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Percentages (F)

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Percentages (F)

Master GCSE Foundation percentages: convert between fractions, decimals and percentages, find percentage increases and decreases, and solve reverse percentage problems with clear steps.

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Fascinating Fact:

At a café tip jar, 12 percent of £18 equals 0.12 × 18 = £2.16, so paying £20 leaves a tip of £2.00 and a little change.

In GCSE Maths, percentages appear everywhere: discounts, interest, VAT, and data comparison. You’ll convert between fractions, decimals and percentages, use multipliers for increase/decrease, and work backwards with reverse percentage questions confidently.

Key Terms

Percentage: A fraction out of 100, written with the % symbol (e.g., 25% = 25/100 = 0.25).
Multiplier: The single number you multiply by to apply a percentage change, e.g., +12% uses 1.12, −15% uses 0.85.
Reverse percentage: Finding the original amount given a final value after a percentage change (divide by the correct multiplier).

Frequently Asked Questions (Click to see answers)

How do I calculate 12% of a number quickly?

Use a multiplier. Convert 12% to 0.12 and multiply by the number. For example, 12% of 18 is 0.12 × 18 = 2.16.

What’s the easiest way to increase or decrease by a percentage?

Multiply by a decimal multiplier. Increase by r% → multiply by (1 + r/100). Decrease by r% → multiply by (1 − r/100).

How do I do reverse percentage to find the original price?

Divide by the multiplier. If £54 includes 20% VAT, original = 54 ÷ 1.20 = £45. For a 15% discount, original = sale price ÷ 0.85.

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You can find more about this topic by visiting BBC Bitesize - Percentages

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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