GCSE Maths Practice: simplifying-ratios

Question 1 of 10

This question tests your ability to recognise which ratios simplify to the same value, a key GCSE Higher skill.

›

\( \begin{array}{l}\text{Select all ratios that simplify to } 4:5.\end{array} \)

Select all correct options:

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

Identifying Equivalent Ratios – GCSE Maths (Higher Tier)

At GCSE Higher level, students are expected not only to simplify ratios accurately but also to recognise when different ratios are equivalent. Equivalent ratios represent the same proportional relationship, even though the numbers used may be different. This skill is essential for solving advanced ratio and proportion problems, including scaling, best-value questions, and algebraic ratios.

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 determine whether they describe the same proportional relationship.

Why Higher-Tier Questions Require Careful Checking

In Higher GCSE exams, ratio questions often include distractors that look similar but simplify to a different form. You must simplify every ratio fully before making comparisons. Relying on visual inspection or assuming ratios are equivalent because the numbers look related can lead to errors.

Systematic Method for Solving This Question

  1. Take each ratio one 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.

This method ensures accuracy and avoids missing valid answers.

Worked Example 1

Does the ratio 20:25 simplify to 4:5?

The highest common factor of 20 and 25 is 5. Dividing both numbers by 5 gives a simplified ratio that can be directly compared with the target.

Worked Example 2

Does the ratio 28:35 match the ratio 4:5?

The HCF is 7. Dividing both parts by 7 produces a simplified ratio suitable for comparison.

Worked Example 3

Does the ratio 18:24 simplify to 4:5?

The highest common factor is 6. Dividing both numbers by 6 gives a simplified ratio that can be checked against the target.

Common Errors at Higher Tier

  • Failing to fully simplify ratios before comparing them.
  • Dividing by a common factor that is not the highest.
  • Assuming all multiples of a ratio are equivalent without checking.
  • Overlooking that order matters in ratios.

Real-Life and Exam Applications

Equivalent ratios are widely used in real-life and exam contexts. In best-value problems, ratios are used to compare price per unit. In science, ratios compare concentrations or reaction quantities. In geometry, ratios are used to describe similar shapes. Being able to identify equivalent ratios accurately is essential for success in GCSE Higher Maths.

Frequently Asked Questions

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

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

Does a larger ratio always represent a larger amount?
No. Ratios describe relationships, not absolute sizes.

Study Tip

For Higher-tier ratio questions, always simplify every option fully and write the result clearly. This systematic approach prevents errors and ensures you identify all correct equivalent ratios.

Related Quizzes