Ratio and Proportion

Ratio and proportion questions are a staple of the CSSE 11+ maths paper. These questions test whether you can compare quantities, share amounts fairly, and solve real-world problems involving scaling. The CSSE is known for embedding ratio concepts within multi-step word problems, so you need to be confident with all the methods in this lesson.

---

What Is a Ratio?

A ratio compares two or more quantities. It tells you how much of one thing there is compared to another.

If there are 4 red sweets and 6 blue sweets, the ratio of red to blue is 4 : 6, which simplifies to 2 : 3.

Key Points

• The order matters: 2 : 3 is different from 3 : 2.
• A ratio does not tell you the actual amounts — only the relationship.
• Ratios can have more than two parts: e.g. red : blue : green = 1 : 3 : 2.

---

Simplifying Ratios

Simplify a ratio by dividing all parts by their Highest Common Factor (HCF).