Percent Increase and Decrease

Percent change tells you how much an amount has gone UP or DOWN compared to the amount you started with. A price tag that drops from $80 to $60 is a percent decrease. A quiz score that climbs from 50 to 60 is a percent increase. The same simple recipe works in both cases: find the change, divide by the ORIGINAL amount, then multiply by 100.

The Three-Step Recipe

1. Find the CHANGE: new amount minus old amount. (If new is bigger, the change is positive. If new is smaller, the change is negative.)
2. Divide the change by the ORIGINAL amount (the old one — never the new one).
3. Multiply by 100 and tag on the % symbol. Positive = increase. Negative = decrease.

Worked Example — From 50 to 60

• Change = 60 - 50 = 10.
• Divide by the original: 10 / 50 = 0.20.
• Multiply by 100: 0.20 x 100 = 20. Answer: 20% INCREASE.
• Sentence: "60 is 20% more than 50."

Worked Example — From 80 to 60

• Change = 60 - 80 = -20 (the new amount is smaller, so the change is negative).
• Divide by the original: -20 / 80 = -0.25.
• Multiply by 100: -0.25 x 100 = -25. Answer: 25% DECREASE.
• Sentence: "60 is 25% less than 80."

Increase or Decrease?

• New amount BIGGER than old amount = INCREASE (the change is positive).
• New amount SMALLER than old amount = DECREASE (the change is negative).
• New amount EQUAL to old amount = 0% change — no increase, no decrease.
• Always state the direction in your answer: "20% increase" or "25% decrease".

Why the Original — Not the New?

Percent change asks "how big was the change compared to where we started?" The starting amount is the OLD value, so dividing by it tells you what fraction of the start the change is. Dividing by the new value would answer a different question and would give the wrong percent.