# How do you simplify ((3v)/(pir^2))/3?

May 13, 2017

$\frac{v}{\pi {r}^{2}}$

#### Explanation:

The process is exactly the same as dividing with arithmetic fractions.

((3v)/(pir^2))/(color(blue)(3) actually means $\frac{\frac{3 v}{\pi {r}^{2}}}{\textcolor{b l u e}{\frac{3}{1}}}$

This can be written as a division as:

$\frac{3 v}{\pi {r}^{2}} \textcolor{b l u e}{\div \frac{3}{1}}$

To divide by a fraction is the same as multiplying by the reciprocal:

$= \frac{3 v}{\pi {r}^{2}} \textcolor{b l u e}{\times \frac{1}{3}} \text{ } \leftarrow$ now cancel if possible

$= \frac{\cancel{3} v}{\pi {r}^{2}} \times \frac{1}{\cancel{3}} \text{ }$ and multiply straight across

$= \frac{v}{\pi {r}^{2}}$