Learn: Percentages

Welcome!Today we'll explore percentages. Percentages are a way to express numbers as parts per hundred. Let's break this down step by step!

What is a Percentage?A percentage is a fraction of 100. For example, 50% means 50 out of 100, or 1/2. Percentages are used in everyday life for discounts, interest rates, and comparisons.

Converting Between Percentages, Fractions, and DecimalsYou can convert between percentages, fractions, and decimals easily. To convert a percentage to a decimal, divide by 100 (e.g., 25% = 0.25). To convert a percentage to a fraction, write it over 100 and simplify (e.g., 25% = 25/100 = 1/4).

Finding Percentages of a QuantityTo find a percentage of a number, multiply the number by the percentage as a decimal. For example, 10% of £50 = 0.1 × 50 = £5.

Percentage ChangePercentage change shows the increase or decrease as a percentage. Use the formula: (change ÷ original) × 100. For example, if a price increases from £40 to £50, the change is £10. Divide £10 by £40 and multiply by 100 to get 25%.

Reverse PercentagesReverse percentages are used to find the original amount before a percentage change. Divide the new amount by (1 + percentage as a decimal) for increases or (1 − percentage as a decimal) for decreases.

Compound InterestCompound interest occurs when interest is added to the principal, and the total earns interest. Use the formula: Final amount = Principal × (1 + rate as decimal)time. For example, £100 at 5% annual interest for 2 years becomes £100 × (1 + 0.05)2 = £110.25.

Review Time!Great work! You've learned about percentages, percentage change, reverse percentages, and compound interest. Let's test your understanding with a few questions.