Comparing Fractions
Sometimes we need to compare two fractions to discover which is larger or smaller. There are two easy ways to compare fractions: using decimals, or using the same denominator.
The Decimal Method of Comparing Fractions
Just convert each fraction to decimals, and then compare the decimals.
Example: which is bigger: \frac{3}{8} or \frac{5}{12 }?
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:
\frac{3}{8} = 0.375, and \frac{5}{12 } = 0.4166...
So \frac{5}{12 } is bigger.
The Same Denominator Method
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:
Example:
\frac{4}{9} is less than \frac{5}{9} (because 4 is less than 5)
But when the denominators are not the same we need to make them the same (using Equivalent Fractions).
Example: Which is larger: \frac{3}{8} or \frac{5}{12 }?
Look at this:
 When we multiply 8 × 3 we get 24,
 and when we multiply 12 × 2 we also get 24,
so let's try that (important: what we do to the bottom we must also do to the top):

and 

We can see that \frac{9}{24} is smaller than \frac{10}{24} (because 9 is smaller than 10).
Making the Denominators the Same
There are two main methods to make the denominator the same:
They both work, use whichever you prefer!
Example: Which is larger: \frac{5}{6} or \frac{13}{15} ?
Using the Common Denominator method we multiply each fraction by the denominator of the other:

and 

We can see that \frac{78}{90} is the larger fraction