Question

Is 55/22 a rational

Answer 1

Answer:

The fraction $\displaystyle \frac{55}{22}$ is indeed a rational number.

Step-by-step explanation:

A number $x$ is rational if and only if there exist two integers $p$ and $q$ (where $q \ne 0$) such that $x = \displaystyle \frac{p}{q}$.

$\displaystyle \frac{55}{22}$, the number in question here is already written in the form of a fraction. The two integers $p = 55$ and $q = 22$ ($q \ne 0$) meet the requirement that $\displaystyle \frac{55}{22} = \frac{p}{q}$. Therefore, $\displaystyle \frac{55}{22}\!$ is indeed a rational number.

Side note: the $p$ and $q$ here ($q \ne 0$) don't have to be unique. For example:

because $\displaystyle \frac{55}{22} = \frac{5 \times 11 }{2 \times 11} = \fraac{5}{2}$, both of the following pairs could satisfy $\displaystyle \frac{55}{22} = \frac{p}{q}$:

• $p = 55$ and $q = 22$;
• $p = 5$ and $q = 2$.