Welcome! PEMDAS was created to remember the math order of operations. Here we will explain the order of operations, explain why the order of operations is important, and show you how you can use PEMDAS to remember the order of operations.
In addition to that, we also have a PEMDAS Calculator and PEMDAS examples and practice problems. Our goal is to make you a PEMDAS expert.
Math operations are binary operations such as addition, subtraction, multiplication, and division. You use operations to add, subtract, multiply, divide, and so on.
Math Order of Operations
If you are doing more than one operation, you must do them in the correct order to get the correct answer. Here is the math order of operations:
1 - Parentheses
2 - Exponents and Roots
3 - Multiplication
4 - Division
5 - Addition
6 - Subtraction
Why is the Order of Operations Important?
The math order of operations is important because it will ensure you get the correct answer. Here is an example to illustrate two ways to calculate 1 + 2 × 3
Incorrect: 1 plus 2 equals 3, and then 3 times 3 equals 9.
Correct: 2 times 3 equals 6, and then 6 plus 1 equals 7.
The example above illustrates that you must do the calculations in the correct order of operations to get the correct answer. You cannot simply calculate from left to right and get the correct answer in all instances.
So what does PEMDAS mean? PEMDAS is an acronym. PEMDAS is an easy way to remember the math order of operations. If you look at the list of operations above, you see that the first letter of each operation in order spells PEMDAS. Here is the order of operations with the corresponding letter to spell PEMDAS:
P - Parentheses
E - Exponents and Roots
M - Multiplication
D - Division
A - Addition
S - Subtraction
The PEMDAS Calculator below allows you to enter different numbers with different operations. We will then use PEMDAS to make sure to calculate the problem in the correct order to get the correct answer.
How to Remember PEMDAS
To remember the term PEMDAS, people have made sentences from the letters. Examples of sentences include "Please Excuse My Dear Aunt Sally" and "Popcorn Every Monday Donuts Always Sunday". Some argue that the operations in PEMDAS become easier and easier. Thus, you just do the parentheses first, then less and less difficult operations.
PEMDAS does not really have a meaning. PEMDAS is the first letter of each math order of operation: First you solve what is inside parentheses, then you calculate exponents and roots, then you multiply, followed by dividing, then adding, and finally subtraction.
Below are some examples of PEMDAS problems to practice. Use the skills you learned on this page to find the answer and then check the solution.
3 + 4 ÷ 2 - 4 = Answer
3 + (4 ÷ 2) - 4 = 1
4 ÷ 2 ^ 2 - 4 = Answer
((4 ÷ (2 ^ 2)) - 4 = -3
1 + 2 - 3 × 3 + 4 ^ 2 = Answer
1 + 2 - (3 × 3) + (4 ^ 2) = 10
1 - 2 × 3 × 4 = Answer
1 - (2 × 3 × 4) = -23
7 - 1 × 0 + 3 ÷ 3 = Answer
7 - (1 × 0) + (3 ÷ 3) = 8
PEMDAS Rank and Priority
Multiplication and Division (MD in PEMDAS) have equal rank in the order of operations and do not need to be in order. Addition and Subtraction (AS in PEMDAS) also have equal rank and do not need to be in order. You could, for example, subtract before you add. The reason they have equal rank or priority is because the operations are inverse or are compliments of each other. Thus, the order of operations could also be interpreted as follows:
1 - Parentheses
2 - Exponents & Roots
3 - Multiplication & Division
5 - Addition & Subtraction
PEMDAS Around the World
Math is math and the order of operations is the same all over the world. However, the operations may be called different things. For example, in Great Britain PEMDAS is called BODMAS because they call their operations Brackets, Orders, Divisions, Multiplications, Additions, and Subtractions. Furthermore, in Canada they also call parentheses brackets and their version of PEMDAS is BEDMAS.