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MathidiaMathematics Academy
Ratio
Lesson 46 of 75
Introduction

Ratio language

Objective. Interpret part-to-part and part-to-whole ratios.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

A ratio compares two or more quantities, showing how much of one there is relative to another, written with a colon such as 3:2. A part-to-part ratio compares two groups directly to each other, such as the ratio of boys to girls being 3:2, while a part-to-whole ratio compares one group to the total, expressed as a fraction such as 3/5 of the group being boys. Understanding which type of comparison is being made is essential before solving a ratio problem. For example, in a ratio of 3:2, the total number of parts is 5, so the first quantity makes up 3/5 of the whole.

Worked example

A fruit bowl has apples and pears in the ratio 4:3. What fraction of the fruit, using ratio language, are apples?

4 … 3
Illustrated card showing 4 … 3
  1. 1Add the parts of the ratio together: 4+3=7.
  2. 2Identify the number of parts that are apples: 4.
  3. 3Write apples as a part-to-whole fraction: 4/7.
  4. 4Check: pears would be 3/7, and 4/7+3/7=1, the whole.

Answer: 4/7

Concept mastery

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Practice

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Common mistake. Pupils sometimes treat a part-to-part ratio as if it were a part-to-whole fraction, saying a ratio of 3:2 means 3/2 of the total. Always add the parts together first to find the whole.

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