Proof from adding and subtracting fractions 
In adding or subtracting fractions with two or more terms, the resulting denominator is always the product of the denominators of the terms.

Can someone prove or disprove this statement. I'm pretty sure this isn't true, but I don't know how to disprove it. Does a statement like 1/2+1/3+2/3 count?

It is true if you consider fractions other than the lowest term (or simplest form).
Consider $\frac ab+\frac cd=\frac{ad+bc}{bd}$. Similarly for subtraction.
Clearly, if you reduce to the lowest term, it isn't true. Simply consider something like $\frac 14+\frac 14=\frac 12$; 2 isn't a product of 4 and 4.
