Introduction to Ratios

Learn what a ratio means and how to simplify, expand, and divide quantities using ratios. Let’s get started! 🚀

Introduction to Ratios - introduction visual

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Introduction to Ratios poster

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Illustration for ratios with 2 apples and 3 bananas as an example. The ratio of apples to bananas is 2:3, and the ratio of bananas to apples is 3:2.Ratio calculation showing flour to sugar ratio of 5:2 with a worked example of 300 g of flour, determining that 120 g of sugar is needed.An example of sharing £200 in the ratio 7:3, total parts calculated as 10, each part worth £20. One person receives £140, the other receives £60.Simplifying the ratio 24:40 by dividing both terms to get 3:5 and expanding the ratio 3:7 by multiplying both terms to get 15:35.

🛎️ What Is a Ratio?

  • A ratio compares quantities and is written as a : b.
  • The order matters (apples : bananas = 2 : 3, but bananas : apples = 3 : 2).

🛎️ Working with Ratio 5:2

  • A ratio of 5 : 2 means for every 5 parts of flour, there are 2 parts of sugar.
  • To find one part, divide 300 g by 5 to get 60 g per part.
  • Multiply 60 g by 2 to get 120 g of sugar needed.

🛎️ Sharing a Whole in a Ratio

  • Add the numbers in the ratio to find the total parts. For example, 7:3 means 7 + 3 = 10 parts.
  • Each part = total amount ÷ total parts. For example, £200 total divided by 10 parts = £20 per part.
  • One person gets 7 parts, so £20 × 7 = £140. The other person gets 3 parts, so £20 × 3 = £60.

🛎️ Simplifying and Expanding Ratios

  • To simplify, divide every part by the same number. For example, 24:40 can be simplified by dividing both by 8 to get 3:5.
  • To expand, multiply every part by the same number. For example, 3:7 can be expanded by multiplying both by 5 to get 15:35.

Practice Questions

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Q1Easy

Simplify the ratio to its simplest form.

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Interactive Activity

Simplifying and expanding ratios by finding equivalent forms

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