Compare Quantities Clearly and Accurately
Ratio is an important maths topic because it helps students compare quantities and share amounts in a structured way. It appears in KS3, GCSE, IGCSE and many real-life situations, including recipes, maps, scale drawings, speed, proportion and finance. Ratio lessons at MasterMaths Tutoring are designed to make the topic clear by showing students how to read ratios, simplify them and use them in problem-solving questions.
A ratio compares one amount with another. For example, a ratio of 2:3 means there are two parts of one quantity for every three parts of another quantity. Students often need support understanding that ratio is about parts, not always the actual amounts. Once the idea of parts is clear, sharing in a ratio, simplifying ratios and finding missing values become much easier.
At KS3, ratio lessons may include simplifying ratios, writing ratios from diagrams, sharing an amount in a ratio and comparing quantities. At GCSE and IGCSE, students may need to solve harder ratio problems involving algebra, scale factors, similar shapes, recipes, maps, percentages and direct or inverse proportion. Higher tier questions often combine ratio with other topics, so students need to know how to set out their working clearly.
Topics covered in ratio lessons may include simplifying ratios, equivalent ratios, sharing in a ratio, finding a missing amount, ratio and fractions, ratio and percentages, scale drawings, map scales, similar shapes, direct proportion, inverse proportion and problem-solving questions. The tutor can choose examples that match the student’s confidence and exam level.
Example exercise: £60 is shared between two people in the ratio 2:3. First find the total number of parts: 2 + 3 = 5 parts. Then divide £60 by 5 to find one part: £60 ÷ 5 = £12. The first person gets 2 parts, so 2 × £12 = £24. The second person gets 3 parts, so 3 × £12 = £36. The share is £24 and £36.
Students often make mistakes in ratio questions because they use the difference between the numbers instead of the total number of parts. For example, in the ratio 2:3, there are 5 parts altogether, not 1 part. A tutor can help students slow down, draw a bar model if helpful and check whether the final amounts add up to the total given in the question.
Ratio is also closely connected to proportion. If one quantity doubles, another may also double in direct proportion. In inverse proportion, one quantity increases while another decreases. These ideas become important in GCSE Maths and can appear in questions about speed, density, pressure, recipes and scaling. Lessons can help students recognise which relationship is being used.
The aim of ratio lessons is to help students compare quantities confidently, use the correct method and explain their working clearly. With regular practice, ratio becomes a useful tool rather than a confusing topic. Strong ratio skills also support fractions, percentages, geometry, similar shapes and many GCSE problem-solving questions.