minus n u m b e r s plus sign



Order Of Operations


When you have finished this page, try the Order of Operations Quiz.

Order of operations sounds like a surgeon's schedule. In math, however, it refers to the order in which one adds, subtracts, multiplies or divides. You may think this is pretty obvious. However, let's look at some examples where it could be confusing and where one could get different answers. In the problem below, five plus three times two, one could add the five and three which would be eight and then multiply that eight times two which would be sixteen.

In another order, one could multiply the three times two which is six and add on the five which would be eleven.

5 + 3 * 2

(5 + 3) * 2

8 * 2 = 16


5 + (3 * 2)

5 + 6 = 11

Mathematicians decided to have an order to operations so that each person would know which order to do things. It is as follows:

Parentheses ( )
Exponents ^
Multiplication *
Division /
Addition +
Subtraction -


This means that one should look first for parentheses in a number sentence and do the work inside the parentheses first. Then one should look to the exponents and deal with them, followed by doing any multiplication, then division, then addition, then subtraction in the number sentence. While many number sentences will not contain all of these operations, all contain some combination of them and it is very important to know in which order to do things.

An important note: Remember when there are several layers of parentheses, do the operations on the inner layers first and then work your way out to the operations in the outer layers. Here is an example: Three times six plus four times three divided by two.

((3 * 6) + (4 * 3)) / 2

(18 + 12)/2

30/2 = 15



Algebra Main Page Positive & Negative Numbers Addition & Subtraction of Positive & Negative Numbers Multiplication of Positive & Negative Numbers Division of Positive & Negative Numbers Order of Operations
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