*Before learning about comparing fractions, please read the primer on fractions.*

When you compare fractions, it’s helpful to consider whether the fractions being compared have like (the same) numerators, like (the same) denominators or unlike (different) denominators.

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*If two fractions have the same numerator, the fraction with the higher denominator
will be of lesser value.*

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For example, 1/2 and 1/3 have the same numerator (1). But 1/3 has a higher denominator than 1/2 (3 compared to 2).

Therefore

**1/3 < 1/2**

- a third is less than a half.

**Next compare 4/5 and 4/9**

4/5 and 4/9 both have numerator 4. However, 4/9's denominator (9) is higher than 4/5's denominator (5).

So

**4/9 < 4/5**

- four ninths is less than four fifths.

*If two fractions have the same denominator, the fraction with the lower numerator will be of lesser value.*

For instance, 4/5 and 2/5 have the same denominator (5), but as 2/5 has a lower numerator than 4/5 (2 compared to 4)

**2/5 < 4/5**

- two fifths is less than four fifths.

**Consider 13/11 and 8/11**

Notice both fractions have denominator 11. Because 8/11's numerator (8) is lower than 13/11's numerator (13)

**8/11 < 13/11**

- eight elevenths is less than thirteen elevenths.

*To compare fractions with unlike denominators, first express as fractions with like denominators by finding the least common denominator, then follow the rules for comparing fractions with like denominators.*

Let's take a look at 3/14 and 2/7.

First work out the **least common denominator** - the lowest number into which the denominators of both fractions will divide exactly. 14 and 7 both divide into 14.

You can leave 3/14 alone as it already contains the denominator 14, but you'll need to express 2/7 as an equivalent fraction with denominator 14. To get from denominator 7 to denominator 14, times by 2 - also multiply the numerator 2 by the same factor

2/7 = 4/14.

You can now compare 3/14 and 4/14 - fractions with the same denominator (14). As 3/14's numerator (3) is lower than 4/14's numerator (4)

**3/14 < 4/14**

or since 2/7 = 14/4

**3/14 < 2/7**

- three fourteenths is less than two sevenths.

**Another example**

Take a look at how the answer to 'Compare 2/3 and 6/7' might be set out in an exam. Notice here how both fractions need to be converted to equivalent fractions.

Ready to move on?

Hopefully you now have a basic grasp of how to compare fractions. It's time to move onto ordering fractions!

For more on fractions click:

Mixed fractions (mixed numbers)