GCSE Maths Practice: simplifying-ratios

Question 1 of 10

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

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\( \begin{array}{l}\text{What is } 15:35 \\ \text{in its simplest form?}\end{array} \)

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 skill in GCSE Maths Foundation and is closely connected to other important topics such as fractions, proportion, and percentages. A ratio is used to compare two quantities and show how much of one quantity there is compared to another. Writing ratios in their simplest form makes them easier to understand, compare, and apply correctly in further questions.

What Does It Mean to Simplify a Ratio?

To simplify a ratio means to reduce it to the smallest whole numbers that still represent the same relationship. This is done by dividing both parts of the ratio by the same number. It is important that both numbers are divided equally; otherwise, the comparison between the quantities would change.

The Role of the Highest Common Factor (HCF)

The highest common factor is the largest whole number that divides exactly into both numbers in the ratio. Using the HCF ensures that 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 the two 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 method works for all Foundation-level simplifying ratio questions.

Worked Example 1

Simplify the ratio 10:25.

The highest common factor of 10 and 25 is 5. Dividing both numbers by 5 gives a simplified ratio.

Worked Example 2

Simplify the ratio 18:42.

The HCF of 18 and 42 is 6. Dividing each number by 6 produces a simpler ratio.

Worked Example 3

Simplify the ratio 21:49.

The highest common factor is 7. Dividing both numbers by 7 reduces the ratio to its lowest terms.

Common Mistakes to Avoid

  • Dividing only one number in the ratio.
  • Using a factor that is not the highest common factor.
  • Stopping before the ratio is fully simplified.
  • Accidentally reversing the order of the ratio.

Real-Life Applications of Ratios

Ratios are used in many real-life situations. Recipes rely on ratios to ensure ingredients are mixed correctly. In maps and scale drawings, ratios help represent real distances accurately. In classrooms, ratios may describe numbers of students or resources. Understanding how to simplify ratios ensures these comparisons are clear and meaningful.

Frequently Asked Questions

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

Can ratios include more than two numbers?
Yes. Ratios such as 3:6:9 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 using factor lists or mental maths. Strong HCF skills make simplifying ratios faster and help avoid mistakes in GCSE Maths exams.

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