GCSE Maths Practice: simplifying-ratios

Recognising Equivalent Ratios (GCSE Maths – Higher Tier)

At GCSE Higher level, you are expected to recognise when different ratios represent the same proportional relationship. These are known as equivalent ratios. Even when the numbers look very different, ratios can still be equivalent if they simplify to the same simplest form.

What Does It Mean for Ratios to Be Equivalent?

Two ratios are equivalent if one can be changed into the other by multiplying or dividing both parts by the same non-zero number. This operation keeps the relationship between the quantities the same. Simplifying ratios to their lowest terms allows you to compare them directly and identify equivalence.

Why Higher-Tier Questions Use Multiple Correct Answers

In Higher GCSE exams, questions often include several ratios that all simplify to the same value. This tests whether students carefully simplify every option rather than assuming only one answer can be correct. Accuracy and method are both essential.

Step-by-Step Method for This Question Type

1. Take one ratio at a time.
2. Find the highest common factor (HCF) of the two numbers.
3. Divide both parts of the ratio by the HCF.
4. Write the simplified ratio clearly.
5. Compare it with the target ratio.

Using this method ensures that no correct options are missed.

Worked Example 1

Does the ratio 12:16 simplify to 3:4?

The highest common factor of 12 and 16 is 4. Dividing both numbers by 4 gives a simplified ratio that can be compared with the target.

Worked Example 2

Does the ratio 18:24 match the ratio 3:4?

The HCF is 6. Dividing both parts by 6 produces a simplified ratio for comparison.

Worked Example 3

Does the ratio 30:40 simplify to 3:4?

Dividing both numbers by their highest common factor allows the simplified ratio to be checked clearly.

Common Mistakes to Avoid

• Comparing ratios without simplifying them first.
• Dividing by a factor that is not the highest common factor.
• Stopping once one correct answer is found.
• Assuming ratios are different because the numbers are larger.

Real-Life and Exam Applications

Equivalent ratios appear frequently in real-life situations such as scaling recipes, mixing ingredients, adjusting map scales, and comparing prices for best value. In exams, they are commonly used in proportion problems, similar shapes, and multi-step calculations. Being confident with equivalent ratios helps you work efficiently and accurately.

Frequently Asked Questions

Can all the options be correct?
Yes. If all ratios simplify to the same simplest form, then all options are correct.

Is simplifying always required?
Yes. GCSE examiners expect ratios to be fully simplified before comparison.

Does order matter in ratios?
Yes. Changing the order changes the meaning of the ratio.

Study Tip

For Higher-tier ratio questions, always simplify every option fully before making a decision. A careful, systematic approach helps you avoid missing correct answers.