BODMAS is a rule used in mathematics to decide the correct sequence for solving an expression that contains more than one operation. When a question has addition, subtraction, multiplication, division, brackets, powers, or roots together, we cannot solve it randomly from left to right. We need a fixed order so that everyone gets the same answer. This fixed order is called the order of operations, and BODMAS is one of the most common ways to remember it.
The word BODMAS is made from the first letters of these operations: Brackets, Orders, Division, Multiplication, Addition, and Subtraction. In many countries, the same idea is also called PEMDAS, BIDMAS, or BEDMAS. The names are slightly different, but the rule is almost the same. First solve the grouped part, then powers or roots, then multiplication and division from left to right, and finally addition and subtraction from left to right.
What is the BODMAS rule?
The BODMAS rule tells us which operation should be done first in a mathematical expression. It is useful when an expression has two or more operations. For example, in 5 + 3 × 2, there is addition and multiplication. If we add first, we get 16. If we multiply first, we get 11. Only one answer can be accepted in mathematics, so BODMAS tells us that multiplication should be done before addition. Therefore, the correct answer is 11.
| Letter | Meaning | What to do |
|---|---|---|
| B | Brackets | Solve expressions inside brackets first |
| O | Orders | Solve powers, square roots, cube roots, and indices |
| D and M | Division and Multiplication | Solve from left to right |
| A and S | Addition and Subtraction | Solve from left to right |
A very important point is that division does not always come before multiplication. Division and multiplication have the same priority. So, when both appear in the same expression, solve them in the order in which they appear from left to right. In the same way, addition and subtraction have the same priority and must also be solved from left to right.
Why do we use BODMAS?
BODMAS removes confusion. Without this rule, the same expression can give different answers. Suppose the expression is 12 – 4 + 2. If someone adds first, they may calculate 12 – 6 = 6. But using the correct rule, addition and subtraction are equal, so we solve from left to right: 12 – 4 = 8, and 8 + 2 = 10. The correct answer is 10.
This rule is also important in science, accounting, computer programming, exams, and daily calculations. When a calculator, spreadsheet, or computer program evaluates a formula, it follows a fixed order of operations. Learning BODMAS helps students write and understand expressions correctly.
Step-by-step method to solve BODMAS questions
- Look for brackets and solve the expression inside them first.
- If there are powers, square roots, cube roots, or other indices, solve them next.
- Now solve division and multiplication from left to right.
- At the end, solve addition and subtraction from left to right.
- Write each step clearly so that mistakes can be checked easily.
Brackets in BODMAS
Brackets show that a part of the expression must be solved first. Common brackets are parentheses ( ), square brackets [ ], and braces { }. If more than one type of bracket is used, start from the innermost bracket and move outward.
Example: 2 × (3 + 5)
First solve the bracket: 3 + 5 = 8
Now multiply: 2 × 8 = 16
So, 2 × (3 + 5) = 16.
If there is a vinculum, or a bar over an expression, the part under the bar should be treated like a bracket. It must be simplified before applying the remaining operations.
Orders in BODMAS
Orders means powers and roots. Examples include 2², 3³, square root, cube root, and other indices. These are solved after brackets and before multiplication, division, addition, and subtraction.
Example: 4 + 3² × 2
First solve the power: 3² = 9
Now the expression becomes 4 + 9 × 2
Multiply: 9 × 2 = 18
Add: 4 + 18 = 22
So, 4 + 3² × 2 = 22.
Division and multiplication rule
Division and multiplication are solved after brackets and orders. But they are not solved by reading the letters D and M separately. They have equal priority. This means we solve whichever comes first from the left side.
Example: 24 ÷ 6 × 2
Start from the left: 24 ÷ 6 = 4
Then multiply: 4 × 2 = 8
So, 24 ÷ 6 × 2 = 8.
If someone multiplies 6 × 2 first, they will get 24 ÷ 12 = 2, which is not correct according to the standard order of operations. The correct method is left to right for division and multiplication.
Addition and subtraction rule
Addition and subtraction are solved at the last stage. They also have equal priority. If both appear together, solve them from left to right.
