Simplifying complex fractions without variables

Students will learn how to simplify complex fractions without variables. Start by relating division of fractions to simplifying complex fractions. Here's an appropriate problem for demonstrating this:

$$\dfrac{\dfrac{-16}{9}}{\dfrac{3}{7}}$$

And here's a demonstration of its solution. Once students are comfortable with that idea, move on to harder problems, where a sum or difference appears in the numerator or denominator. Here's an example:

$$\dfrac{\dfrac{1}{2} + \dfrac{2}{3}}{\dfrac{3}{4} + \dfrac{5}{6}}$$

These types of problems can be solved in two ways. The first way is to simplify the numerator using just the LCD of fractions in the numerator, then simplifying the denominator using just the LCD of fractions in the denominator. An excellent demonstration can be found here. The second method uses the LCD of all fractions occuring in both the numerator and denominator. A wonderful explanation of this method is here.