Percentages • Topic 2 of 8

Percentage Increase

A percentage increase raises a quantity by a fraction of itself. To increase a number by P%, multiply it by (1 + P/100): a 20% rise means × 1.20. To find the percent increase from an old value to a new one, divide the increase (new − old) by the original value and multiply by 100. The original amount is always the base, not the new amount — a common trap. Percentage increase models price rises, population growth and "by what percent did it grow" questions, all frequent on the SAT.

✅ Solved examples

1. Increase 80 by 25%.
Multiply by 1.25: 80 × 1.25 = 100.
2. A price rises from $40 to $50. What is the percent increase?
Increase = 10; 10 ÷ 40 = 0.25 = 25%.
3. A salary of $2,000 increases by 8%. What is the new salary?
2000 × 1.08 = $2,160.
4. A town grows from 5,000 to 6,000 people. By what percent?
Increase 1,000; 1000 ÷ 5000 = 0.20 = 20%.

✏️ Practice — try these, take hints as needed

1. Increase 60 by 30%.
Multiply by 1.30.
60 × 1.3.
Compute.
78.
2. A value rises from 25 to 30. What is the percent increase?
Increase = 5.
Divide by the original 25.
× 100.
20%.
3. A $150 item increases by 12%. What is the new price?
Multiply by 1.12.
150 × 1.12.
Compute.
$168.
4. Sales grow from 200 to 260. By what percent?
Increase = 60.
60 ÷ 200.
× 100.
30%.
5. Increase 45 by 20%.
Multiply by 1.20.
45 × 1.2.
Compute.
54.

📝 Topic test — 8 questions

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