Question

Find each quotient. Write in simplest form. keep answer as fraction - not decimal

Answer 1

So we are given the expression:

$\frac{mn^{2}}{4}$ ÷ $\frac{m^{2}n}{8}$

When we divide fractions, we must flip the second term and change the sign to multiplication:

$\frac{mn^{2}}{4} *\frac{8}{m^{2}n}$

And then we multiply across:

$\frac{mn^{2}}{4} *\frac{8}{m^{2}n}= \frac{8mn^{2}}{4m^{2}n}$

Then we can break apart all of the like variables for simplification:

$\frac{8mn^{2}}{4m^{2}n}=\frac{8}{4} * \frac{m}{m^{2}} *\frac{n^{2}}{n}$

When we simplify variables through division, we subtract the exponent of the numerator from the exponent of the denominator. So we then have:

$\frac{8}{4} =2$

$\frac{m}{m^{2}}=m^{-1} =\frac{1}{m}$

$\frac{n^{2}}{n}=n^{1}=\frac{n}{1}$

So then we multiply all of these simplified parts together:

$\frac{2}{1}*\frac{1}{m}*\frac{n}{1} =\frac{2n}{m}$

So now we know that the simplified form of the initial expression is: $\frac{2n}{m}$.