Question

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

Answer 1

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

`(-16 * r^2)/(20 * r^3) = (-16)/20 * 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

`stackrel(color(blue)(-4))(cancel(-16))/stackrel(color(blue)(5))(cancel(20)) * r^2/r^3 = -4/5 * r^2/r^3`

Since `r^3` can be written as

`r^2 * 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 * 1/r = -0.8/r`