Last updated on July 5th, 2025
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.
BODMAS is an abbreviation that helps remember the sequence of steps followed when solving mathematical expressions. The word BODMAS stands for:
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, 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.
Mathematical operations are the basic arithmetic operations we perform on numbers. The four main operations in BODMAS are:
The pattern of the operations in BODMAS is:
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.
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.
The simple tips and tricks that should be kept in mind while dealing with the BODMAS rule are:
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:
Simplify the expression by using the BODMAS rule: 9 + [12 ÷ (3 × 2)] − 5
6
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
Simplify the expression by using the BODMAS rule: 30 − [5 + 2 × (8 − 4)]
17
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
Simplify the expression by using the BODMAS rule: 10 ×[2^2 – (10 ÷ 5)]
20
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
Solve the given expression applying the BODMAS rule: 7 + 4 × 2
15
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
Solve the given expression applying the BODMAS rule: (6 + 3) × (5 − 1)
36
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
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.
: She loves to read number jokes and games.