Question

What is the quotient of `369` and `12` ?

Answer 1

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:

`369/12 = 30" "` with remainder `9`

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

`369/12 = (123*color(red)(cancel(color(black)(3))))/(4*color(red)(cancel(color(black)(3)))) = 123/4`

As a mixed fraction, we have:

`369/12 = 30+9/12 = 30+3/4 = 30 3/4`

Using long division, we can find a decimal expansion:

`369/12 = 30.75`

Note that `123/4`, `30 3/4` and `30.75` are all the same number - just different representations.