102 LearnersLast updated on July 5th, 2025
BODMAS Rule
BODMAS is an acronym that helps us recall the correct order of operations we should follow while performing various mathematical operations. BODMAS stands for B for brackets, O for order of powers or roots, D for division, M for multiplication, A for addition, and S for subtraction. If a given expression has multiple operators, it must be solved from left to right in a sequential order. In an expression, brackets are solved first, followed by powers or roots, then division or multiplication (whichever appears first from left to right), and finally addition or subtraction (depending on which comes first). By following the BODMAS rule, we can determine the correct answer. In this topic, we will explore the BODMAS rule, its sequential order, and its concepts in detail.
What is the BODMAS Rule?
BODMAS is an abbreviation that helps remember the sequence of steps followed when solving mathematical expressions. The word BODMAS stands for:
- B = Brackets ( )
- O = Order (powers or roots)
- D = Division (÷)
- M = Multiplication (×)
- A = Addition (+)
- S = Subtraction (-)
This rule states that if a given expression has multiple operators, they must be performed from left to right by following the rule. It means that brackets should be solved first, then the powers of roots, division or multiplication, and finally addition or subtraction.
Depending on which comes first in the given expression, division and multiplication are performed from left to right, based on which comes first, as they are of equal precedence.
Let us take an example to get a better understanding of the BODMAS rule.
Solve 25 ÷ 5 × 2 + 22 - (4 + 5)
25 ÷ 5 × 2 + 22 - 9 (brackets: (4 + 5)
25 ÷ 5 × 2 + 4 - 9 (order of powers: 22 = 4)
5 × 2 + 4 - 9 (division: 25 ÷ 5)
10 + 4 - 9 (multiplication: 5 × 2)
14 - 9 (addition: 10 + 4)
5 (Subtraction: 14 - 9)
BODMAS vs PEMDAS vs BIDMAS
BODMAS, PEMDAS, and BIDMAS are acronyms that help recall the correct order of mathematical operations in expressions that have multiple operators.
| Characteristics | BODMAS | PEMDAS |
BIDMAS |
| Full Form | Brackets, Orders, Division, Multiplication, Addition, Subtraction | Parentheses, Exponents, Multiplication, Division, Addition, Subtraction | Brackets, Indices, Division, Multiplication, Addition, Subtraction |
| Prevalent in | Used in the UK, India, and several other countries. |
Widely used in the USA. | Commonly used in the UK. |
|
Order of operations (Brackets and Parentheses) |
Brackets are solved first. | Parentheses are solved first. |
Brackets are solved first. |
| Orders/ Exponents/ Indices | Followed by the brackets, the order of powers and roots is calculated. |
After solving the parentheses, the exponents are solved. | Followed by the brackets, indices are solved. |
| Division and Multiplication | Depending on which appears first, division and multiplication are performed from left to right. | Performed from left to right, depending on whichever comes first. | Depending on which comes first, the operations are performed from left to right. |
| Addition and Subtraction | Based on the order they appear, performed from left to right. |
According to whichever appears first, they are performed from left to right | Depending on which comes first, addition and subtraction are performed from left to right. |
These terms help us solve complex mathematical problems easily and accurately. Parentheses are utilized to group expressions and must be solved first. Exponents, also called indices, are the same as powers, which indicate the number of times a number is repeatedly multiplied by itself.
What are the Mathematical Operations in BODMAS?
Mathematical operations are the basic arithmetic operations we perform on numbers. The four main operations in BODMAS are:
- Addition (+): Solve addition from left to right.
- Subtraction (-): Solve subtraction from left to right.
- Multiplication (×): Solve multiplication from left to right.
- Division (÷): Solve division from left to right.
The pattern of the operations in BODMAS is:
- First, solve the brackets.
- Solve the powers, square roots, and other exponents.
- Then division and multiplication.
- Followed by addition and subtraction.
Why is the BODMAS Rule Important?
These rules are used for systematic calculation of all the mathematical operations. The rule reduces the chances of misinterpretation of various operators. For example, if the given expression is 6 + 4 × 2. If we do not follow the BODMAS rule, it will result in an incorrect answer.
