Question

Simplify the following term: \[\left( {8{m^2} - 9m} \right) \div 3m\]
\[
  A. {\text{ }}\dfrac{1}{3}\left( {8m - 9} \right) \\
  B. {\text{ }}8m - 9 \\
  C. {\text{ }}\dfrac{1}{3}\left( {8m - 3} \right) \\
  D. {\text{ 5}}m - 3 \\
 \]

Answer 1

Hint: In order to solve such questions first look for some common terms that can be cancelled out then further proceed with simplification.

Complete step-by-step answer:
We have to simplify \[\left( {8{m^2} - 9m} \right) \div 3m\]
We can write the given term in fraction as
\[\dfrac{{\left( {8{m^2} - 9m} \right)}}{{3m}}\]
Now let us cancel out the common term in numerator and denominator.
$
   = \dfrac{{m\left( {8m - 9} \right)}}{{3m}} \\
   = \dfrac{{8m - 9}}{3} \\
 $
After separation of numerator and denominator the above term can also be written in following form:
$ \Rightarrow \dfrac{{8m - 9}}{3} = \dfrac{1}{3}\left( {8m - 9} \right)$
Hence, simplification of the above term gives the result $\dfrac{1}{3}\left( {8m - 9} \right)$.
So, option A is the correct option.

Note: In order to solve the problem related to simplification of terms the best way to proceed is to find out some common terms in numerator and denominator and cancel them out. Also the given question could have been solved by dividing each of the numerator terms by the denominator separately by breaking the fraction in two parts.