# What is the quotient of 369 and 12 ?

Mar 8, 2017

It depends...

#### Explanation:

The word quotient comes to us from the Latin quotiens, meaning "how many times?". So what we are being asked is "How many times does $12$ go into $369$?".

If you are dealing with arithmetic of whole numbers then:

$\frac{369}{12} = 30 \text{ }$ with remainder $9$

As an improper fraction, we find $12$ and $369$ are both divisible by $3$, so:

$\frac{369}{12} = \frac{123 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}{4 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \frac{123}{4}$

As a mixed fraction, we have:

$\frac{369}{12} = 30 + \frac{9}{12} = 30 + \frac{3}{4} = 30 \frac{3}{4}$

Using long division, we can find a decimal expansion:

$\frac{369}{12} = 30.75$

Note that $\frac{123}{4}$, $30 \frac{3}{4}$ and $30.75$ are all the same number - just different representations.