6 + (4 × 2)
According to the BODMAS rule, multiplication comes before addition. Therefore, the multiplication problem must be resolved first:
First, solve the brackets: 4 × 2 = 8
Then, solve the addition: 6 + 8 = 14
If we perform mathematical operations differently, the answers will be incorrect. The BODMAS rule maintains consistency and ensures everyone gets the correct answer.
Common Mistakes and How to Avoid Them on the BODMAS Rule
Understanding the BODMAS rule is crucial in solving expressions with multiple operations. However, students often make some errors when they work with various operations in a single expression. Here are some common mistakes and the solutions to avoid them.
Mistake 1
Confusion with Multiple Brackets
Students often get confused when dealing with multiple brackets in an expression. If the given expression contains parentheses ( ), square brackets [ ], and curly braces { }, we should follow an order of operations. Solve the parentheses first, followed by the square brackets, and then the curly braces.
For example, {(5 + 1) × [10 ÷ (2 - 1)]}.
First, solve parentheses ( ): (2 - 1) = 1
Then the [ ]: [10 ÷ 1] = 10
Solve { }: (5 + 1) × 10 = 60
This is the correct order for solving brackets in a given expression.
Mistake 2
Using Negative Numbers and Subtraction Operations Incorrectly
Students should keep in mind that the sequence in which addition and subtraction occur is determined by which one comes first in the expression. Sometimes, they make mistakes when dealing with negative numbers and subtraction operations. Always follow the BODMAS rule and solve the operations from left to right.
For example, if the given expression is (4 + 2) × (- 3).
The correct method for finding the answer is to solve from left to right.
Step 1: 4 + 2 = 6
Step 2: 6 × (- 3) = -18
The answer is -18.
Mistake 3
Assuming Division is More Important than Multiplication
Remember that division and multiplication are interchangeable, and they rely on which one comes first. In BODMAS, “D” comes before “M”, and kids mistakenly perform multiplication before division without checking the order. Both of them must be done from left to right according to which one appears first in the expression.
For instance, 10 ÷ 2 × 4
The correct method is:
10 ÷ 2 = 5
5 × 4 = 20
The correct answer is 20.
Mistake 4
Thinking Addition Must Be Done Before Subtraction
Students mistakenly think that addition must be performed before subtraction because “A” comes before “S” in BODMAS. Addition and subtraction are on the same level, and the operators that come first must be done from left to right.
For example, 12 - 4 + 3
The correct method is:
12 - 4 = 8
8 + 3 = 11
The correct answer is 11.
Mistake 5
Neglecting Exponents or Order of Powers
Kids should solve the order of powers or roots before division and multiplication. If they ignore the exponents or solve them after division or multiplication can lead to incorrect answers.
For instance, 4 × 22
The correct method is:
22 = 4
Multiply 4 by 4: 4 × 4 = 16
The correct answer is 16.
Tips and Tricks of the BODMAS Rule
The simple tips and tricks that should be kept in mind while dealing with the BODMAS rule are:
- Solve the brackets first, then follow the exponents. Perform division or multiplication, then addition or subtraction from left to right.
- Use parentheses to break down complicated expressions and ensure accuracy in the answers. For example, if the given expression is (12 ÷ 2) × 5.
(12 ÷ 2) × 5 = 6 × 5 = 30
- Practice the BODMAS rule and expressions with multiple operators daily to build a proper understanding of the concept.
- Perform division or multiplication as well as addition or subtraction from left to right to avoid mistakes.
Real-Life Applications of the BODMAS Rule
Learning the concept and properties of the BODMAS rule plays a vital role in our daily lives and makes complex mathematical calculations easier. The practical uses of the BODMAS rule are listed below:
- The BODMAS rule is used by professionals in the field of finance and banking to calculate interest rates on savings and loans. This rule helps them solve calculations involving exponents and other operations easily and efficiently.
- If we go shopping, the final price of an item that has a discount and tax can be calculated by the BODMAS rule. For example, a refrigerator costing $200 with a 30% discount and a 4% tax can be calculated by following the rule.
