Here you will learn about order of operations, including what it means and how to calculate and solve order of operations problems using PEMDAS.
Students will first learn about order of operations as a part of operations and algebraic thinking in elementary school.
Order of operations refers to the rule that explains the sequence of steps necessary for correctly evaluating a mathematical expression or math problem.
You will use the acronym PEMDAS to help recall the correct order, or priority, in which you complete mathematical operations.
Mathematical operations such as multiplication and addition have to be completed in a specific order. This sequence of steps helps us to evaluate any mathematical expression, both with numerical values and algebraic expressions.
To evaluate an expression using PEMDAS, you need to understand what PEMDAS represents and be able to apply the PEMDAS rule to any calculation.
PEMDAS stands for:
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
Parentheses have a higher priority than exponents, so we calculate what is inside a pair of parentheses first. Exponents have a higher priority than division and multiplication, so any exponent that can be evaluated is calculated next, and so on.
The order can be remembered using the mnemonic device for PEMDAS, ‘Please Excuse My Dear Aunt Sally.’
| Priority of Operation | PEMDAS | Mathematical Symbol |
|---|---|---|
| 1 | Parentheses | |
| 2 | Exponents | |
| 3 | Division |
It is important to note that multiplication and division are given equal priority, and addition and subtraction are given equal priority.
When completing calculations that involve multiplication and division or addition and subtraction, you work from left to right.
Consider the following expression 12-7+6.
12-7=5 and then 5+6=11
Consider the following expression 10 \div 5 \times 2.
10 \div 5=2 and then calculate 2 \times 2=4.
Visually you could represent PEMDAS as: