Doing and undoing

Whenever you encounter a mathematical action you might think about ‘doing’ or ‘undoing’ something. We often think of simple processes, for example, the undoing of adding is subtracting, and the undoing of subtracting is adding. However, if you think of multiplying two numbers or expressions, the doing, then the undoing is factorising. Often ‘undoing’ is harder, and may involve creativity because of the multiplicity of possibilities.