Question

For rational numbers a and b, a/b is always a rational number.
True?

Answer 1

Almost always. There is one possibility for b such that this statement would fail. What is it?

Answer 2

(If you add one condition on b, then it would be true.)

Answer 3

No not always
1/3 divided by 1/9=3

Answer 4

If b is a factor of a then it is an interger

Answer 5

Not exactly of course, but you get what I'm saying

Answer 6

like .5 / .25 =2

Answer 7

Integers ARE rational numbers.

Write the integer z as z/1. Ta-dah! It's a ratio of two integers.

Integers are a subset of the rationals.

Answer 8

As to why it is always true except for the 1 special case I hinted at above:

Suppose m and n are rational numbers. Then m=a/b and n=c/d for some integers, a b c and d.

Then: m/n=(a/b)/(c/d)=(a/b)*(d/c)=(ad)/(bc) which is the ratio of integers (because integer * integer = integer).

Answer 9

Well @KelliRovesSkittles, I hope you understand the question and the correct answer. I don't really care about the medal, but the fact that you medaled someone who gave you an incorrect answer and explanation, and ignored my attempt to teach you something about the concept, suggests that you don't really understand it.

what I was getting at, by the way, is that 0 is a rational number. So if a and b are rational but b=0, then a/b is not rational since it is undefined.

It has nothing to do with the quotient reducing to an integer, though.