GCSE Maths Practice: simplifying-ratios

Question 9 of 10

This question tests your ability to recognise ratios that simplify to the same form.

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\( \begin{array}{l}\text{Which ratios simplify to } 2:3\text{?}\end{array} \)

Select all correct options:

Simplify each ratio completely before comparing it with the target ratio.

Identifying Equivalent Ratios – GCSE Maths Foundation

In GCSE Maths, it is not enough to simplify a single ratio on its own. You are also expected to recognise when different-looking ratios are actually equivalent. Equivalent ratios describe the same relationship between quantities, even though the numbers used may be different. This question focuses on identifying ratios that simplify to the same target form.

What Are Equivalent Ratios?

Equivalent ratios are ratios that represent the same comparison between quantities. They are created when both parts of a ratio are multiplied or divided by the same number. Although the values may look larger or smaller, the relationship remains unchanged. Recognising equivalent ratios is essential for topics such as proportion, scaling, and sharing problems.

Why Simplifying Ratios Is Essential

Simplifying ratios allows you to see their true form. Two ratios can only be compared accurately once they have been simplified. Without simplifying, it is easy to assume ratios are different when they actually describe the same relationship. GCSE exam questions often test this skill by asking you to select all ratios that simplify to a given target ratio.

Step-by-Step Strategy for This Type of Question

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

Following this method carefully helps avoid mistakes and ensures no correct options are missed.

Worked Example 1

Does the ratio 6:9 simplify to 2:3?

The highest common factor of 6 and 9 is 3. Dividing both numbers by 3 produces a simplified ratio that can then be compared with the target.

Worked Example 2

Does the ratio 12:18 match the ratio 2:3?

The HCF is 6. Dividing both parts by 6 reduces the ratio, making comparison straightforward.

Worked Example 3

Does the ratio 14:21 simplify to 2:3?

The highest common factor is 7. After simplifying, the resulting ratio can be checked against the target.

Common Mistakes Students Make

  • Comparing ratios without simplifying them first.
  • Dividing the two numbers by different values.
  • Assuming all ratios with larger numbers are different.
  • Forgetting that ratios must be in the same order to be equivalent.

Real-Life Applications of Equivalent Ratios

Equivalent ratios are used frequently in everyday life. In recipes, ingredient quantities are scaled up or down while keeping the same ratio. In maps and scale drawings, distances are enlarged or reduced proportionally. In finance, ratios are used to compare costs or profits consistently. Understanding equivalent ratios ensures accuracy in all these situations.

Frequently Asked Questions

Can more than one ratio simplify to the same form?
Yes. Many different ratios can simplify to the same simplest form.

Is simplifying always required before comparing ratios?
Yes. Simplifying removes confusion and makes comparisons clear.

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

Study Tip

Always simplify every ratio fully before comparing it to a target ratio. Writing each simplified ratio clearly will help you spot equivalent ratios quickly and confidently in GCSE Maths exams.

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