Rational by rational always rational?

Here's a statement that I've come across in the app. It reads: "Dividing a rational number by a rational number will always produce a rational number." I immediately chose True, but apparently this was not the correct answer.

I thought that you cannot get an irrational number by dividing two rational numbers. I'm obviously missing something. Can you give me a couple of concrete examples when this is not the case?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

Divide $7$ by $0$ , both are separately rational but the result which comes on division is not even a real number( and hence not rational). Indeed you could choose both zero and we very well know $\frac{0}0$ is an undetermined form.

Rishabh Jain - 4 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$