The purpose of this application is to give a model of fraction multiplication and a connection between multiplication and “composition”. The setup is the same as the simple fraction wheel model except for the addition of a multiplication button which is initially disabled. After selecting an initial fraction pulley to connect to the paddle wheel, the multiplication button changes color indicating that it is enabled. After clicking it the student is offered the chance to select a second fraction pulley to connect to the first. The result is a double compound pulley. In the example pictured above, a pulley representing 1/4 is connected to a pulley representing 1/6. The initial pulley reduces each turn of the paddle wheel by 4 and the second reduces each of the quarter-turns by six for a net reduction of 24. Thus, the compounded system represents the fraction 1/4 × 1/6 = 1/24. As for the simple fraction model, this model ties in nicely with operation of mechanical devices like the pair of gearng systems in a typical 10-speed bicycle. It also ties in nicely with mathematical concept of “composition”. We can view a pulley as a kind of “input-output” machine. It takes “inputs” in the form of “turns” and produces “outputs” also in the form of “turns”. If we have two such machines, we can combine them to form a new machine by connecting the output of one to the input of the second as shown below. More generally if we have any two input-output machines where the output of the first is of the same kind as the input of the second then we can form a new input-output machine by connecting the output of the first to the input of the second. This operation is called “composition”. Multiplication is a special case of composition!