# What rational numbers are equal to 9?

Aug 30, 2016

$\frac{9 q}{q}$ ($q \ne 0$ for $q \in \mathbb{Z}$)

#### Explanation:

A rational number is one of the form: $\frac{p}{q}$ ($q \ne 0$ for $\left\{p , q\right\} \in \mathbb{Z}$)

In the sense that $9 = \frac{9}{1}$, 9 is already a rational number.

However, in general, we can set $9 = \frac{p}{q} \to p = 9 q$

Hence any $\frac{9 q}{q}$ ($q \ne 0$ for $q \in \mathbb{Z}$) form rational numbers that equal 9.