Order of Operations Definition Problems Examples

What is Order of Operations?

Order of operations is the hierarchy of mathematical operations. It is the set of rules that determines which operations should be done before or after others.

Operations should be done in this order:

• Parentheses
• Exponents
• Multiplication or division (from left to right, as found in the problem)
• Addition or subtraction (from left to right, as found in the problem)

Note that multiplication and division as well as addition and subtraction do not have a set order. There is a common misconception that multiplication must be done before division and addition must be done before subtraction; however, this is not true.

After you solve any parentheses and exponents in a problem, then you'll solve any multiplication or division problems that remain, moving from left to right in the equation. Similarly, after completing all the other operations, you should complete all addition or subtraction problems, moving from left to right in the equation.

Memorization Tricks

One way people try to remember the order of operations is with the acronym PEMDAS. Here, each letter stands for one of the operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Alternatively, some people will use the sentence: 'Please Excuse My Dear Aunt Sally' to help them remember the order. Here, the first letter of each word in the sentence refers to one of the operations.

These are both helpful mnemonic devices, but there is one significant draw back. Both of these memory devices can imply that multiplication is always done before division and that addition is always done before subtraction. In truth, as we've discussed, multiplication and division are at the same importance level; you should do whichever one comes first in the problem as you read from left to right. Addition and subtraction work the same way.

Examples

Question:1

Evaluate: (11 - 5) x 2 - 3 + 1

1. Do the parenthesis: 6 x 2 - 3 + 1
2. Do the multiplication: 12 - 3 + 1
3. Do the subtraction: 9 + 1
4. Do the addition: 10

Explanation:

The Correct Answer: 10So, your final answer is 10. Again, note that in line three we did subtraction before addition, because that is how they are found from left to right on the problem.

Question: 2

Evaluate: 48 / 6 x 2 - 3^2

1. Do the exponent: 48 / 6 x 2 - 9
2. Do the division: 8 x 2 - 9
3. Do the multiplication: 16 - 9
4. Do the subtraction: 7

Explanation:

The Correct Answer: 7Notice that, in line two, we did the division before the multiplication, because those two operations are at the same level and should be done from left to right as found in the problem.

Question: 3

Evaluate: (4 - 10)^2 / 3 x 4 + 5 - 2

1. Do the parenthesis: (-6)^2 / 3 x 4 + 5 - 2 (×It's helpful to leave negative numbers in parentheses so that you square it correctly.)
2. Do the exponent: 36 / 3 x 4 + 5 - 2
3. Do the division: 12 x 4 + 5 - 2
4. Do the multiplication: 48 + 5 - 2
5. Do the addition: 53 - 2
6. Do the subtraction: 51

Explanation:

The Correct Answer:51