Learn: Ratios and Proportions

Welcome!Today we'll explore ratios and proportions, an important topic in iGCSE Mathematics. You'll learn how to compare quantities and solve problems involving ratios step by step.

What are Ratios?A ratio shows the relationship between two or more quantities, expressing how much of one quantity exists compared to another. For example, if there are 2 apples for every 3 oranges, the ratio is written as 2:3.

What are Proportions?A proportion is an equation that states two ratios are equal. For example, if the ratio of apples to oranges remains the same in two baskets, we can say the quantities are in proportion.

Simplifying RatiosTo simplify a ratio, divide both sides by their highest common factor (HCF). For example, the ratio 6:9 simplifies to 2:3 because both numbers can be divided by 3.

Using Ratios to Divide QuantitiesRatios can be used to divide quantities into parts. For example, if £60 is shared between two people in the ratio 3:2, the total parts are 3 + 2 = 5. Each part is £60 ÷ 5 = £12. The first person gets £12 × 3 = £36, and the second person gets £12 × 2 = £24.

Proportions in Real LifeProportions are used to solve problems where quantities scale up or down while maintaining the same ratio. For example, if 2 litres of paint cover 10 square metres, then 4 litres will cover 20 square metres because the ratio remains constant.

Solving Proportion ProblemsTo solve proportion problems, set up an equation with two equal ratios and solve for the unknown. For example, if 3 pencils cost £1.50, how much do 5 pencils cost? Solve: 3/1.50 = 5/x. Cross-multiply to find x = £2.50.

Review Time!Great work! You've learned about ratios, proportions, simplifying ratios, and solving proportion problems. Let's test your understanding with a few questions.