GCSE Maths Practice: simplifying-ratios

Question 4 of 10

This question focuses on simplifying ratios that include decimals, an essential GCSE Higher Maths skill.

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\( \begin{array}{l}\text{What is the simplified ratio of } 3:0.75\text{?}\end{array} \)

Choose one option:

Always remove decimals first and then simplify the resulting whole-number ratio fully.

Simplifying Ratios That Contain Decimals (GCSE Maths – Higher Tier)

At GCSE Higher level, ratio questions often include decimals to test whether students can apply the rules of simplifying ratios in less familiar situations. Although ratios with decimals may look more complicated than those with whole numbers, the underlying process remains exactly the same once the decimals are removed.

Why Decimal Ratios Appear in Higher Questions

Decimal ratios are commonly used because they reflect real-life quantities such as money, measurements, time, and rates. Higher-tier exam questions use decimals to discourage guessing and ensure that students apply a clear, structured method rather than relying on visual inspection.

Key Principle: Remove Decimals First

It is difficult to identify common factors when decimals are present. For this reason, the first step in any decimal ratio question is 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 can be simplified easily.

Step-by-Step Method

  1. Identify how many decimal places are present in the ratio.
  2. Multiply both parts of the ratio by a suitable power of 10 to remove all decimals.
  3. Write the resulting ratio using whole numbers.
  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 method works for all decimal ratios, regardless of whether one or both terms contain decimals.

Worked Example 1

Simplify the ratio 2 : 0.5.

Multiply both numbers by 10 to remove the decimal. The resulting whole-number ratio can then be simplified using the highest common factor.

Worked Example 2

Simplify the ratio 1.5 : 0.75.

Multiply both parts by 100 to remove decimals. Once written as whole numbers, divide by the HCF to simplify fully.

Worked Example 3

Simplify the ratio 4 : 0.8.

Removing the decimal by multiplying by 10 allows the ratio to be simplified using standard methods.

Common Mistakes to Avoid

  • Trying to simplify decimals directly without removing them.
  • Multiplying only one part of the ratio by a power of 10.
  • Choosing a power of 10 that does not remove all decimals.
  • Forgetting to simplify the resulting whole-number ratio fully.

Why This Skill Is Important

Decimal ratios appear frequently in Higher GCSE questions involving proportion, rates of change, best value, and real-life contexts. Being confident with this skill allows you to focus on the reasoning in longer questions without losing marks on basic simplification.

Frequently Asked Questions

Do I always need to multiply by 100?
No. Multiply by whatever power of 10 removes all decimals.

Can I convert decimals to fractions instead?
Yes, but multiplying by powers of 10 is usually quicker and clearer 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 removing decimals quickly and confidently. A clear, consistent method will help you avoid careless errors under exam conditions.

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