To find the discounted price:
200 - 200 × 30% = 200 × 30/100 = 200 × 0.3 = 60
200 - 60 = 140
Then add 4% tax:
140 × 4% = 140 × 4/100
140 × 0.04 = 5.6
Final price = 140 + 5.6 = $145.6
- Engineers use the BODMAS rule to estimate and calculate the total quantities of materials they need for construction or to calculate the cost of materials. For instance, if an engineer plans to build a 2-storey house and each floor needs 15 bags of cement. Therefore, he can use the BODMAS rule to calculate the total cost of construction and materials.
- In medicine and research, doctors and pharmacists can calculate the dosage of medicine based on the patient’s body weight, age, or duration of illness.
Solved Examples of BODMAS Rule
Problem 1
Simplify the expression by using the BODMAS rule: 9 + [12 ÷ (3 × 2)] − 5
6
Explanation
We must follow the BODMAS rule to simplify the given expression.
So, we must start with the parentheses brackets: 3 × 2 = 6
Now the expression becomes: 9 + [12 ÷ 6] - 5
Next, the square brackets: 12 ÷ 6 = 2
Here, the expression simplifies to: 9 + 2 - 5
First, we can perform addition and then subtraction: 9 + 2 = 11
Subtraction: 11 - 5 = 6
Thus, 9 + [12 ÷ (3 × 2)] − 5 = 6
Problem 2
Simplify the expression by using the BODMAS rule: 30 − [5 + 2 × (8 − 4)]
17
Explanation
We can start by solving the brackets.
(8 - 4) = 4
Now, the expression is:
30 - [5 + 2 × 4]
Now we can solve the multiplication inside the square brackets:
2 × 4 = 8
The expression simplifies to:
30 - [5 + 8]
Next, the addition inside the brackets:
5 + 8 = 13
So, the expression becomes:
30 - 13
Last, perform the final subtraction:
30 - 13 = 17
Thus, 30 − [5 + 2 × (8 − 4)] = 17
Problem 3
Simplify the expression by using the BODMAS rule: 10 ×[2^2 – (10 ÷ 5)]
20
Explanation
First, we need to simplify the brackets.
10 ÷ 5 = 2
The expression becomes:
10 × [22 - 2]
Next, the exponent.
22 = 4
Now the expression is:
10 × [4 - 2]
Then we can solve the subtraction inside the square brackets:
4 - 2 = 2
Here, the expression simplifies to:
10 × 2
10 × 2 = 20
Thus, 10 ×[22 – (10 ÷ 5)] = 20
Problem 4
Solve the given expression applying the BODMAS rule: 7 + 4 × 2
15
Explanation
The given expression contains addition and multiplication. According to the BODMAS rule, multiplication must be done before addition.
So, perform multiplication first:
4 × 2 = 8
Now the expression simplifies to:
7 + 8
Next, we can perform the addition:
7 + 8 = 15
Hence, 7 + 4 × 2 = 15
Problem 5
Solve the given expression applying the BODMAS rule: (6 + 3) × (5 − 1)
36
Explanation
According to the BODMAS rule, we have to solve the brackets first.
In the given expression, we have addition, subtraction, and multiplication.
First, we can solve the addition in the brackets:
(6 + 3) = 9
Next, the subtraction inside the brackets:
(5 - 1) = 4
Now the expression simplifies to:
9 × 4
So, we can perform the multiplication:
9 × 4 = 36
Therefore, (6 + 3) × (5 − 1) = 36
FAQs of BODMAS Rule
1.Define the BODMAS rule.
2.How does the BODMAS rule operate?
3. How to solve multiple brackets in an expression?
4.Which comes first in BODMAS, addition or subtraction?
5.What is PEMDAS and BIDMAS?
6.How can children in United States use numbers in everyday life to understand BODMAS Rule?
7.What are some fun ways kids in United States can practice BODMAS Rule with numbers?
8.What role do numbers and BODMAS Rule play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve BODMAS Rule skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
