How to Use Order of Operations? (+FREE Worksheet!)
Use Order of Operations: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Handle groupingSimplify inside parentheses or other grouping symbols first.
- Apply powersEvaluate exponents before ordinary multiplication or division.
- Move by levelWork multiplication/division left to right, then addition/subtraction left to right.
Worked examples
Multiplication before addition
- Multiply 3 and 6 first.
- Keep the 4 until that product is done.
- Add 4 + 18.
Parentheses change the path
- Parentheses make 4 + 3 happen first.
- That gives 7.
- Multiply 7 by 6.
Try one before moving on
Use Order of Operations: pop-up practice
Whenever a math expression contains more than one operation, you need the order of operations to get the right answer. Without a consistent set of rules, two people could evaluate the same expression and reach two different results. The acronym PEMDAS — Parentheses, Exponents, Multiplication/Division, Addition/Subtraction — tells you exactly which steps to take first.
What Is the Order of Operations?
The order of operations is the agreed-upon sequence for evaluating a mathematical expression. It ensures that every mathematician in the world gets the same answer for a given expression. PEMDAS is the most common mnemonic for remembering the sequence:
- P — Parentheses (and all grouping symbols)
- E — Exponents (powers and roots)
- \(\color{blue}{\frac{M}{D}}\) — Multiplication and Division (left to right)
- \(\color{blue}{\frac{A}{S}}\) — Addition and Subtraction (left to right)
The PEMDAS Rules in Detail
Step 1 — Parentheses and Grouping Symbols
Always simplify inside parentheses, brackets, or braces first.
- \(\color{blue}{(3 + 4) \times 2 = 7 \times 2 = 14}\)
Step 2 — Exponents
Evaluate all powers (and roots) after clearing grouping symbols.
- \(\color{blue}{2^{3} + 5 \times (10 – 3) = 8 + 5 \times 7 = 8 + 35 = 43}\)
Step 3 — Multiplication and Division (left to right)
Work multiplication and division together, moving left to right. Neither takes priority over the other.
- \(\color{blue}{18 \div (3 + 3) – 1 = 18 \div 6 – 1 = 3 – 1 = 2}\)
Step 4 — Addition and Subtraction (left to right)
Finally, work addition and subtraction left to right.
- \(\color{blue}{3 + 4 \times 2 = 3 + 8 = 11}\) (multiply first, then add)
Step-by-Step Summary
- Simplify inside all Parentheses (innermost first).
- Evaluate all Exponents.
- Perform Multiplication and Division left to right.
- Perform Addition and Subtraction left to right.
Watch: Order of Operations Explained (PEMDAS)
Math Antics walks through PEMDAS with step-by-step numerical examples:
Order of Operations – Worked Examples
Example 1: Evaluate \(\color{blue}{3 + 4 \times 2}\).
No parentheses or exponents. Multiply first: \(\color{blue}{4 \times 2 = 8}\). Then add: \(\color{blue}{3 + 8 = 11}\).
Example 2: Evaluate \(\color{blue}{2^{3} + 5 \times (10 – 3)}\).
Parentheses first: \(\color{blue}{10 – 3 = 7}\). Exponent: \(\color{blue}{2^{3} = 8}\). Multiply: \(\color{blue}{5 \times 7 = 35}\). Add: \(\color{blue}{8 + 35 = 43}\).
Example 3: Evaluate \(\color{blue}{18 \div (3 + 3) – 1}\).
Parentheses: \(\color{blue}{3 + 3 = 6}\). Divide: \(\color{blue}{18 \div 6 = 3}\). Subtract: \(\color{blue}{3 – 1 = 2}\).
Example 4: Evaluate \(\color{blue}{7 + 2 \times (3 + 4^{2})}\).
Inside parentheses, exponent first: \(\color{blue}{4^{2} = 16}\). Add inside: \(\color{blue}{3 + 16 = 19}\). Multiply: \(\color{blue}{2 \times 19 = 38}\). Add: \(\color{blue}{7 + 38 = 45}\).
More Practice: Khan Academy Video on PEMDAS
Khan Academy works through challenging order of operations problems:
Exercises for Order of Operations
Evaluate each expression using PEMDAS.
- \(\color{blue}{5 + 3 \times (8 – 2)}\)
- \(\color{blue}{(12 – 4) \div 2 + 3^{2}}\)
- \(\color{blue}{4 \times 3 + 6 \div 2 – 1}\)
- \(\color{blue}{(5 + 3)^{2} \div 4}\)
- \(\color{blue}{7 + 2 \times (3 + 4^{2})}\)
- \(\color{blue}{60 \div (2 + 3) \times 2 – 1}\)
Answers
- \(\color{blue}{23}\)
- \(\color{blue}{13}\)
- \(\color{blue}{14}\)
- \(\color{blue}{16}\)
- \(\color{blue}{45}\)
- \(\color{blue}{23}\)
Pre-Algebra for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test
Frequently Asked Questions
Does multiplication always come before division?
No. Multiplication and division have equal priority; you perform them left to right. For example, \(\color{blue}{8 \div 4 \times 2 = 2 \times 2 = 4}\), not \(\color{blue}{8 \div 8 = 1}\).
What does BODMAS mean?
BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) is the British equivalent of PEMDAS. Both acronyms describe the same rule set.
Why do we need an order of operations at all?
Without it, \(\color{blue}{2 + 3 \times 4}\) could equal 20 (add first) or 14 (multiply first). The order of operations gives every expression a single, unambiguous value.
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jessicarobarge98 –
could use more worksheet to prectice with