# Help with simple proving

• Mar 2nd 2010, 05:52 PM
Mathwizard4
Is this rational and why?
if a, b, c, d, e, and f are all integers prove that r is rational

$r = [(a/b) - (e/f)] / c/d$
• Mar 2nd 2010, 05:58 PM
Drexel28
Quote:

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

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

....isn't the quotient of integers always rational? Simplify that monstrosity.
• Mar 2nd 2010, 06:08 PM
Mathwizard4
Quote:

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.
• Mar 3rd 2010, 03:42 AM
emakarov
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).