GCSE Maths Practice: simplifying-ratios

Question 7 of 10

This question focuses on simplifying ratios that include decimals, a key GCSE Higher Maths skill.

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\( \begin{array}{l}\text{Simplify the ratio } 1.2:2.4 \\ \text{to its lowest terms.}\end{array} \)

Choose one option:

Always remove decimals first before attempting to simplify a ratio.

Simplifying Decimal Ratios to Whole Numbers (GCSE Maths – Higher)

At GCSE Higher level, ratio questions frequently involve decimals rather than whole numbers. These questions test whether you understand the underlying process of simplifying ratios, rather than relying on spotting obvious factors. Decimal ratios often appear in exam questions linked to real-life contexts such as money, measurements, speed, and rates.

Why Decimal Ratios Can Be Tricky

Decimals make it harder to identify common factors directly. For example, it is not easy to see a highest common factor when values include decimal points. Because of this, the key strategy is always to remove the decimals first before attempting to simplify the ratio.

Key Strategy: Remove Decimals Using Powers of 10

To remove decimals, multiply both parts of the ratio by the same power of 10. This keeps the ratio equivalent while converting it into whole numbers. The power of 10 you choose depends on the number of decimal places present. Once the ratio contains only whole numbers, it can be simplified in the usual way.

Step-by-Step Method

  1. Identify how many decimal places are in the ratio.
  2. Multiply both numbers by a suitable power of 10 to remove all decimals.
  3. Write down the new whole-number ratio.
  4. Find the highest common factor (HCF) of the two numbers.
  5. Divide both numbers by the HCF.
  6. Check that the final ratio is in its simplest form.

This structured method works for all decimal ratios at Higher GCSE level.

Worked Example 1

Simplify the ratio 0.6 : 1.2.

Multiply both numbers by 10 to remove the decimals, then divide by the highest common factor to simplify.

Worked Example 2

Simplify the ratio 1.5 : 3.0.

Remove the decimal point by multiplying by 10. Once written as whole numbers, simplify using the HCF.

Worked Example 3

Simplify the ratio 0.9 : 1.8.

Multiplying by 10 converts the ratio to whole numbers, which can then be reduced to their lowest terms.

Common Mistakes to Avoid

  • Trying to divide decimals directly instead of removing them first.
  • Multiplying only one part of the ratio by 10.
  • Using an incorrect power of 10 that does not remove all decimals.
  • Forgetting to simplify fully after converting to whole numbers.

Why This Skill Is Important

Decimal ratios appear regularly in Higher GCSE questions involving proportion, rates, and comparisons. Being able to simplify them confidently prevents the loss of easy marks and allows you to focus on the more challenging parts of multi-step problems.

Frequently Asked Questions

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

Can I turn decimals into fractions instead?
Yes, but multiplying by powers of 10 is usually quicker and safer in exams.

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

Study Tip

When revising Higher-tier ratio questions, practise converting decimal ratios into whole numbers quickly. A consistent method will help you work accurately under time pressure.

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