Numerator and denominator definition

Question

I am studying fractions and how to calculate them and the terms numerator and denominator appear a lot when I read about it, but I do not know the numerator and denominator definition.

i.e.

$$ \frac{4}{2} + \frac{8}{2} = \frac{4+8}{2} = \frac{12}{2} $$

Would I like to know your definition?

Answer 1

In the fraction $$\frac{p}{q}$$ where $q\ne 0$

$p$ is called Numerator and $q$ is called denominator

Answer 2

I'd like to point out more elaborate definition on the matter.

A numerator is an integer above the vinculum, also known as the dividend if the fraction is interpreted as division.

A denominator is a natural number below the vinculum, also known as the divisor if fraction is interpreted as division.

If $\gcd(p,q)=1$, with the definitions above, then the fraction is irreducible and is in its canonical form.