GCSE Maths Practice: simplifying-ratios

Question 7 of 10

This question focuses on simplifying ratios, a core GCSE Maths Foundation skill.

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\( \begin{array}{l}\text{Simplify the ratio } 6:9 \\ \text{to its simplest form.}\end{array} \)

Choose one option:

Always divide both parts of a ratio by the highest common factor and check your final answer.

Simplifying Ratios – GCSE Maths Foundation

Simplifying ratios is one of the most important skills in GCSE Maths and appears regularly in Foundation exam papers. A ratio compares two quantities and shows how much of one thing there is compared to another. Writing a ratio in its simplest form makes it easier to understand, compare, and use in further calculations.

What Does It Mean to Simplify a Ratio?

To simplify a ratio means to reduce the numbers involved so that they are as small as possible while keeping the same relationship. This is done by dividing both parts of the ratio by the same number. Just like simplifying fractions, both values must be treated equally to preserve the meaning of the comparison.

The Role 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 the ratio is fully simplified. If you divide by a smaller factor, the ratio may still be reducible, which would not be accepted as a final answer in a GCSE exam.

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 by the HCF.
  4. Check that the resulting numbers have no common factor greater than 1.

This method 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 8:12.

The HCF of 8 and 12 is 4. Dividing both parts by 4 reduces the ratio to its lowest terms.

Worked Example 3

Simplify the ratio 21:28.

The highest common factor is 7. Dividing each number by 7 produces a clearer and simpler ratio.

Common Mistakes to Avoid

  • Dividing only one part of the ratio instead of both.
  • 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 in many everyday situations. In recipes, ratios ensure ingredients are mixed correctly. In classrooms, ratios can describe numbers of students. In sports, ratios are used to compare statistics such as wins and losses. Understanding how to simplify ratios helps make these comparisons accurate and meaningful.

Frequently Asked Questions

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

Can ratios have more than two numbers?
Yes. Ratios such as 2:4:6 can also be simplified by dividing all parts by the highest common factor.

What if the numbers have 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 efficiently and avoid mistakes in GCSE Maths exams.

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