# How do you simplify (-16r^2)/(20r^3)?

May 2, 2015

Use the fact that the nominator and the denominator are a product of a number and a variable to break up the fraction into two distinct ones

$\frac{- 16 \cdot {r}^{2}}{20 \cdot {r}^{3}} = \frac{- 16}{20} \cdot {r}^{2} / {r}^{3}$

You can simplify this by dividing the nominator and the denominator of the first fraction by 4, the greatest common divisor of -16 and 20, to get

$\frac{\stackrel{\textcolor{b l u e}{- 4}}{\cancel{- 16}}}{\stackrel{\textcolor{b l u e}{5}}{\cancel{20}}} \cdot {r}^{2} / {r}^{3} = - \frac{4}{5} \cdot {r}^{2} / {r}^{3}$

Since ${r}^{3}$ can be written as

${r}^{2} \cdot {r}^{1} = {r}^{2 + 1} = {r}^{3}$, you get

-4/5 * cancel(r^2)/(cancel(r^2) * r) = color(green)("-4/5 * 1/r)

If you want, you can divide -4 and 5 to get

$- 0.8 \cdot \frac{1}{r} = - \frac{0.8}{r}$