Algebra: Algebraic Notation

Algebraic Notation

In this video, we explain how to interpret algebraic notation. Confusion of about algebraic notation is one of the most common difficulties in learning algebra. Much of that confusion is fueled by the tricks that are introduced to teach algebra. In particular, we explain why the commonly used order of operations does not fit with how algebra works.

Instead, we introduce our list of grouping priorities. That may seem like the same idea with a different name. However, the order of operations implies that a linear ordering exists, when in reality it does not. Looking that the left-hand expression below that we showed in our video, we see the grouping priorities indicated by the parentheses in the expression at the top-right.

Even though we perform the operation (12 - 4) first, it is not necessary to do so. We could perform 2 to the power 2 or (2 * 4) first and we would still end up with the correct answer as long as we observe the priorities when we evaluate the expression. It may seem that this makes the situation more complex than having a simple linear order of operations, and it is does.

However, the simplicity gained by using the order of operations is false and it leads to difficulties in understanding, particularly when we deal with variables and more complex expressions.