Algebra Tutorials - Fractions
A fraction corresponds to a number of the form
where  and  are integer numbers, and it can be thought as " divided by . For example, the numbers
 ,  , 
are fractions. The only restriction for the fraction is that  , because in that case the fraction is undefined.
Sum of Fractions
The easiest case is when the denominators coincide. In fact, in that case, we find that
This makes sense because can be interpreted as " times  ", and hence, " times " plus
" times " must be " times "
Example: The the sum
is computed as
This shows that a fraction can become simply a number, in the way that  is simply 2.
Sum of Fractions with different numerator
This case is more difficult than the other one, because we cannot sum the numerators. What we need to do is to
amplify the fractions (multiply both numerator and denominator by the same number) in such a way that they have the same denominator.
In fact, consider the fraction
We can amplify this fraction by 2:
The resulting fraction is completely equivalent to the original one. How do we use this to add fractions?
Example: The the sum
is computed by first amplifying the first fraction by 2, which leads to  , and then
This last fraction can be simplified by dividing both numerator and denominator by 3, so the final answer is 
In general: The the sum of fractions is computed
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