Learn: Percentages and Percentage Change

Welcome!Today we're exploring percentages and percentage change. This is useful for understanding discounts, interest rates, and comparing values in everyday life.

What is a Percentage?A percentage is a way to express a number as a fraction of 100. For example, 50% means 50 out of 100. Percentages are helpful for comparing quantities in a standardised way.

Converting Between Fractions, Decimals, and PercentagesTo convert a fraction to a percentage, multiply by 100. To convert a decimal to a percentage, also multiply by 100. For example, 0.5 × 100 = 50%.

What is Percentage Change?Percentage change measures how much something has increased or decreased. Use the formula: (Change ÷ Original) × 100. For example, if a price increases from £40 to £50, the change is £10, and the percentage change is (10 ÷ 40) × 100 = 25%.

Reverse PercentagesA reverse percentage finds the original value before a percentage change. Divide the new value by (1 ± percentage change as a decimal). For example, if the new price after a 20% increase is £120, the original price is £120 ÷ 1.2 = £100.

Working with DiscountsA discount reduces the original amount by a percentage. For example, a 20% discount on £50 reduces the price by (50 × 0.2) = £10, so the new price is £40.

Review Time!Great work! You've learned about percentages, percentage change, and reverse percentages. Let's review what we've covered.