Order of operations and handling brackets

Order of operations

The famous acronym BEDMAS helps us remember the order of operations. It goes as follows.

1. Brackets. Everything within brackets is evaluated first;
2. Exponents are evaluated second;
3. Division and Multiplication are evaluated next from left to right; then
4. Addition and Subtraction are evaluated last, also from let to right.

Brackets can be ‘nested’ within each other. For example, consider \(3\times(5 + 2\times(4+1))\). In this case, we evaluate the innermost brackets first, because we cannot evaluate the outer brackets until everything inside has been evaluated.

Handling brackets

• Sometimes brackets are not really needed, but they may be used only for emphasis or to draw attention to something in particular. These are redundant brackets. Simply removing redundant brackets does not affect the result. We know redundant brackets when they do not affect the order of operations. Consider the following. \[3 + (2\times 5) + (4 - 1) = 3 + 2\times 5 + 4 - 1\]

  With or without those brackets, we would get the same final result, and not by chance. It takes some knowledge and experience to spot redundant brackets. If you are not sure if a set of brackets is not needed, deal with it as if it was needed. Better safe than sorry!

• When brackets are needed, they are to be treated as a closed, see-through box. You can see what is inside, but you cannot take it out of the box. Like a box, there is a proper way for opening each set of brackets. You will learn more about this later.