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

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Answer 1 · 2015-05-02T11:42:14

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

$-0.8 * 1/r = -0.8/r$

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