GCSE Maths Practice: simplifying-ratios

Question 6 of 10

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

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\( \begin{array}{l}\text{Simplify the ratio } 0.75:1.25 \\ \text{to its simplest form.}\end{array} \)

Choose one option:

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

Simplifying Ratios with Decimals (GCSE Maths – Higher Tier)

At GCSE Higher level, ratio questions often involve decimals rather than whole numbers. These questions test whether you can apply the same simplifying principles in a less straightforward context. Although decimal ratios may look more difficult, they follow the same logical steps as any other ratio problem once the decimals are removed.

Why Decimal Ratios Are Used in Higher Questions

Decimal ratios reflect real-life data such as prices, weights, measurements, and timings. Higher-tier questions use decimals to check that students understand ratios conceptually, rather than relying on simple factor spotting. Being confident with decimal ratios is essential for success in proportion, scaling, and best-value problems.

Key Principle: Remove Decimals First

Decimals make it difficult to identify a highest common factor directly. For this reason, the first step is always to multiply both parts of the ratio by the same power of 10 so that all decimals are removed. This keeps the ratio equivalent while converting it into whole numbers that can be simplified easily.

General Method for Simplifying Decimal Ratios

  1. Identify the number of decimal places in each value.
  2. Multiply both parts of the ratio by a suitable power of 10.
  3. Write the resulting whole-number ratio.
  4. Find the highest common factor (HCF).
  5. Divide both parts by the HCF.
  6. Check that the final ratio is fully simplified.

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

Worked Example 1

Simplify the ratio 0.4 : 1.0.

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 1.2 : 2.0.

Multiplying by 10 removes the decimal point. Once converted to whole numbers, the ratio can be reduced to its simplest form.

Worked Example 3

Simplify the ratio 0.6 : 1.5.

Multiply both values by 10. The resulting ratio can then be simplified by dividing both numbers by their highest common factor.

Common Mistakes to Avoid

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

Why This Skill Matters

Decimal ratios appear frequently in Higher GCSE questions involving proportion, rates of change, and comparisons. Being able to simplify them confidently allows you to focus on the later steps of multi-mark questions without losing easy marks.

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 convert decimals to fractions instead?
Yes, but multiplying by powers of 10 is usually faster in exams.

Does the order of the ratio matter?
Yes. Reversing 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 clear, consistent method helps prevent mistakes under exam pressure.

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