Question

How to add fractions?

Answer 1

To add fractions by hand:
1) Make sure that they have the same denominator. If not, first start by finding a common denominator.
Ex. Let's find the sum of $\frac{1}{2} + \frac{1}{4}$, which have different denominators. To give them the same denominator, you need to multiply both or one of the fractions by a number over itself (aka 1) to get the same denominator. Since the least common multiple of 2 and 4 is 4, you need to multiply 1/2 by 2/2 (aka 1):
$\frac{1}{2} + \frac{1}{4} \\ = (\frac{1}{2} \times \frac{2}{2} ) + \frac{1}{4} \\ = \frac{2}{4} + \frac{1}{4}$

2) Once you have the same denominator, add the numerators and put the sum over the denominator: 
$\frac{2}{4} + \frac{1}{4} = \frac{2+1}{4} = \frac{3}{4}$

Answer 2

Adding Fractions with Unlike Denominators

If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators.

To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.