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#