What would you do if you didn't know what the values of the denominators were, such as when there are variables in the denominators? For example, what denominator would you use if you were adding 1/a and 1/b? How would your new denominator affect the numerators?

To add two fractions you have to find a common denominator, this can be done by multiplying them together (a*b=ab), if you do this you also have to times each numerator by the opposing denominator (so 1*b=b and 1*a=a)

So:

1/a+1/b = ((1*b) + (1*b)) / (a*b) = (a+b) / ab

The answer is going to be 1 because anytime u have a varible by itself you always have to put a one before it. so your fraction would be 1/1+1/1=2/1