50+ Order of Operations Worksheet Samples to Download

What Is the Order of Operations?

The order of operations is a set of rules that determine the correct sequence to solve mathematical expressions. Without these rules, the same equation could have different answers. To avoid confusion, we use PEMDAS or BODMAS, which dictate the order in which operations should be performed.

PEMDAS Rule (U.S. Standard)

PEMDAS stands for:

• P – Parentheses (Brackets)
• E – Exponents (Powers, Squares, Cubes)
• MD – Multiplication and Division (From Left to Right)
• AS – Addition and Subtraction (From Left to Right)

BODMAS Rule (Used in Some Countries)

BODMAS follows the same logic as PEMDAS:

• B – Brackets
• O – Orders (Exponents, Roots)
• DM – Division and Multiplication (From Left to Right)
• AS – Addition and Subtraction (From Left to Right)

By following these rules, students can solve expressions step by step and avoid calculation errors.

Why Is the Order of Operations Important?

Using the correct order ensures mathematical accuracy. For example:

🔴 Without PEMDAS:
8 + 2 × 3 = (8 + 2) × 3 = 30 (Incorrect!)

✅ With PEMDAS:
8 + 2 × 3 = 8 + (2 × 3) = 8 + 6 = 14 (Correct!)

Understanding this concept helps students solve problems in basic arithmetic, algebra, and real-life applications like finance and engineering.

How to Use These Order of Operations Worksheets?

1️⃣ Start with Basic Problems – If you’re new to PEMDAS/BODMAS, begin with worksheets that focus on simple addition, subtraction, multiplication, and division.
2️⃣ Move to Parentheses & Exponents – Once comfortable, try solving problems that include brackets and exponents.
3️⃣ Solve Mixed Operation Problems – Practice real-world math problems that combine all operations.
4️⃣ Check Your Answers – Each worksheet comes with an answer key for self-assessment.
5️⃣ Increase Difficulty Gradually – Use advanced worksheets to build confidence in solving complex algebraic expressions.

Order of Operations Examples for Better Understanding

Try solving these using PEMDAS/BODMAS:

Who Can Use These Worksheets?

✅ Students – Improve math skills and practice solving problems step by step.
✅ Teachers – Use these worksheets for classroom activities and homework assignments.
✅ Parents & Homeschoolers – Help kids strengthen their math foundation at home.

Types of Order of Operations Worksheets Available

✔ Basic Order of Operations (No Exponents) – Perfect for beginners learning multiplication and division rules.
✔ Order of Operations with Parentheses – Focuses on problems that require solving inside brackets first.
✔ Order of Operations with Exponents – Introduces squares, cubes, and higher powers.
✔ Mixed Operations Worksheets – Combines addition, subtraction, multiplication, and division.
✔ Algebraic Order of Operations – Advanced problems for students learning pre-algebra and algebra concepts.
✔ Fun Word Problems – Real-life application problems for better understanding.

Real-Life Applications of Order of Operations

Understanding PEMDAS/BODMAS isn’t just useful in school; it applies to daily life situations such as:

📊 Finance & Budgeting – Calculating expenses, taxes, and discounts.
🏗 Engineering & Science – Solving formulas in physics and chemistry.
🛒 Shopping & Sales – Applying discounts and tax calculations.
📈 Business & Data Analysis – Using formulas to analyze statistics and profits.

Common Mistakes Students Make in Order of Operations

🚫 Solving from left to right without following PEMDAS – Always prioritize parentheses and exponents before multiplication, division, addition, and subtraction.
🚫 Ignoring Parentheses – If parentheses are present, solve them first before applying other operations.
🚫 Confusing Multiplication & Addition Priority – Remember that multiplication and division come before addition and subtraction.
🚫 Forgetting to Work Left to Right – When multiplication and division or addition and subtraction appear together, solve from left to right.