GCSE Maths Practice: simplifying-ratios

Question 10 of 10

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

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\( \begin{array}{l}\text{Which ratios simplify to } 3:4\text{?}\end{array} \)

Select all correct options:

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

Identifying Ratios That Simplify to the Same Form

In GCSE Maths Foundation, you are often asked to recognise which ratios simplify to a given target ratio. This requires a solid understanding of simplifying ratios using the highest common factor (HCF). Even when ratios look different at first glance, they may still represent the same relationship once simplified.

What Does It Mean for Ratios to Simplify to the Same Form?

Two ratios simplify to the same form if, after dividing both numbers by their highest common factor, they become identical. This means the ratios are equivalent and describe the same proportional relationship between quantities. Recognising equivalent ratios is an essential skill for ratio, proportion, and scaling questions.

Why You Must Always Simplify First

Comparing ratios without simplifying them can be misleading. Larger numbers do not necessarily mean a different ratio. GCSE exam questions often include several options that look different but simplify to the same form. Simplifying each ratio carefully ensures that no correct answers are missed.

Step-by-Step Method for This Question Type

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

This structured approach helps avoid careless mistakes and ensures accuracy.

Worked Example 1

Does the ratio 18:24 simplify to 3:4?

The highest common factor of 18 and 24 is 6. Dividing both numbers by 6 produces a simplified ratio that can be compared with the target.

Worked Example 2

Does the ratio 21:28 match the ratio 3:4?

The HCF is 7. After dividing both numbers by 7, the simplified ratio can be checked against the target.

Worked Example 3

Does the ratio 12:20 simplify to 3:4?

The highest common factor is 4. Dividing both parts by 4 gives a simplified ratio that can be compared clearly.

Common Mistakes to Avoid

  • Assuming a ratio is not equivalent because the numbers are larger.
  • Failing to divide both numbers by the same value.
  • Stopping simplification too early.
  • Comparing ratios before simplifying them.

Real-Life Applications of Equivalent Ratios

Equivalent ratios appear frequently in everyday life. In recipes, ingredient quantities can be scaled up or down while keeping the same ratio. In maps and scale drawings, distances are increased or reduced proportionally. In science, ratios are used to compare measurements consistently. Being confident with equivalent ratios helps ensure accuracy in these situations.

Frequently Asked Questions

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

Should every ratio be simplified fully?
Yes. GCSE examiners expect ratios to be fully simplified before comparison.

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

Study Tip

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

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