# Thread: Help with simple proving

1. ## Is this rational and why?

if a, b, c, d, e, and f are all integers prove that r is rational

$\displaystyle r = [(a/b) - (e/f)] / c/d$

2. Originally Posted by Mathwizard4
if a, b, c, d, e, and f are all integers prove that r is rational

$\displaystyle r = [[((e)(f))/d] - [((f)(a))/d ]]/(f)(c)/d$
....isn't the quotient of integers always rational? Simplify that monstrosity.

3. Originally Posted by Drexel28
....isn't the quotient of integers always rational? Simplify that monstrosity.
sorry not good with using this site yet. basically the numerator is a ratio of integers minus a ratio of integers and the denominator is a ratio of integers. I'm having trouble proving that the result is a rational number.

I made my original equation more clear.

4. First, you need to make sure that you never divide by 0.

Second, all integers are rational, and rational numbers are closed under addition, subtraction, multiplication and division by a non-zero (i.e., the result of the operation is again rational).