Unit Fraction - GCSE Maths Definition

Definition

A unit fraction is a fraction that has a numerator (top number) of 1. The denominator would be any other positive whole number (integer).

Explanation

Unit fractions have a numerator of 1. The denominator will be a natural number (positive integer (whole number)). Understanding unit fractions is the first step in understanding the wider world of fractions - what value they represent and how they are useful.

For example, comparing unit fractions is very easy - as every numerator is 1, we need only to consider the denominators. The larger the denominator, the smaller (the value of) the fraction. This is because the denominator of a fraction indicates how many ‘parts’ the ‘whole’ has been split into; in the diagram below, of the shape has been shaded.

Example

Question: By first simplifying any fractions that are not unit fractions, write them in size order, starting with the smallest.

Solution:

Step 1:
Simplify fractions that do not have a numerator of 1.
(It is implied by the question that any such fractions will be able to be simplified to a unit fraction.)

(simplify by dividing numerator and denominator by 6)
(divide numerator and denominator by 5)
(divide both by 7)

Step 2:
The list of fractions now becomes

Step 3:
The list is now easy to compare - look at the denominators, remembering that the larger the denominator, the smaller the fraction.
Remember to start with the smallest fraction, as per the question instructions!

Answer:
The final answer should be written using the form of the fractions given in the original question.

Common mistakes (and how to avoid them)

Mistake 1: Thinking that all fractions can be simplified to a unit fraction

When simplifying fractions, some students will go too far by thinking that the numerator can always be reduced to 1.  Whilst this is technically true if we allowed the denominator to be a non-whole number, the definition of a unit fraction does not allow this.

Expecting the numerator to be 1 can lead to errors when reducing the value of the denominator in the simplifying process.

How to avoid this: Take care when dividing numbers, avoid ‘guessing’ or ‘assuming’ because you are expecting a whole number. In simplifying, both the numerator and denominator need to be divisible by the same number. If there isn’t such a number (other than 1) then the fraction is fully simplified, whether the numerator is 1 or otherwise.

Frequently asked questions

Why are unit fractions useful?

Fractions with a numerator of 1 crop up in various are useful when reciprocals are required. Loosely speaking, “reciprocal” means “one over” (so the reciprocal of 7 is - which is a unit fraction). Reciprocals are particularly important when working with the gradients of perpendicular lines.

Related GCSE Mathematics glossaries

• Fraction

• Numerator

• Denominator

• Simplify

Related GCSE Mathematics Revision Notes

• Introduction to Fractions

• Equivalent & Simplified Fractions