# How do you simplify (16x^2y)/(24xy^3) div (9xy)/(8x^2y^2)?

Jul 13, 2015

#### Answer:

Dividing by a fraction is multiplying by its opposite. Then rewrite and cancel.

#### Explanation:

$= \frac{16 {x}^{2} y}{24 x {y}^{3}} \cdot \frac{8 {x}^{2} {y}^{2}}{9 x y}$

$= \frac{2 \cdot 8 \cdot x \cdot x \cdot y}{3 \cdot 8 \cdot x \cdot y \cdot y \cdot y} \cdot \frac{8 \cdot x \cdot x \cdot y \cdot y}{3 \cdot 3 \cdot x \cdot y}$

Now we cancel:

$= \frac{2 \cdot \cancel{8} \cdot \cancel{x} \cdot x \cdot \cancel{y}}{3 \cdot \cancel{8} \cdot \cancel{x} \cdot \cancel{y} \cdot y \cdot y} \cdot \frac{8 \cdot \cancel{x} \cdot x \cdot \cancel{y} \cdot y}{3 \cdot 3 \cdot \cancel{x} \cdot \cancel{y}}$

And after working this out we can cancel one more $y$:

$= \frac{2 \cdot 8 \cdot x \cdot x \cdot \cancel{y}}{3 \cdot 3 \cdot 3 \cdot y \cdot \cancel{y}} = \frac{16 {x}^{2}}{27 y}$