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.

Watch these Khan Academy videos:

Do these Khan Academy exercises:

Next, give your students these challenges:

- Code Breaker by NRICH
- Making Boxes by NRICH
- A Day with Grandpa by NRICH

Conclude by leading this investigation:

Ballast – multiplication puzzles

by MathPickle

7.NS.A.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.