Learn: Ratio and Proportion

Welcome!Today, we’ll explore Ratio and Proportion, a key topic in iGCSE Mathematics. This topic is essential for solving real-world problems involving comparisons and scaling. Let’s dive in!

What is Ratio?A ratio is a way to compare two or more quantities. It shows how much of one thing there is compared to another. For example, if you have 2 apples and 3 oranges, the ratio of apples to oranges is 2:3.

What is Proportion?Proportion shows that two ratios are equal. For example, if 1:2 = 2:4, then these two ratios are in proportion. Proportion is useful in solving problems like scaling recipes or calculating distances.

Simplifying RatiosYou can simplify a ratio by dividing its terms by their highest common factor (HCF). For example, the ratio 12:16 can be simplified by dividing both numbers by their HCF, which is 4. This gives 3:4.

Dividing a Quantity in a Given RatioTo divide a quantity into a ratio, you add the parts of the ratio together to find the total number of parts. Then divide the quantity by this total and multiply by each part of the ratio. For example, to divide £60 in the ratio 2:3, the total number of parts is 5. Each part is £60 ÷ 5 = £12. So the shares are £24 (2 × £12) and £36 (3 × £12).

Direct ProportionIf two quantities are in direct proportion, they increase or decrease together at the same rate. For example, if you buy more apples, you pay more. If one quantity doubles, the other doubles too.

Inverse ProportionIn inverse proportion, as one quantity increases, the other decreases. For example, if you travel faster, the time taken to reach your destination decreases.

Using Ratios and ProportionsRatios and proportions can be used in real-life situations, like mixing ingredients, calculating speeds, or dividing money. They help you solve problems efficiently by understanding relationships between quantities.

Review Time!Great work! You've learned about ratios, proportions, and their applications. Now let's test your understanding with a few questions.