GCSE Maths Revision: Mastering Ratio and Proportion with Real-Life Problem...

Understanding Ratio and Proportion

Ratio and proportion are fundamental concepts in GCSE Maths, helping students compare quantities and solve real-life problems. Mastering these topics is essential for exam success and practical applications.

What Is a Ratio?

A ratio compares two or more quantities, showing how many times one value contains or is contained within the other. Ratios are often written with a colon, such as 3:2.

• Example: If a recipe uses 3 cups of flour to 2 cups of sugar, the ratio of flour to sugar is 3:2.

What Is Proportion?

Proportion shows that two ratios are equal. It is used to solve problems where one value changes in relation to another.

• Example: If 4 apples cost £2, then 8 apples cost £4. The proportion is 4:2 = 8:4.

Solving Real-Life Ratio Problems

Ratio and proportion are used in everyday situations, such as sharing costs, mixing ingredients, or scaling recipes. Here’s a step-by-step approach to solving these problems:

1. Identify the quantities involved and write them as a ratio.
2. Simplify the ratio if possible.
3. Set up a proportion if you need to find an unknown value.
4. Solve for the unknown using cross-multiplication or equivalent fractions.

Example Problem

Question: A bag of sweets is shared between Alice and Ben in the ratio 5:3. If there are 40 sweets, how many does each person get?

Solution:

• Total parts = 5 + 3 = 8
• Each part = 40 ÷ 8 = 5
• Alice gets 5 × 5 = 25 sweets
• Ben gets 3 × 5 = 15 sweets

Tips for Exam Success

• Always check if ratios can be simplified.
• Use units consistently throughout your calculations.
• Practice with real-life scenarios to build confidence.
• Show all working for full marks in exams.

Further Practice

Regular practice with past papers and real-world examples will help reinforce your understanding of ratio and proportion. Focus on word problems to develop strong problem-solving skills.