What is the Order of Operations?
The order in which operations are to be performed in a given problem
The order of operations is a set of rules that tells us the correct order to solve different parts of a math problem. When a problem has more than one operation like addition, subtraction, multiplication, or division, following the right order makes sure everyone gets the same answer.
The standard order of operations is often remembered with the acronym PEMDAS:
- P → Parentheses first
- E → Exponents (like squares and cubes)
- MD → Multiplication and Division (from left to right)
- AS → Addition and Subtraction (from left to right)
For example, how would you solve 3 + 5 × 2 = ?
If you simply go from left to right, adding 3 and 5 first and then multiplying their sum (8) with 2, you get 16.
But with the correct order (multiplication first and addition last), you get:
3 + (5 × 2) = 3 + 10 = 13
That’s why the order of operations is so important; it keeps math consistent and correct.
We use the order of operations all the time:
- Calculating totals on bills or receipts
- Following multi-step formulas in science
- Solving word problems that have more than one operation
When Do Students Learn About the Order of Operations?
Students are introduced to the order of operations in upper elementary school, and they build on it through middle school and beyond as problems become more complex.
Grades 3–5 – Introduction to the Order of Operations
Students begin learning to solve multi-step problems with addition, subtraction, multiplication, and division. They practice using parentheses and understand the need for a specific solving order.
Grades 6–8 – Mastering the Order of Operations
Students work with exponents, parentheses, and more complex expressions. They solve multi-step problems that require strict attention to the order of operations.
Grades 9+ – Applying the Order of Operations in Algebra and Beyond
Students use the order of operations to solve algebraic expressions, work with radicals, and simplify complex equations.
