GCSE Maths Practice: simplifying-ratios

Question 2 of 10

This question focuses on simplifying ratios, a key GCSE Maths skill used in many real-life and exam situations.

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\( \begin{array}{l}\text{Simplify the ratio } 18:27 \\ \text{to its simplest form.}\end{array} \)

Choose one option:

Always check your final ratio has no common factor greater than 1.

Understanding Simplifying Ratios (GCSE Maths)

Ratios are used to compare quantities and show how much of one thing there is compared to another. In GCSE Maths, simplifying ratios is a core skill that appears frequently in both calculator and non-calculator papers. A simplified ratio is one where the numbers are in their lowest possible whole-number form, similar to simplifying fractions.

Why Simplifying Ratios Is Important

Simplifying ratios makes them easier to understand, compare, and use in further calculations. For example, a ratio like 18:27 gives the same information as its simplified form, but the simplified version is clearer and more practical. Many GCSE problems require you to simplify a ratio before using it in a real-life context such as sharing money, mixing ingredients, or comparing quantities.

Step-by-Step Method

  1. Write down the ratio clearly.
  2. Find the highest common factor (HCF) of both numbers.
  3. Divide each part of the ratio by the HCF.
  4. Check that the final numbers have no common factor greater than 1.

This process ensures the ratio is in its simplest form and ready for further use.

Worked Example 1

Simplify the ratio 12:20.

The HCF of 12 and 20 is 4. Dividing both parts by 4 gives a simplified ratio.

Worked Example 2

Simplify the ratio 15:45.

The HCF of 15 and 45 is 15. Dividing both parts by 15 gives a much simpler ratio.

Worked Example 3

Simplify the ratio 8:10.

The HCF is 2. Dividing both numbers by 2 produces a simpler and clearer ratio.

Common Mistakes to Avoid

  • Forgetting to find the highest common factor and only dividing by a smaller number.
  • Dividing only one part of the ratio instead of both.
  • Leaving the ratio unsimplified when a simpler form is required.
  • Confusing ratios with fractions and trying to convert unnecessarily.

Real-Life Applications

Ratios are used in many everyday situations. Recipes often use ratios to mix ingredients correctly, such as flour to sugar. Maps use ratios to represent real distances. In sports, ratios can describe wins to losses. Understanding simplified ratios helps ensure accuracy in all these contexts.

Frequently Asked Questions

Do ratios always need to be simplified?
Yes, unless the question specifically says otherwise. GCSE examiners expect ratios in simplest form.

Can ratios include more than two numbers?
Yes. For example, 2:4:6 can also be simplified by dividing all parts by their HCF.

What if there is no common factor?
If the only common factor is 1, the ratio is already in its simplest form.

Study Tip

When revising ratios for GCSE Maths, always practise finding the HCF quickly. This skill will save time in exams and reduce mistakes when simplifying ratios.

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