Percentages • Topic 3 of 8

Percentage Decrease

A percentage decrease lowers a quantity by a fraction of itself. To decrease a number by P%, multiply by (1 − P/100): a 30% drop means × 0.70. To find the percent decrease, divide the decrease (old − new) by the original value and multiply by 100. As with increases, the original is the base. Percentage decrease models discounts, depreciation and "by what percent did it fall" questions. A useful check: decreasing by P% and then increasing by P% does not return the original, because the second percentage acts on a different base.

✅ Solved examples

1. Decrease 200 by 15%.
Multiply by 0.85: 200 × 0.85 = 170.
2. A price falls from $80 to $60. What is the percent decrease?
Decrease = 20; 20 ÷ 80 = 0.25 = 25%.
3. A $500 laptop depreciates 20%. What is its new value?
500 × 0.80 = $400.
4. Attendance drops from 250 to 200. By what percent?
Decrease 50; 50 ÷ 250 = 0.20 = 20%.

✏️ Practice — try these, take hints as needed

1. Decrease 120 by 25%.
Multiply by 0.75.
120 × 0.75.
Compute.
90.
2. A value falls from 50 to 40. What is the percent decrease?
Decrease = 10.
10 ÷ 50.
× 100.
20%.
3. A $90 coat is reduced by 30%. What is the new price?
Multiply by 0.70.
90 × 0.7.
Compute.
$63.
4. A population drops from 800 to 600. By what percent?
Decrease = 200.
200 ÷ 800.
× 100.
25%.
5. Decrease 75 by 40%.
Multiply by 0.60.
75 × 0.6.
Compute.
45.

📝 Topic test — 8 questions

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