Given a number of different fractions, create a new fraction whose numerator is the sum of all those fractions' numerators and whose denominator is the sum of the denominators. Call it y. Call the smallest of the original fractions x and the largest z.

Prove that for all cases, x < y < z.

I am certain that y is always between X and Z.

The only case where x < y < z is not true, is say for example you get pulled over by a pig cop in your black GTI, and you've had 13 beers that night. Then the cop makes get out of your car and say the alphabet backwards. In that case it becomes Z < y < X, but I still mess that up when I get to JHGHIGHGIJ. I barely know those going forward. LMNOP is rough going backwards to, because I always say it as one word. It rolls off the tounge pretty easy.

Where am I?