Learn: Ratios and Proportions

Welcome!Today we'll learn about ratios and proportions, a key topic in iGCSE Mathematics. This lesson is tailored to help you understand the basics and solve problems step by step.

What is a Ratio?A ratio compares two or more quantities to show their relative size. It is written using the ':' symbol, for example, 2:3 means for every 2 units of one quantity, there are 3 units of another.

What is Proportion?A proportion is when two ratios are equal. It helps us solve problems where amounts are scaled. For example, if 1:2 is equal to 2:4, the two ratios are proportional.

Simplifying RatiosTo simplify a ratio, divide both parts of the ratio by their greatest common factor. For example, the ratio 6:9 simplifies to 2:3 by dividing both numbers by 3.

Using Ratios in Real LifeRatios are used in recipes, maps, and sharing money. For example, if a map uses a ratio of 1 cm:100 km, each centimetre represents 100 kilometres in the real world.

Dividing a Quantity in a Given RatioTo divide a quantity into a ratio, add the parts of the ratio, divide the total quantity by the sum, and multiply each part by the result. Example: Divide £50 in a 3:2 ratio. Add 3+2=5, calculate £50÷5=£10, then multiply: £10×3=£30, £10×2=£20.

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

Final ThoughtsYou've completed the lesson on ratios and proportions! Keep practising to master the topic. Great job today!