Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

when the numerator is less than the denominator the result is always between 0 and 1? for example if I have a number like x/y where x<y then the result will be between 0 and 1 always? Is there a proof for this?

share|cite|improve this question
If the numerator is negative it could be between -1 and 0, e.g. $\displaystyle-\frac{3}{4}$ –  manthanomen May 9 '13 at 6:27
Assuming both $x$ and $y$ are positive, and we have existence of inverses, then $x < y \implies x \cdot \frac{1}{y} < y \cdot \frac{1}{y} \implies \frac{x}{y} < 1$. –  Alex Wertheim May 9 '13 at 6:28
so basically depending on it's sign it would be either -1->0 or 0->1? –  themhz May 9 '13 at 6:28

2 Answers 2

up vote 5 down vote accepted

Assuming that $x$ and $y$ are positive, you have $0<x<y$, so $\frac1y>0$, and $$0\cdot\frac1y<x\cdot\frac1y<y\cdot\frac1y\;,$$ which on simplification becomes


share|cite|improve this answer
so that is also the proof. Looks great thank you. –  themhz May 9 '13 at 6:35
@themhz: You’re welcome. –  Brian M. Scott May 9 '13 at 9:03

If $0 < x < y$, then by dividing all three numbers by the positive quantity $y$, you have $$ 0 < \frac{x}{y} < 1. $$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.