease 50 by 20%.
Answer: 40
20% of 50 is 10, so 50 − 10 = 40.
A price rises from 100 to 125. Find the percent increase.
Answer: 25%
Change is 25, and 25 ÷ 100 = 0.25, which is 25%.
What is 15% of 60?
Answer: 9
0.15 × 60 = 9.
A value falls from 40 to 30. Find the percent decrease.
Answer: 25%
Change is 10, and 10 ÷ 40 = 0.25, which is 25%.
A jacket costs $60 and is reduced by 15%. Find the sale price.
Answer: $51
15% of 60 is 9, so 60 − 9 = 51. Or 60 × 0.85 = 51.
A population grows from 1200 to 1440. Find the percent increase.
Answer: 20%
Change is 240, and 240 ÷ 1200 = 0.2, which is 20%.
After a 25% increase a price is $75. What was the original?
Answer: $60
The new price is 1.25 times the original, so original = 75 ÷ 1.25 = 60.
A $200 item rises 10% then falls 10%. Find the final price.
Answer: $198
200 × 1.1 = 220, then 220 × 0.9 = 198. The two changes use different bases.
After a 20% discount an item costs $48. What was the original price?
Answer: $60
The sale price is 0.8 of the original, so original = 48 ÷ 0.8 = 60.
Generate a percent increase and decrease test at the grade and difficulty you need, with a complete worked answer key and equivalent versions for retakes.
Prefer free practice first? free percentage worksheets with answers
The highest-value questions in this topic give the final amount and ask for the original. A price is $75 after a 25% increase; the original is not $75 minus 25%. The new price is 1.25 times the original, so the original is 75 ÷ 1.25 = $60. Checking confirms it: 60 × 1.25 = 75, whereas 75 × 0.75 = 56.25, which is clearly not right.
The reliable method is to write the multiplier first. An increase of 25% is a multiplier of 1.25; a decrease of 20% is a multiplier of 0.8. Going forwards you multiply, going backwards you divide. Students who work with multipliers rather than adding and subtracting percentages handle both directions with the same single operation.
Finding 15% and then subtracting takes two steps and two chances to slip. Multiplying by 0.85 takes one. The saving looks small on a single question and becomes substantial on compound problems, tax calculations and anything involving repeated change, where the multiplier method is simply raised to a power.
It also makes the increase-then-decrease result obvious rather than surprising. Multiplying by 1.2 and then by 0.8 gives 0.96, which is visibly not 1, so the price cannot return to where it started. Students who see the arithmetic that way rarely fall for the question again.
✗ Dividing the change by the new value instead of the original.
✓ The original value is always the denominator. A fall from 80 to 68 is 12 ÷ 80, not 12 ÷ 68.
✗ Assuming a 20% rise followed by a 20% fall returns to the start.
✓ The two changes are calculated on different amounts, so $100 becomes $120 and then $96.
✗ Subtracting the percentage from the price, so 15% off $60 becomes $45.
✓ Find 15% of 60 first, which is 9, then subtract to get $51.
✗ Working backwards by adding the percentage back on.
✓ To reverse a 25% increase, divide by 1.25. Subtracting 25% from the new price gives the wrong original.