GCSE Maths Practice: simplifying-ratios

Question 6 of 10

This question focuses on simplifying ratios by using the highest common factor, an essential GCSE Maths Foundation skill.

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\( \begin{array}{l}\text{What is the simplest form of } 8:12 \\ \text{?}\end{array} \)

Choose one option:

Always divide both parts of a ratio by the highest common factor and check that no further simplification is possible.

Simplifying Ratios – GCSE Maths Foundation

Simplifying ratios is a core topic in GCSE Maths Foundation and is closely linked to other important ideas such as fractions, proportion, and percentages. A ratio is used to compare quantities and show how much of one quantity there is compared to another. Writing ratios in their simplest form makes them easier to interpret and use correctly in further calculations.

What Does It Mean to Simplify a Ratio?

When you simplify a ratio, you reduce the numbers so that they are as small as possible while keeping the same relationship between the quantities. This is done by dividing both parts of the ratio by the same whole number. Just like simplifying fractions, both numbers must be treated equally to ensure the comparison remains accurate.

The Importance of the Highest Common Factor (HCF)

The highest common factor is the largest number that divides exactly into both numbers in the ratio. Using the HCF ensures the ratio is fully simplified. If you divide by a smaller factor, the ratio might still be reducible, which would not be accepted as a final answer in GCSE exams.

Step-by-Step Method

  1. Write the ratio clearly using a colon.
  2. Find the highest common factor of both 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 structured approach works for all Foundation-level simplifying ratio questions.

Worked Example 1

Simplify the ratio 10:15.

The highest common factor of 10 and 15 is 5. Dividing both numbers by 5 gives a simplified ratio.

Worked Example 2

Simplify the ratio 16:24.

The HCF of 16 and 24 is 8. Dividing both parts by 8 reduces the ratio to its lowest terms.

Worked Example 3

Simplify the ratio 18:30.

The highest common factor is 6. Dividing each number by 6 produces a simpler comparison.

Common Mistakes to Avoid

  • Dividing only one part of the ratio instead of both.
  • Using a factor that is not the highest common factor.
  • Stopping before the ratio is fully simplified.
  • Rewriting the ratio in the wrong order.

Real-Life Applications of Ratios

Ratios appear in many everyday situations. Recipes rely on ratios to mix ingredients correctly. In art and design, ratios help keep drawings and models in proportion. In sports, ratios are used to compare statistics such as wins to losses. Being confident with simplifying ratios ensures these comparisons are meaningful and accurate.

Frequently Asked Questions

Do ratios always need to be simplified?
Yes. Unless a question specifically says otherwise, ratios should be written in their simplest form in GCSE Maths.

Can ratios include more than two numbers?
Yes. For example, a ratio like 4:8:12 can be simplified by dividing all parts by the highest common factor.

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

Study Tip

Practise finding the highest common factor quickly by listing factors or using mental maths. This will help you simplify ratios accurately and confidently in GCSE Maths exams.

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