Comparing unit fractions

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Tutor: Toby


Comparing unit fractions

In a nutshell

A unit fraction is any fraction which has a numerator of 11 and a denominator that is a whole number. When comparing unit fractions, the larger the denominator, the smaller the fraction.

Example 1

If you were offered 18\frac{1}{8} or 16\frac{1}{6} of a pizza, which slice would be larger?

Maths; Fractions; KS2 Year 3; Comparing unit fractions
Maths; Fractions; KS2 Year 3; Comparing unit fractions
   18<16\longrightarrow \frac{1}{8} < \frac{1}{6}

These two unit fractions have different denominators. Therefore  18\frac{1}{8}  is the smaller fraction, as it has the larger denominator of the two fractions.

Fraction bar models

Fractions can also be compared using bar models.  Bar models are helpful because they allow you to compare the size of different unit fractions.


  1. Draw two 'bars' of equal length, one above the other.
  2. Look at the denominator of the first fraction. Split the first bar into the number of parts given by the denominator. They should all be equal sized.
  3. Shade in one of the parts.
  4. Repeat steps 2 and 3 with the second fraction.
  5. Compare the marked lengths.

Example 2

Which fraction is larger, 13\frac{1}{3} or 15\frac{1}{5} ?

Fraction bar models:

Maths; Fractions; KS2 Year 3; Comparing unit fractions

From the bar models, you can see that 13\frac{1}{3}} is larger than 15\frac{1}{5}


If you want to use greater than or less than signs, you could write 13>15\frac{1}{3} > \frac{1}{5}.

Example 3

Which fraction is bigger, 110\frac{1}{10} or 18\frac{1}{8}?

From the bar models, you can see that 18\frac{1}{8} is bigger than 110\frac{1}{10}, so you can write that like this: 18>110\frac{1}{8}>\frac{1}{10}.

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FAQs - Frequently Asked Questions

How do I compare unit fractions?

What is a unit fraction?

How do I compare fractions with different denominators?