Learn: Ratio and Proportion

Welcome!Today we'll learn about ratio and proportion. This is an important topic that helps us compare quantities and solve real-world problems. Let's explore step by step!

What is a 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 there are 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 2:3 is proportional to 4:6, it means the relationship between the numbers in the first ratio is the same as in the second.

Simplifying RatiosTo simplify a ratio, divide both parts by their greatest common divisor (GCD). For example, to simplify 12:8, divide both numbers by their GCD, which is 4. This gives 3:2.

Using Ratios to Divide QuantitiesWe can use ratios to divide quantities into parts. For example, if £80 is divided in the ratio 3:2, first add the parts (3 + 2 = 5). Then divide £80 by 5 to find the value of one part (£80 ÷ 5 = £16). Multiply each part by £16: 3 × £16 = £48 and 2 × £16 = £32. So the amounts are £48 and £32.

Proportional ReasoningProportional reasoning lets you solve problems using relationships between quantities. For example, if 3 pens cost £6, how much do 5 pens cost? First, find the cost of 1 pen (£6 ÷ 3 = £2), then multiply by 5 (£2 × 5 = £10).

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