Is $\frac{1}{\sqrt{2}}$ a fraction or not? Is $\frac{1}{\sqrt{2}}$ a fraction or not? 

I just came across a Grade 8 student's class work where the teacher has given the above as an example to differentiate fractions from rational numbers. I think this is wrong fundamentally, as $\sqrt2$ is irrational while all fractions would be rational. Please advise. Thanks!
The word &quot;fraction&quot; is used outside of the scope of rational numbers as well. In that case, it's better not to use the term &quot;fraction&quot; to denote a kind of number, but rather to refer to the way of writing or representing it: i.e. as a structure with a numerator and a denominator.
Loosely speaking you could say &quot;$\pi$ is not a fraction&quot; because it cannot be written as a quotient of integers, but it's safer to say &quot;$\pi$ is not a rational number&quot; where you rely on a precise definition of rational number.

Generally, you want to be able to call anything of the form
$$\frac{a}{b}$$
a fraction because then you can refer to its two characterizing components: the numerator $a$ and the denominator $b$ with $a$ and $b$ not necessarily integers but any numbers or even more general expressions. Note that you can write any number $x$, not necessarily integer, as a fraction:
$$x = \frac{x}{1}$$but we generally don't refer to &quot;$x$&quot; as &quot;a fraction&quot;. We do want to be able to call something like
$$\frac{1+\sqrt{3}}{1-\sqrt{3}}$$a fraction, although it's not a rational number, because then we can say things such as &quot;multiply numerator and denominator with $1+\sqrt{3}$&quot;. The same goes for more complicated expressions (with fractions in fractions!), or even with one or more variables, such as:
$$\frac{e^2 - \frac{\sqrt{5}}{1+\sin\frac{\pi}{7}}}{1-\frac{\sqrt{3}}{2}} \quad ; \quad \frac{e^x-\sin y}{x^2+y}$$

Summarizing:

Is $\frac{1}{\sqrt{2}}$ a fraction or not?

I think we prefer to be able to call this a fraction, with numerator $1$ and denominator $\sqrt{2}$, but then obviously we shouldn't mix &quot;fraction&quot; with &quot;rational number&quot; or use them interchangeably.
"Fraction" just means "not a whole number."  For instance, irrational numbers can be written as "decimal fractions", like $\pi = 3.14159\ldots.$  If you had said "rational numbers" instead of "fractions", you'd be right.