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
`(1)/(2) + (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):

`(1)/(2) + (1)/(4) \\ = ((1)/(2) * (2)/(2) ) + (1)/(4) \\ = (2)/(4) + (1)/(4)`

2) Once you have the same denominator, add the numerators and put the sum over the denominator:

`(2)/(4) + (1)/(4) = (2+1)/(4) = (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.