Simplify $\frac{8xy^2}{6x^2y}$ with $x=2$ and $y=3.$
I notice that both the numerator and denominator have a factor of 2, so I can divide both by 2 to get $\frac{4xy^2}{3x^2y}.$ I also notice that both the numerator and denominator have a factor of x, so I can divide both by x to get $\frac{4y^2}{3xy}.$ Finally, I see that both the numerator and denominator have a factor of y, so I can divide both by y to get $\frac{4y}{3x}.$ Now I have simplified the fraction as much as possible, and I can plug in the given values of x and y. I get $\frac{4(3)}{3(2)} = \frac{12}{6} = 2.$ 