GCSE Maths Practice: simplifying-ratios

Question 5 of 10

This question focuses on simplifying ratios that contain decimals, a common GCSE Higher skill.

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\( \begin{array}{l}\text{Simplify the ratio } 0.5:1.5 \\ \text{to lowest terms.}\end{array} \)

Choose one option:

Always remove decimals first by multiplying both parts of the ratio by the same power of 10.

Simplifying Ratios That Contain Decimals (GCSE Maths – Higher)

At GCSE Higher level, ratio questions often include decimals or fractions rather than whole numbers. These questions test whether you can apply the same simplifying principles in a slightly more complex setting. Although decimal ratios may look harder, the process for simplifying them is systematic and reliable when done step by step.

Why Decimal Ratios Are Used

Decimal ratios appear frequently in Higher-tier questions because they reflect real-life measurements such as money, time, mass, and distance. Using decimals also prevents simple trial-and-error methods and encourages students to apply a clear mathematical strategy.

Key Idea: Remove the Decimals First

You cannot easily find a highest common factor when a ratio contains decimals. For this reason, the first step is always to remove the decimals by multiplying both parts of the ratio by the same power of 10. This keeps the ratio equivalent while converting it into whole numbers that are easier to work with.

General Method for Simplifying Decimal Ratios

  1. Identify how many decimal places are present.
  2. Multiply both parts of the ratio by a power of 10 to remove all decimals.
  3. Find the highest common factor (HCF) of the resulting whole numbers.
  4. Divide both parts by the HCF.
  5. Check that the final ratio is in its simplest form.

This method works for all decimal ratios, regardless of how many decimal places are involved.

Worked Example 1

Simplify the ratio 0.4 : 1.2.

Multiply both numbers by 10 to remove the decimals, giving a whole-number ratio. Then find the highest common factor and divide both parts to simplify.

Worked Example 2

Simplify the ratio 1.5 : 2.5.

Multiplying both values by 10 removes the decimals. The resulting whole-number ratio can then be simplified using the highest common factor.

Worked Example 3

Simplify the ratio 0.75 : 1.25.

Multiply both parts by 100 to remove decimals. Once converted to whole numbers, the ratio can be simplified in the usual way.

Common Mistakes to Avoid

  • Dividing decimals directly instead of removing them first.
  • Multiplying only one part of the ratio by 10.
  • Forgetting to simplify after removing decimals.
  • Stopping at whole numbers that are not in lowest terms.

Why This Skill Matters at Higher Tier

Decimal ratios often appear in multi-step Higher GCSE problems, including proportion questions, best-value calculations, and problems involving rates. Being confident with decimal ratios helps you move smoothly through these questions without unnecessary errors.

Frequently Asked Questions

Do I always multiply by 10?
No. Multiply by whatever power of 10 is needed to remove all decimals.

Can I use fractions instead?
Yes, but converting to whole numbers using powers of 10 is usually faster in exams.

Is the order of the ratio important?
Yes. Changing the order changes the meaning of the ratio.

Study Tip

When revising Higher-tier ratio questions, practise converting decimals to whole numbers quickly. A clear, step-by-step method will help you simplify ratios accurately under exam pressure.

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