GCSE Maths Practice: simplifying-ratios

Question 5 of 10

This question helps you practise simplifying ratios using the highest common factor, a core GCSE Maths skill.

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\( \begin{array}{l}\text{Simplify the ratio } 48:16 \\ \text{to lowest terms.}\end{array} \)

Choose one option:

Always divide both numbers by the highest common factor and check your final ratio carefully.

Simplifying Ratios in GCSE Maths

Simplifying ratios is an essential skill in GCSE Maths and is closely linked to topics such as fractions, proportion, and percentages. A ratio shows how two quantities compare with each other. Writing a ratio in its simplest form makes this comparison clearer and easier to work with in both exam questions and real-life situations.

What Does It Mean to Simplify a Ratio?

To simplify a ratio means to reduce it so that the numbers involved are as small as possible while still showing the same relationship. This is done by dividing both parts of the ratio by the same number. The key rule is that both values must be treated equally, otherwise the comparison would change.

The Importance of the Highest Common Factor (HCF)

The highest common factor is the largest whole number that divides exactly into both parts of a ratio. Using the HCF ensures that the ratio is fully simplified. If a smaller factor is used, the ratio may still be reducible, which would not be accepted as the final answer in GCSE exams.

Step-by-Step Method

  1. Write the ratio clearly using a colon.
  2. Find the highest common factor of the two numbers.
  3. Divide each number in the ratio by the HCF.
  4. Check that the resulting numbers share no common factor greater than 1.

This method applies to all Foundation-level simplifying ratio questions.

Worked Example 1

Simplify the ratio 36:12.

The highest common factor of 36 and 12 is 12. Dividing both numbers by 12 produces a simplified ratio.

Worked Example 2

Simplify the ratio 24:8.

The HCF is 8. Dividing both parts by 8 reduces the ratio to its lowest terms.

Worked Example 3

Simplify the ratio 50:25.

The highest common factor is 25. Dividing both numbers by 25 gives a much simpler ratio.

Common Mistakes to Avoid

  • Dividing only one part of the ratio.
  • Using a factor that is not the highest common factor.
  • Leaving the ratio partially simplified.
  • Reversing the order of the ratio by mistake.

Real-Life Applications of Ratios

Ratios are used widely in everyday life. In recipes, ratios help ensure ingredients are mixed in the correct amounts. In sport, ratios compare statistics such as wins to losses. In construction and design, ratios are used to scale drawings accurately. Being confident with simplifying ratios helps you apply maths correctly in these situations.

Frequently Asked Questions

Is simplifying ratios the same as simplifying fractions?
They use a similar idea, but ratios compare quantities, while fractions describe parts of a whole.

Do ratios always need to be simplified?
Yes, unless the question specifically states otherwise.

What if one number is much larger than the other?
You still follow the same method: find the HCF and divide both numbers by it.

Study Tip

Practise finding the highest common factor quickly by listing factors or using mental maths. Strong HCF skills make simplifying ratios faster and help reduce mistakes in GCSE Maths exams.

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