T/F: any number that can be written as a fraction is rational.

Question

Any number that can be written as a fraction is rational.

I am being asked this question, and I believe it is true but for some reason,I feel that there is a trick. However, the definition of rational numbers is similar to this hence why i believe this is true.

Any objections?

Answer 1

A rational number is a number $k$ such that

$k=\frac{a}{b}$

where both $a$ and $b$ are integers.

In other words $a,b \in\mathcal Z$

Hope this helps!

Answer 2

Well, if you take just 'a fraction' then, $x=\frac{x}1$ is a way to represent every number as a fraction. What this is getting at the fact that it matters that a rational number if 'a fraction of two integers' - and the above form only works in that definition when $x$ is an integer. This means that the condition that numerator and denominator are integers actually is a substantial restriction on the possible forms.