Math - as a field of study, a tool, or a language - has many conventions. The order of operations is one of those conventions. The order of operations is a standard collection of rules about the order by which mathematical procedures are to be performed.

Consider, for example, the following mathematical expression:

If one were to perform the calculations in the order in which the numbers appear, the calculation would look like this:

But one could also perform the calculations in other orders, like these two examples:

With this example, it’s easy to see the need for a standardized order of operations. The standardized order we will cover is used universally (in math, science, technology, etc. around the world) and calls for the following general order of operations:

1. Exponents and roots

2. Multiplication and division

3. Addition and subtraction

In Canada, we use the following mnemonic to remember the standard order:

B - Brackets, or parentheses like [ ] or ( )

E - Exponents

D - Division

M - Multiplication

A - Addition

S - Subtraction

Though the mnemonic has division coming before multiplication, as well as addition before subtraction, division and multiplication are of equal rank in terms of order - and the same is true for addition and subtraction. That is, addition does not always need to be performed before subtraction and division does not always need to be performed before multiplication.

In cases where one has to decide between performing addition or subtraction first, the procedure is to complete the operations from left to right.

Consider the following expression. The correct answer to the expression is 11, with the subtraction performed before the addition.

The best way to get comfortable with the order of operations is practice. Let’s do some examples together. In the video, we will evaluate the following expressions.

Let’s try a trickier problem - it’s less direct, but a cool exercise. Attempt the problem on your own, and then watch the video if you get stuck or to check your work.

Place brackets (any number of pairs, anywhere) to make the following statement true.

(2) Insert brackets to make the following equations true.