How to add fractions?

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.

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ali015 ali015 · Answer 2 · 2018-04-12T01:21:24+02:00

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 [tex] \frac{1}{2} + \frac{1}{4} [/tex], 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):
[tex]\frac{1}{2} + \frac{1}{4} \\ = (\frac{1}{2} \times \frac{2}{2} ) + \frac{1}{4} \\ = \frac{2}{4} + \frac{1}{4} [/tex]

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