What Is The Order of Operations in Math? – Definition & Examples

The order of operations is the steps used to simplify any mathematical expression. In this video, learn how to solve problems using these steps and easy tricks to remember them.
What Is the Order of Operations?
Hello! My name is Bob, and I live with my wonderful Aunt Sally. My Aunt Sally does a great job of raising me. She fixes my meals, cleans the house and tucks me in at night. However, Aunt Sally often gets the order of these events mixed up. For example, yesterday my Aunt Sally cleaned the house, tucked me into bed and then made my meals.
I keep telling my Aunt Sally that order is important, but she doesn’t seem to understand. Just like in math, there is a particular order that we work problems. Without this order, it is possible that we could all get different answers. The order that we use to simplify expressions in math is called the order of operations. The order of operations is the order in which we add, subtract, multiply or divide to solve a problem.
Order of Operations Steps
The steps we use to solve any mathematical expression are:
Simplify all of the parentheses. This includes all forms of grouping symbols, such as brackets and braces, in addition to parentheses.
Simplify all exponents.
Simplify all multiplication and division from left to right. When simplifying the multiplication and division, work from left to right.
Simplify all addition and subtraction from left to right. Again, when simplifying the addition and subtraction, work from left to right.
By following this order, we can all solve the problem and get the same solution.
After explaining all of those rules to my Aunt Sally, she seems a little overwhelmed. However, I do have a shortcut to help her remember these steps. It’s called PEMDAS.
It stands for:
P – Parentheses
E – Exponents
M – Multiplication
D – Division
A – Addition
S – Subtraction
Remember that the steps for multiplication and division is one step. We work all of the multiplication and division in one step from left to right. Multiplication does not always come before division; they are worked in the order that they appear. This is also true for addition and subtraction. They are worked in the same step from left to right. An easy way for me to remember these steps is to remember the phrase Please Excuse My Dear Aunt Sally, where the:
P – Parentheses – Please
E – Exponents – Excuse
M – Multiplication – My
D – Division – Dear
A – Addition – Aunt
S – Subtraction – Sally
Let’s show Aunt Sally how the order of operations helps us to solve problems. I want to show Aunt Sally a problem from my homework tonight. The problem is 3 + [6 (11 + 1 – 4)] ÷ 8 x 2. Remember, to work this problem, we will follow the order of operations. Let’s think PEMDAS.
The first step to solve this problem is to work the P (parentheses). In this problem, they used both parentheses and brackets. We will need to start inside the parentheses and work out until we complete all of the grouping symbols. Also, when working inside the grouping symbols, we must follow the remaining order. To begin, we will need to add the 11 + 1 and then subtract 4, which is 8. We still must now work inside the bracket, 6 times 8 is 48.
The next letter in our acronym is E for exponents. Since there are no exponents, we continue on. The next step is to simplify the M and the D (multiplication and division) from left to right. Since division actually comes first, we work it from left to right. We’ll first divide 48 ÷ 8, which is 6. There is still multiplication in our problem, so next we will need to multiply 6 times 2, which equals 12. The only step remaining is AS (addition and subtraction). There is only one thing left in this problem, which is 3 plus 12, which equals 15. So, as you can see Aunt Sally, the answer to this problem would be 15.
Let’s do another problem together. Let’s solve 20 – 4 + 52/5.
Step 1: Check for any parentheses and there are none, so we can go step 2.
Step 2: Exponents are next and we have an exponent in 52, which simplifies to 25. This changes the problem to look like 20 – 4 + 25 / 5.
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