BODMAS Rules: Complete Guide to Order of Operations
Today at 12:00 AM
TL;DR: BODMAS is the mathematical rule that determines the order in which operations should be performed in expressions. It stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. Use our interactive calculator above to practice BODMAS step-by-step!
BODMAS Calculator
Learn the order of operations step by step!
Score: 0
Remember BODMAS Order:
Brackets
( )
Orders
^
Division
÷
Multiplication
×
Addition
+
Subtraction
-
Choose an expression:
3+3÷3+3
Interactive BODMAS Calculator - Learn the order of operations step-by-step with our educational widget. Practice BODMAS rules (Brackets, Orders, Division, Multiplication, Addition, Subtraction) through guided examples like 3+3÷3+3=7. This hands-on calculator shows each mathematical step with visual highlights and explanations, helping students master the correct sequence for solving mathematical expressions. Choose from multiple practice problems including 2×3+4, 10-2×3, and 8÷2+3×2 to build confidence in applying BODMAS principles. Perfect for elementary and middle school students learning foundational math concepts.
What is BODMAS?
BODMAS is an acronym that helps students remember the correct order of mathematical operations. Following BODMAS rules ensures that mathematical expressions are solved consistently and correctly every time.
The BODMAS rule states that mathematical operations should be performed in this specific order:
Brackets
Solve everything inside brackets ( ), square brackets [ ], or curly brackets first.Orders (Powers/Exponents)
Calculate any powers, exponents, or roots (like x², √x, etc.).Division and Multiplication
Perform division (÷) and multiplication (×) from left to right.Addition and Subtraction
Finally, perform addition (+) and subtraction (-) from left to right.
BODMAS vs PEMDAS: What's the Difference?
Both BODMAS and PEMDAS refer to the same mathematical concept - the order of operations. The difference is simply regional:
| BODMAS (UK/Australia) | PEMDAS (US/Canada) | Operation |
|---|---|---|
| Brackets | Parentheses | ( ) |
| Orders | Exponents | x² |
| Division | Division | ÷ |
| Multiplication | Multiplication | × |
| Addition | Addition | + |
| Subtraction | Subtraction | - |
Step-by-Step BODMAS Examples
Let's work through the classic BODMAS example: 3 + 3 ÷ 3 + 3
Example
Problem:
Calculate 3 + 3 ÷ 3 + 3 using BODMAS rules
Solution:
Step 1: Look for brackets, orders - none present
Step 2: Perform division first: 3 ÷ 3 = 1
Step 3: Expression becomes: 3 + 1 + 3
Step 4: Perform addition from left to right: 3 + 1 = 4, then 4 + 3 = 7
Answer: 7
Step 2: Perform division first: 3 ÷ 3 = 1
Step 3: Expression becomes: 3 + 1 + 3
Step 4: Perform addition from left to right: 3 + 1 = 4, then 4 + 3 = 7
Answer: 7
More BODMAS Practice Problems
Practice
Example 1:
2 × 3 + 4
Solution:
First multiply: 2 × 3 = 6
Then add: 6 + 4 = 10
Then add: 6 + 4 = 10
Practice
Example 2:
10 - 2 × 3
Solution:
First multiply: 2 × 3 = 6
Then subtract: 10 - 6 = 4
Then subtract: 10 - 6 = 4
Common BODMAS Mistakes to Avoid
- Working left to right without considering order: Always check for multiplication and division before addition and subtraction
- Forgetting that multiplication and division have equal priority: Work from left to right when both are present
- Ignoring brackets: Always solve brackets first, even if they contain simple operations
- Misunderstanding negative numbers: Remember that -3² = -(3²) = -9, not (-3)² = 9
Why is BODMAS Important?
Understanding BODMAS is crucial because:
Mathematical Consistency
Ensures everyone gets the same answer when solving mathematical expressionsFoundation for Advanced Math
Essential for algebra, calculus, and higher-level mathematicsReal-world Applications
Used in programming, engineering, finance, and scientific calculationsAcademic Success
Critical for passing math exams and standardized tests
BODMAS in Different Contexts
Programming and Computer Science
In programming languages, the order of operations follows BODMAS/PEMDAS rules. For example:
result = 3 + 3 / 3 + 3 # This equals 7.0 in Python
print(result) # Output: 7.0
Advanced Mathematical Expressions
BODMAS applies to complex expressions with multiple operations:
Tips for Mastering BODMAS
- Practice regularly: Use our interactive calculator above to work through problems step-by-step
- Remember the acronym: BODMAS or PEMDAS - choose whichever is easier for you to remember
- Work systematically: Always scan the entire expression first before starting calculations
- Use brackets wisely: When in doubt, add brackets to clarify the intended order of operations
- Check your work: Verify answers by working through the problem again or using a calculator
Teaching BODMAS to Students
When teaching BODMAS to students:
Start with Simple Examples
Begin with expressions that only involve two operationsUse Visual Aids
Color-code different operations or use our interactive calculatorPractice Mental Math
Encourage students to work through simple BODMAS problems mentallyConnect to Real Life
Show how BODMAS applies in everyday situations like calculating costs or measurements
Conclusion
Mastering BODMAS is essential for mathematical success. The order of operations - Brackets, Orders, Division, Multiplication, Addition, Subtraction - provides a universal framework for solving mathematical expressions correctly and consistently.
Remember: Division and Multiplication have equal priority (work left to right), and Addition and Subtraction have equal priority (work left to right). Practice with our interactive BODMAS calculator above to reinforce these concepts and build confidence in applying the rules.
Whether you're a student learning basic algebra or an adult refreshing your math skills, understanding BODMAS will help you tackle mathematical problems with confidence and accuracy.
Practice makes perfect! Use our interactive BODMAS calculator above to work through various problems and see step-by-step solutions. Master the order of operations today!