# How do you find the product of (10n^2)/4*2/n?

Dec 22, 2016

$5 n$

#### Explanation:

$\frac{10 {n}^{2}}{4} \times \frac{2}{n} = \frac{20 {n}^{2}}{4 n} = \frac{\cancel{\left(4 n\right)} 5 n}{\cancel{4 n}} = 5 n$

Dec 22, 2016

$5 n$

#### Explanation:

There are 2 approaches here. We could $\textcolor{b l u e}{\text{simplify}}$ the fractions and then multiply what remains or we can multiply the fractions and then $\textcolor{b l u e}{\text{simplify}}$

$\textcolor{red}{\text{Simplify and multiply}}$

To simplify we $\textcolor{b l u e}{\text{cancel}}$ common factors between the numerators/denominators.
Here we can cancel 10 and 4 by 2 or 4 and 2 by 2. ${n}^{2}$ and n have a common factor of n.

$\Rightarrow \frac{{\cancel{10}}^{5} \times n \times {\cancel{n}}^{1}}{\cancel{4}} ^ 2 \times \frac{2}{\cancel{n}} ^ 1$

$= \frac{5 n \times 2}{2} = \frac{5 n \times {\cancel{2}}^{1}}{\cancel{2}} ^ 1 = 5 n$

$\textcolor{red}{\text{multiply and simplify}}$

$\frac{10 {n}^{2}}{4} \times \frac{2}{n} = \frac{10 {n}^{2} \times 2}{4 n} = \frac{20 {n}^{2}}{4 n}$

now simplify by cancelling.

$= \frac{{\cancel{20}}^{5} \times n \times {\cancel{n}}^{1}}{{\cancel{4}}^{1} {\cancel{n}}^{1}} = 5 n$