GCSE Maths Practice: simplifying-ratios

Question 3 of 10

This question focuses on simplifying ratios, an essential GCSE Maths skill used in exams and real-life contexts.

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\( \begin{array}{l}\text{Simplify the ratio } 20:30 \\ \text{to lowest terms.}\end{array} \)

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 a fundamental skill in GCSE Maths and appears frequently across many exam questions. A ratio compares two or more quantities and shows their relative sizes. Writing a ratio in its simplest form makes it easier to understand and use, just like simplifying fractions makes them clearer and more manageable.

What Does It Mean to Simplify a Ratio?

When you simplify a ratio, you reduce it to the smallest whole numbers that still represent the same relationship between quantities. The key idea is that both parts of the ratio must be treated equally. This ensures that 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 parts of a ratio. Using the HCF guarantees that the ratio is fully simplified. Dividing by any smaller factor may reduce the numbers but may not give the simplest possible form.

Step-by-Step Method

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

This method works for all simplifying ratio questions at GCSE Foundation level.

Worked Example 1

Simplify the ratio 16:24.

The highest common factor of 16 and 24 is 8. Dividing both parts by 8 gives a simplified ratio.

Worked Example 2

Simplify the ratio 14:21.

The HCF of 14 and 21 is 7. Dividing each number by 7 produces a simpler ratio that is easier to interpret.

Worked Example 3

Simplify the ratio 9:12.

The highest common factor is 3. Dividing both numbers by 3 reduces the ratio to its lowest terms.

Common Mistakes Students Make

  • Dividing only one number instead of both.
  • Using a factor that is not the highest common factor.
  • Leaving the ratio partially simplified.
  • Confusing ratios with fractions and changing the format unnecessarily.

Real-Life Uses of Ratios

Ratios are used in many real-world situations. Recipes use ratios to ensure ingredients are mixed correctly. Maps use ratios to represent distances accurately. In classrooms, ratios are used to compare groups of students. Understanding how to simplify ratios ensures calculations remain accurate and meaningful.

Frequently Asked Questions

Is it always necessary to simplify ratios?
Yes. Unless the question says otherwise, GCSE examiners expect ratios in their simplest form.

Can ratios include more than two values?
Yes. For example, a ratio like 4:6:10 can be simplified by dividing all parts by their 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. This skill will help you simplify ratios efficiently and avoid common mistakes in GCSE Maths exams.

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