In order to add two fractions together they must have the same denominator. If that’s not the case, you need to find some equivalent fractions that satisfy this.
When the two fractions have common denominators, you just add the two numerators, the result of which becomes the numerator of the new fraction. The denominator of the new fraction is also the common denominator:
You can always find a common denominator of two fractions by multiplying their denominators together, and then find the equivalent fractions to both of them that satisfy having this common denominator. But often you can find a smaller common denominator than the product of the two denominators.
Example of addition of two fractions:
Since the two denominators are different, we must find a common denominator.
Now we find the equivalent fractions that satisfy having the common denominator 18:
(both numerator and denominator is multiplied by 3)
(both numerator and denominator is multiplied by 6)
The complete calculation looks like this:
The fraction can be simplified, because both numerator and denominator can be divided evenly by 9.
The attentive reader will know, that the calculation of could have been more simple form the very beginning, if we had used the common denominator 6 instead of 18: