Why do the denominators have to be equal when adding fractions, but not when multiplying them?

When adding fractions we need to make sure that we're adding numbers that are in the same proportion.Take for example 1/2 add 1/2, if we simply added the numerator and the denominator we would get 2/4 - which simplifies to a half!Multiplying fractions is a little more tricky. Think of 3/4 as taking a whole, dividing it into 4 pieces and then taking 3 of them. What would happen if I took one of those quarters and divided it in half? I would have 2/8th of the whole.Now consider what would happen if I had 1/4 of a pizza and wanted to take 3/5s of that (1/4 x 3/5). I would start by dividing my 1/4 slice into five equal pieces. How big in comparison to the whole pizza would each slice be? It would be 1/20 because there are 4 quarters that are each divided into 5 pieces (4 x 5). Since we are only going to take 3 of them (because of 3/5), therefore we end up with 3/20 of the whole pizza, which as you can see is akin to multiplying the numerator and denominator.