Comparing Fractions

Sometimes we need to compare two fractions to discover which is larger or smaller.

There are two main ways to compare fractions: using decimals, or using the same denominator.

The Decimal Method of Comparing Fractions

Convert each fraction to decimals, and then compare the decimals.

Convert each fraction to a decimal.

We can use a calculator (3÷8 and 5÷12), or the method on Converting Fractions to Decimals.

Anyway, these are the answers I get:

3 8 = 0.375, and 5 12 = 0.4166...

So 5 12 is bigger.

$fraction$

The denominator is the bottom number in a fraction.

It shows how many equal parts the item is divided into

When two fractions have the same denominator they are easy to compare:

$frac 4/9$	is less than	$frac 5/9$
4 9		5 9

But when the denominators are not the same we need to make them the same (using Equivalent Fractions).

Look at this:

so let's try that (important: what we do to the bottom we must also do to the top):

and

We can now see that 9 24 is smaller than 10 24 (because 9 is smaller than 10).

so 5 12 is the larger fraction.

$frac 3/8$	is less than	$frac 5/12$
3 8		5 12

There are two main methods to make the denominator the same:

They both work, use which one you prefer!

Using the Common Denominator method we multiply each fraction by the denominator of the other:

and

We can see that 75 90 is the larger fraction (because 75 is more than 66)

so 5 6 is the larger fraction.

$frac 5/6$	is more than	$frac 11/15$
5 6		11 15

922, 1390, 1677, 923, 1392, 1678, 3552, 3553, 3554, 3555