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

1 Answer
Mar 8, 2017

Answer:

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.