Percentage Change and Reverse Percentages

Percentages are essential throughout GCSE Mathematics and everyday life. This lesson focuses on calculating percentage increase and decrease, expressing one quantity as a percentage of another, and solving reverse percentage problems — where you must work backwards from a final amount to find the original. These skills are tested frequently on AQA GCSE papers at both Foundation and Higher tiers.

---

Expressing One Quantity as a Percentage of Another

To express A as a percentage of B:

Formula: (A / B) x 100

Worked Example 1: There are 12 girls in a class of 30. What percentage are girls?

• (12 / 30) x 100 = 40%

Worked Example 2: A student scored 56 out of 80 on a test. What percentage is this?

• (56 / 80) x 100 = 70%

---

Calculating a Percentage of an Amount

Method 1: Divide and Multiply

• Find 1% by dividing by 100, then multiply by the required percentage.

Method 2: Use a Decimal Multiplier