Example: 20 – 8 + 3
Start from the left: 20 – 8 = 12
Then add: 12 + 3 = 15
So, 20 – 8 + 3 = 15.
Example 1: Addition and multiplication
Solve: 7 + 4 × 5
Multiplication comes before addition.
4 × 5 = 20
7 + 20 = 27
Answer: 27
Example 2: Bracket and multiplication
Solve: (7 + 4) × 5
First solve the bracket.
7 + 4 = 11
11 × 5 = 55
Answer: 55
Notice that 7 + 4 × 5 and (7 + 4) × 5 have different answers because the bracket changes the order.
Example 3: Division and subtraction
Solve: 30 – 18 ÷ 3
Division comes before subtraction.
18 ÷ 3 = 6
30 – 6 = 24
Answer: 24
Example 4: Multiple operations
Solve: 8 + 12 ÷ 4 × 3 – 2
First solve division and multiplication from left to right.
12 ÷ 4 = 3
3 × 3 = 9
Now the expression becomes 8 + 9 – 2.
Solve addition and subtraction from left to right.
8 + 9 = 17
17 – 2 = 15
Answer: 15
Example 5: Brackets, powers, and multiplication
Solve: 3 × (2 + 4)² – 5
First solve the bracket: 2 + 4 = 6
Now solve the power: 6² = 36
Now multiply: 3 × 36 = 108
Now subtract: 108 – 5 = 103
Answer: 103
Example 6: Nested brackets
Solve: 5 + [18 ÷ (3 + 3)] × 4
Start with the innermost bracket.
3 + 3 = 6
Now the expression becomes 5 + [18 ÷ 6] × 4.
18 ÷ 6 = 3
Now multiply: 3 × 4 = 12
Finally add: 5 + 12 = 17
Answer: 17
Example 7: Using negative numbers
Solve: -4 + 6 × 3
First multiply: 6 × 3 = 18
Now add: -4 + 18 = 14
Answer: 14
Negative numbers do not change the BODMAS rule. We still follow the same order of operations.
Example 8: Fraction bar as grouping
Solve: (6 + 4) / (3 + 2)
The numerator and denominator are treated like grouped expressions.
6 + 4 = 10
3 + 2 = 5
10 / 5 = 2
Answer: 2
Common mistakes in BODMAS
The first common mistake is solving the expression strictly from left to right without checking operation priority. For example, in 6 + 5 × 2, multiplication must be done first, so the answer is 16, not 22.
The second common mistake is thinking that division must always be solved before multiplication. This is not true. Division and multiplication are solved from left to right because they have the same priority.
The third common mistake is thinking that addition must always be solved before subtraction. Addition and subtraction also have the same priority. They must be solved from left to right.
The fourth common mistake is ignoring brackets. Brackets can completely change the answer, so they must always be checked first.
Practice questions
- 10 + 5 × 2
- (10 + 5) × 2
- 36 ÷ 6 × 3
- 25 – 8 + 4
- 2³ + 4 × 5
- 50 – (6 + 4) × 3
- 7 + [20 ÷ (2 + 3)]
- 4 × (3 + 2)²
Answers
- 20
- 30
- 18
- 21
- 28
- 20
- 11
- 100
Frequently asked questions
Is BODMAS and PEMDAS the same?
Yes, both explain the same order of operations. BODMAS uses Brackets and Orders, while PEMDAS uses Parentheses and Exponents. The main idea is the same.
Do we divide before multiplication in BODMAS?
Not always. Division and multiplication have the same priority. Solve them from left to right.
Do we add before subtraction in BODMAS?
Not always. Addition and subtraction have the same priority. Solve them from left to right.
What should be solved first in BODMAS?
Brackets should be solved first. If brackets contain another bracket, solve the innermost bracket first.
Conclusion
BODMAS is a simple but important rule for solving mathematical expressions correctly. It tells us to solve brackets first, then orders such as powers and roots, then division and multiplication from left to right, and finally addition and subtraction from left to right. The most important thing to remember is that division and multiplication are equal in priority, and addition and subtraction are also equal in priority. With regular practice, BODMAS becomes easy and helps students avoid common calculation mistakes.