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

The method used to add fractions depends on whether their denominators are the same (**like denominators**) or different (**unlike denominators**).

Let's start with some easy examples.

For instance,

**1/4 + 1/4**

Don’t mess with the denominators when they’re the same - just add the numerators

**1/4 + 1/4 = 2/4**

Notice how the denominator remains 4. You can also simplify by dividing numerator and denominator by 2

In summary

**1/4 + 1/4 = 2/4 = 1/2**

A quarter plus a quarter equals a half.

**How about 1/2 + 1/2 ?**

** **

Again, leave the denominators alone - simply add the numerators

**1/2
+ 1/2 = 2/2**

** **

2 divided by 2 equals 1 so you can also write

**1/2
+ 1/2 =
2/2 = 1**

** **

A half plus a half equals one.

**Let's step it up a little - consider 1/3 + 1/3 + 2/3**

Follow the same rules regarding the denominators (do nothing!) and the numerators (add!)

**1/3 + 1/3 + 2/3 = 4/3**

A third plus a third plus two thirds equals four thirds.

This is easy once you know how!

Take a look at

**1/3 + 1/6**

You need to find a way of expressing these fractions so that they have like denominators.

Ask yourself what’s the
lowest number into which both 3 and 6 will divide exactly? The answer of course
is 6 – this is the **least** **common denominator**.

The fraction 1/6 can be left alone – its denominator is already 6.

But how can 1/3 be expressed as a fraction with denominator 6? To get from denominator 3 to denominator 6 you need to multiply by 2. But you’ll also need to times the numerator 1 by the same factor 2 to get a fraction of equivalent value.

So

**1/3 + 1/6 = 2/6 + 1/6**

Now just follow the rules for addition of fractions with like denominators (don't change the denominators, add the numerators)

**2/6 + 1/6 = 3/6**

To simplify divide numerator and denominator by 3

**3/6 = 1/2**

Bringing everything together

**1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2**

**Let’s work out 1/6 + 1/4 + 2/3**

** **

First express as fractions with like denominators. Ask yourself what’s the least common denominator, i.e. the lowest number into which 6, 4 and 3 divide exactly? The answer’s 12.

Consider 1/6 - to get from denominator 6 to denominator 12, you need to times by 2. You also need to multiply the numerator 1 by the same factor 2.

1/6 = 2/12.

What about 1/4? Multiply by 3 to get from denominator 4 to denominator 12. Times the numerator 1 by the same factor 3.

1/4 = 3/12.

Next consider 2/3 - to get from denominator 3 to denominator 12, times by 4. Multiply the numerator 2 by the same factor 4.

2/3 = 8/12.

Therefore

**1/6 + 1/4 + 2/3 = 2/12 + 3/12 + 8/12**

** **

Now you’re adding fractions with like denominators

**2/12 + 3/12 + 8/12 = 13/12**

** **

Putting it all together

**1/6 + 1/4 + 2/3 = 2/12 + 3/12 + 8/12 =
13/12**

... with
like denominators - leave the denominators alone, add the numerators, then
simplify if possible.

... with unlike denominators - first express as fractions with like denominators by finding the least common denominator, then follow the rules for adding fractions with like denominators.

For more on fractions click:

Mixed fractions (mixed numbers)