Multiplying & Dividing Fractions - Application

From the book: "A special on a cruise to the Bahamas is advertised to be $\displaystyle \frac{2}{3}$ of the regular price. If the regular price is $2757, what is the sale price?"

I know I veered way off course at some point here, but I couldn't find any common factors to divide out.

My answer:

$\displaystyle x = sale\ price$

$\displaystyle x = 2,757 \div \frac{2}{3}$

$\displaystyle = \frac{2,757}{1} \div \frac{2}{3} = \frac{2,757}{1} \cdot \frac{3}{2} = \frac{2,757 \cdot 3}{1 \cdot 2} = \frac{8,271}{2}$

Thanks for getting me unstuck!

Quote:

Originally Posted by **topsquark**

As a check, note that the sale price should be less than the regular price.

Yeah that's what tipped me off that I'd goofed up. I know the key word in the application is the word **of**, but at some point I started incorrectly thinking that meant "divide."