# How do you simplify ( 4x^2) /( 5y^2) * ( 15xy) /( 24x^2 y^2) ?

Aug 2, 2015

$\frac{x}{2 {y}^{3}}$

#### Explanation:

You can simplify this expression by cancelling like terms that can be found in the numerator and denominator of the two fractions that are being multiplied.

Your starting expression looks like this

$\frac{4 {x}^{2}}{5 {y}^{2}} \cdot \frac{15 x y}{24 {x}^{2} {y}^{2}}$

You can emphasize the terms that can be cancelled by rewriting the expression as

$\frac{4 {x}^{2}}{5 \cdot {y}^{2}} \cdot \frac{5 \cdot 3 \cdot x \cdot y}{4 {x}^{2} \cdot 6 \cdot y \cdot y}$

The simplified expression will thus be

(color(red)(cancel(color(black)(4x^2))))/(color(orange)(cancel(color(black)(5))) * y^2) * (color(orange)(cancel(color(black)(5))) * 3 * x * color(purple)(cancel(color(black)(y))))/(color(red)(cancel(color(black)(4x^2))) * 6 * color(purple)(cancel(color(black)(y))) * y) = (3x)/(6y^3) = color(green)(x/(2y^3)