Question

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

Answer 1

So we are given the expression:

`(mn^(2))/(4)` ÷
`(m^(2)n)/(8)`

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

`(mn^(2))/(4) *(8)/(m^(2)n)`

And then we multiply across:

`(mn^(2))/(4) *(8)/(m^(2)n)= (8mn^(2))/(4m^(2)n)`

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

`(8mn^(2))/(4m^(2)n)=(8)/(4) * (m)/(m^(2)) *(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:

`(8)/(4) =2`

`(m)/(m^(2))=m^(-1) =(1)/(m)`

`(n^(2))/(n)=n^(1)=(n)/(1)`

So then we multiply all of these simplified parts together:

`(2)/(1)*(1)/(m)*(n)/(1) =(2n)/(m)`

So now we know that the simplified form of the initial expression is:
`(2n)/(m)`.