Skip to 0 minutes and 7 secondsPAULA KELLY: there's lots of different ways to compare the relative size of fractions. For this case, we'll assume that we're comparing fractions where the whole is just 1. So we can see, from my diagram, we have back to our rectangle diagrams. We have our 1/5 and our 1/7. So one diagram has been split into five equal parts, one into seven equal parts. We can see quite clearly here, when the numerators are the same, that 1/5 is larger than 1/7. So generally, as a rule, if your denominator is smaller, your fraction is larger because it's been split into fewer parts, so you can compare the numerators if they are the same.

Skip to 0 minutes and 46 secondsSay, for example, we know that 1/5 is bigger than 1/7. 2/5 is bigger than 2/7, and so on. So we can say when you have the same numerator, it's really easy to compare the size of fractions. We can see that 3/7 is larger than 3/10. Similarly, if we have the same denominator, it's easy to compare fractions. Whether 2/5 is larger than 1/5, same denominator. Or if we had 7/10, that would be larger than 3/10. However, if we haven't got equal numerators or denominators, we need another method to find some equivalent fractions.

Understanding fractions: terminology

The English National Curriculum states: “The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum - cognitively, socially and linguistically. The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof.”

The number on the top of a fraction is the numerator. The number on the bottom of the fraction is the denominator. The ‘fraction bar’, the line separating the numerator from the denominator, is called the vinculum.

In this video we use this terminology to explain how fractions can be compared when the numerators are the same and when the denominators are the same. By considering the numerators and denominators, we can use a fundamental understanding of what a fraction is in order to decide which fraction has the larger value.

When comparing fractions, students are sometimes taught just one method. Learning this method can produce the correct answer without students necessarily requiring a deep understanding of fractions, or why the process works.

Teaching resources

Comparing fractions is a good opportunity to challenge students’ understanding of what a fraction is. You can use the following resources as part of questioning activities to identify your students’ understanding.

  • What is a fraction? is a useful document to help develop teachers thinking when planning this topic.
  • A selection of games published by BEAM for students to practise using their understanding of the mathematical topics of fractions, decimals and percentages whilst developing a strategic approach.

Just a reminder that you will need a free account on the STEM Learning website in order to access these additional resources. Completion of the course is not dependent upon access. If you are not based in the UK, please ensure you register as an international user.

Discovery task

The vinculum has a number of uses in mathematics. What can you find out about the vinculum? Research other uses of the vinculum and post your findings in the comments below.

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This video is from the free online course:

Maths Subject Knowledge: Fractions, Decimals, and Percentages

National STEM Learning Centre