GCSE Maths Practice: simplifying-ratios

Question 2 of 10

This question tests your ability to identify ratios that simplify to the same value.

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\( \begin{array}{l}\text{Which of these ratios simplify to } 5:2\text{?}\end{array} \)

Select all correct options:

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

Identifying Equivalent Ratios (GCSE Maths – Higher Tier)

At GCSE Higher level, you are expected to recognise when different ratios are equivalent. Equivalent ratios represent the same proportional relationship, even though the numbers used may look very different. These questions often require careful simplification of each option rather than quick visual judgement.

What Does It Mean for Ratios to Be Equivalent?

Two ratios are equivalent if one can be obtained from the other by multiplying or dividing both parts by the same non-zero number. This preserves the relationship between the quantities. Simplifying ratios to their lowest terms allows you to compare them directly and decide whether they describe the same proportion.

Why Higher-Tier Questions Use Multiple Options

Higher GCSE questions often include several options that all simplify to the same value. This tests whether students simplify every ratio carefully rather than stopping once one correct answer is found. Multiple-answer questions also check accuracy and attention to detail.

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.

Following this method ensures that no correct answers are missed.

Worked Example 1

Does the ratio 30:12 simplify to 5:2?

The highest common factor of 30 and 12 is 6. Dividing both numbers by 6 produces a simplified ratio that can be compared with the target.

Worked Example 2

Does the ratio 40:16 match the ratio 5:2?

The HCF is 8. Dividing both parts by 8 reduces the ratio to its simplest form for comparison.

Worked Example 3

Does the ratio 45:18 simplify to 5:2?

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

Common Mistakes to Avoid

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

Real-Life and Exam Applications

Equivalent ratios appear frequently in real-life contexts such as scaling recipes, mixing ingredients, map scales, and best-value problems. In exams, they are commonly used in proportion questions, similar shapes, and financial calculations. Being confident with equivalent ratios helps you solve these problems efficiently.

Frequently Asked Questions

Can more than one option be correct?
Yes. Many ratios can simplify to the same form.

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

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

Study Tip

For Higher-tier ratio questions, always simplify every option fully and write the result clearly. This systematic approach helps you identify all correct equivalent ratios without making careless errors.

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