📖Definition
Order of operations is the agreed sequence for evaluating a mathematical expression that contains more than one operation. Without a fixed order, the same expression could give several different answers, so everyone follows the same rule: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
📐Formula
Work through the letters in order, but treat multiplication and division as one step (left to right), and addition and subtraction as one step (left to right). PEMDAS is a memory aid, not four separate passes.
📝Step-by-Step Guide
Parentheses
Simplify everything inside brackets or parentheses first, working from the innermost pair outward.
Exponents
Evaluate any powers or roots next.
Multiplication and division
Work left to right, doing whichever comes first — multiplication is not automatically done before division.
Addition and subtraction
Finish by working left to right, again treating + and − as equal-priority operations.
🧭Why PEMDAS is a memory aid, not four separate stages
PEMDAS is often taught as six distinct steps, which leads students to always multiply before dividing and always add before subtracting. That is not the rule.
Multiplication and division share the same priority and are done together, left to right, in the order they appear. The same is true for addition and subtraction.
In 20 ÷ 4 × 5, working left to right gives (20 ÷ 4) × 5 = 25. Doing the multiplication first would incorrectly give 20 ÷ 20 = 1.
🧭BODMAS, BIDMAS and other names for the same rule
Outside the US, the same idea is often taught as BODMAS or BIDMAS: Brackets, Orders (or Indices), Division/Multiplication, Addition/Subtraction.
These are all the same rule with different letters. "Orders" and "Indices" both refer to exponents and roots.
⚠️Common Mistakes to Avoid
- Always doing multiplication before division instead of working left to right
- Always doing addition before subtraction instead of working left to right
- Solving left to right for the whole expression and ignoring precedence entirely
- Forgetting to simplify inside parentheses before applying an outside exponent
- Mistyping expressions into a calculator without checking it follows the same order
✏️Practice Problems
Evaluate 3 + 4 × 2
💡 Hint: Multiply before you add.
Answer: 11
Evaluate (3 + 4) × 2
💡 Hint: The parentheses change the order.
Answer: 14
Evaluate 2 + 3²
💡 Hint: Square 3 before adding.
Answer: 11
Evaluate 6 ÷ 2 × 3
💡 Hint: Work left to right since division comes first.
Answer: 9
Evaluate 10 − 2 × 3 + 1
💡 Hint: Do the multiplication before either addition or subtraction.
Answer: 5
Evaluate 2 × (3 + 4)² − 5
💡 Hint: Parentheses, then the exponent, then multiply, then subtract.
Answer: 93
Printable Order of Operations practice
Need more than a few examples? Build a worksheet with a worked answer key, balanced difficulty, and a teacher-reviewed PDF.
Ready to Practice Order of Operations?
Generate a personalized practice test with MathQuizily. Get instant PDF downloads with answer keys.
❓Order of Operations FAQ
Do calculators always follow PEMDAS?
Most scientific and graphing calculators do, but some basic calculators evaluate strictly left to right. Test your calculator with 2 + 3 × 4 — it should show 14, not 20.
What do I do with nested parentheses?
Work from the innermost pair outward. Simplify what is inside the deepest brackets first, then move one layer out at a time.
Is multiplication always done before division?
No. They have equal priority and are done left to right, in whichever order they appear in the expression.