Add and subtract fractions: Same denominator

In a nutshell

Fractions which have the same denominator are called 'like' fractions.  You can add or subtract like fractions using the following simple steps.

Adding fractions with the same denominator

procedure

1. ​Make sure the bottom numbers (denominators) are the same.
   
2. Add the top numbers (numerators) together. Leave the denominator as it is.
   
3. If necessary, simplify the fraction.
   

Example 1

Jeremy and Sonia are at a party and they both eat one quarter of a pizza.  How much pizza did they eat altogether?

They both had an equal sized portion of pizza:

$$\frac{1}{4} + \frac{1}{4}$$​

Add together the numerators:

$$\frac{1}{4} + \frac{1}{4} = \frac{1+1}{4} = \frac{2}{4}$$​​

Simplify the fraction:

$$\frac{2}{4} = \frac{1}{2}$$​​

​

Subtracting fractions with the same denominator

PROCEDURE

1. ​Make sure the bottom numbers (denominators) are the same.
   
2. Subtract the top numbers (numerators). Leave the denominator as it is.
   
3. If necessary, simplify the fraction.
   

Example 2

A pie is split into eight equal slices. Three guests each take one slice of the pie. What fraction of the pie remains?

Eight slices of pie were present at the start of the problem.  Three slices the size of an eighth were removed:

$$\frac{8}{8} - \frac{3}{8}$$​​

Subtract the numerators:

$$\frac{8}{8}-\frac{3}{8} = \frac{8-3}{8}= \frac{5}{8}$$​​

Note: In this example, the fraction cannot be simplified.  Not every fraction can be simplified.