Comparing and ordering fractions

In a nutshell

To compare and order fractions you may need to change the fractions so they have a common denominator. Once you find the common denominator, you can compare the numerators of each fraction to see which is larger.

Procedure

1.	Find the common denominator. For fractions which are multiples of the same number, this will be the largest denominator.
2.	Multiply up the fraction with the smallest denominator so the fractions have a common denominator.
3.	Compare the numerators of the fractions found in Step Two. The fraction with the larger numerator is the greater fraction. Note: Make sure to give your answer as the fraction given in the question. Do not answer with your 'multiplied up' fraction from Step Two.

Example

Which is larger $\frac{7}{8}$ or $\frac{3}{4}$ ?

The common denominator here is the larger denominator:

$8$ 

Multiply up the fraction with the smallest denominator:

$\frac{3\times2}{4\times2}=\frac{6}{8}$ 

Compare the numerators of the fractions:

$6 < 7$ therefore $\frac{6}{8}<\frac{7}{8}$ 

Give the answer back into the fraction form given in the question:

$\frac{3}{4}<\frac{7}{8}$ so $\underline{\frac{7}{10}}$ is the larger fraction.