Question

how do you add fractions with different denominators

Answer 1

in general, you cannot
you must find a common denominator, then just add the numerators

Answer 2

in general: if b and d have no common factors
a/b + c/d = (ad + bc)/(bd)

otherwise, you should have a method for finding the lowest common denominator.
e.g.
3/5 + 7/25 + 1/3 + 5/27
5 = 5
25 = 5*5
3 = 3
27 = 3*3*3
so LCD = 5*5*3*3*3 = 25*27 = 675

3/5 + 7/25 + 1/3 + 5/27
= 3*135/675 + 7*27/675 +225/675 + 5*25/675
= (404 + 189 + 225 + 125)/675
= 944/675

Answer 3

A / B + C / D

_____

A / B

Multiply numerator and denominator by D

A / B becomes

A ∙ D / B ∙ D
_____

C / D

Multiply numerator and denominator by B

C / D becomes

C ∙ B / B ∙ D

Now:

A / B + C / D = A ∙ D / B ∙ D + C ∙ B / B ∙ D

A / B + C / D = ( A D + C B ) / B D

For example:

1 / 7 + 2 / 3 = ( 1 ∙ 3 + 2 ∙ 7 ) / 7 ∙ 3 = ( 3 + 14 ) / 21 = 17 / 21

Answer 4

all that fancy math provided above is just the steps you need to follow to find a general common denominator.

Answer 5

I agree with oobleck, but i think it is greatest common factor