Order of Operations (PEMDAS)
Parentheses, Exponents, Multiply/Divide, Add/Subtract.
Formula
Variables
Example
2 + 3×4 = 14, not 20
How it works
Order of operations is a rule for reading an expression the same way every time, so everyone gets the same answer. It starts with grouping symbols, then powers, then multiplication and division from left to right, and finally addition and subtraction from left to right. This works because some operations change the meaning of the whole expression if they are done too early, so the order prevents ambiguity.
When to use it
Use this whenever an expression has more than one kind of operation, such as in algebra, calculator work, spreadsheets, or mental math. It is essential any time parentheses, exponents, multiplication/division, and addition/subtraction appear together.
Worked example, step by step
Evaluate: 8 + 6 ÷ 3 × 2 Step 1: Do division and multiplication from left to right 8 + 2 × 2 Step 2: Multiply 8 + 4 Step 3: Add 12
Common mistakes to avoid
- Adding before doing multiplication or division
- Doing multiplication before division when they appear together from left to right
- Ignoring parentheses or treating them like they are optional
Did You Know?
PEMDAS is a convention, not a law of nature — different countries teach BODMAS or BIDMAS, but they all mean the same order.
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