The order of operations is a set of rules of precedence (what comes first, what comes next, etc.) that have been established in order to eliminate confusion when an expression contains more than one operation.
For example take a look at this expression that contains two operations:
(An expression is a combination of numbers, variables, and operation signs. In this case, there are the numbers 3 and 4 and 2, and the operation signs + and x.)
Do you add the 3 + 4 first and then multiply by 2? 7 x 2 = 14 ???
or
Do you multiply the 4 x 2 first and then add the 3? 3 + 8 = 11 ???
In this case, the correct evaluation of the expression is 11. Why?
The Order of Operations that has been established says the operations must be done in the following order:
- Parentheses (Simplify what is inside the grouping symbols until you are left with just a number.) Technically, there are other "grouping symbols" which should be considered as well, including fraction bars, brackets, and braces...in fifth grade, we are primarily concerned with parentheses).
- Exponents (Simplify any number with an exponent so you are left with just a number*)
At this point, only the four "basic operations" should be left in the expression.
- Multiplication and Division (Simplify these operations from left to right. Multiplication does not necessarily come before division.)
A this point, the expression should include only addition and subtraction.
- Addition and Subtraction (Simplify these operations from left to right. Addition does not necessarily come before subtraction.)
Need more explanation of the Order of Operations?
Watch this Khan Academy video. Or...watch the whole series of videos where you can work out the examples that are shown and find out right away if you are correct.
Online activities to practice the Order of Operations