Learn: Ratio and Proportion

Welcome!Today, we'll explore Ratio and Proportion, an important topic in mathematics that helps us compare quantities and solve real-world problems. Let's dive in and understand how ratios and proportions work step by step!

What is Ratio?A ratio is a way to compare two quantities by showing the relative sizes of the two values. For example, if there are 3 apples and 2 oranges, the ratio of apples to oranges is 3:2. Ratios help us understand how one quantity relates to another.

What is Proportion?A proportion is an equation that shows two ratios are equal. For example, if 2:3 is equal to 4:6, then we say these ratios are proportional. Proportions help us solve problems where one ratio depends on the other.

Understanding Ratios in Real LifeRatios are common in everyday life! For example, if a recipe calls for 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is 2:1. If you double the recipe, the ratio remains the same, but the quantities change to 4 cups of flour to 2 cups of sugar.

Solving ProportionsTo solve a proportion, we use cross-multiplication. For example, if \( \frac{2}{x} = \frac{4}{6} \), we multiply across the equals sign: \( 2 \times 6 = x \times 4 \). Solving for \( x \), we get \( x = 3 \).

Using Ratios and ProportionsRatios and proportions are used in problems involving scale drawings, recipes, and sharing quantities. For instance, if you need to share £120 in the ratio 2:3, you divide 120 by the sum of the ratio (5), to find the value of one part (£24). Then multiply by each ratio number: £48 and £72.

Review Time!Great work understanding Ratio and Proportion! Let's test what you've learned with a few questions.

Well done!You've completed this lesson on Ratio and Proportion. Keep practising to master the concepts and apply them to real-life situations!