BODMAS Rule Definition, Full Form, Explanation & Examples | Testbook

The BODMAS rule helps us solve math problems in the right order.
BODMAS stands for:

• B – Brackets
• O – Orders (like powers or square roots)
• D – Division
• M – Multiplication
• A – Addition
• S – Subtraction

It tells us what to do first, second, and so on in a math expression.
We always solve what's inside the brackets first, then any powers or roots. After that, we do division and multiplication (from left to right), and finally addition and subtraction (also from left to right).

When solving math problems with many operations like addition, subtraction, multiplication, and division, things can get confusing. That’s where the BODMAS rule helps.This rule tells us to always start by solving what’s inside the brackets first. After that, we handle powers or roots, then division and multiplication (from left to right), and finally addition and subtraction (from left to right).

Learn more: Mathematics

Defining the BODMAS RULE

BODMAS is an acronym that stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. In some regions, people use the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Both acronyms represent the same order of operations.

The BODMAS rule helps us solve math problems step by step in the right order. When a problem has many operations like brackets, powers, division, multiplication, addition, or subtraction, this rule shows us what to do first.

BODMAS stands for:

• B – Brackets
• O – Orders (like powers and square roots)
• D – Division
• M – Multiplication
• A – Addition
• S – Subtraction

How to Use the BODMAS Rule:

1. Start with Brackets – Always solve the expressions inside brackets first. If there are many brackets, begin with the innermost one and then move outward.
2. Then Orders – Solve any squares, cubes, or roots next.
3. Division and Multiplication – After orders, do any division or multiplication. Go from left to right as they appear.
4. Addition and Subtraction – Finally, do addition or subtraction from left to right.

BODMAS Rule Full form

As mentioned earlier, BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. It's crucial to follow this order when applying the BODMAS rule.

B	Brackets	( ), { }, [ ]
O	Order of	Square roots, indices, exponents and powers
D	Division	÷, /
M	Multiplication	×, *
A	Addition	+
S	Subtraction	–

To get accurate results, it's crucial to follow this order.

Conditions and Rules

Here are a few conditions and rules for general simplification:

Condition	Rule
x + (y + z) ⇒ x + y + z	Open the bracket and add the terms.
x – (y + z) ⇒ x – y – z	Open the bracket and multiply the negative sign with each term inside the bracket. (All positive terms will become negative and vice-versa)
x(y + z) ⇒ xy + xz	Multiply the term outside the bracket with each term inside the bracket

Tips to Remember the BODMAS Rule:

Here are some tips to remember the BODMAS rule:

• First, simplify the brackets
• Solve the exponent or root terms
• Perform division or multiplication operation (from left to right)
• Perform addition or subtraction operation (from left to right)

BODMAS or PEMDAS

BODMAS and PEMDAS are both helpful rules used to remember the order of operations in math. They are nearly the same but use different words depending on the country.

Here’s what they stand for:

• BODMAS = Brackets, Orders, Division, Multiplication, Addition, Subtraction
• PEMDAS = Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Key Point:

Even though the names are different, both follow the same logic. When you reach division and multiplication (or addition and subtraction), solve them in the order they appear from left to right.

So, whether you use BODMAS or PEMDAS, the steps are the same — and they help you solve problems the right way!

Easy Ways to Remember the BODMAS Rule

Here’s a simple way to remember how to use the BODMAS rule:

1. Start with brackets – Always solve the expressions inside brackets first.
2. Next, handle exponents – Solve squares, cubes, square roots, etc.
3. Then do division or multiplication – Solve from left to right, depending on which comes first.
4. Finally, do addition or subtraction – Also solve from left to right.

Common Mistakes While Using the BODMAS Rule

Sometimes, mistakes happen when we don't follow the rules properly. Here are some common errors:

• Confusion with multiple brackets: If an expression has many brackets, it can be confusing. Solve the same types of brackets together to avoid mistakes.
• Mistakes with negative numbers: Some people get confused when dealing with subtraction and negative numbers.
  For example,
  Correct way: 1 − 3 + 4 = (−2) + 4 = 2
  Wrong way: 1 − 3 + 4 = 1 − 7 = −6 (This is incorrect.)
• Thinking division comes before multiplication: Division and multiplication are at the same level. Always do the one that comes first from the left.
• Same with addition and subtraction: They are also equal level operations. Solve them left to right.
  For example, don’t assume subtraction is always last just because “S” comes after “A” in BODMAS.

Following left-to-right steps while doing division/multiplication or addition/subtraction will help you get the right answer every time.

Examples of the BODMAS Rule

Example 1:

Solution-

Step 1: Solve the fractions inside the bracket first-

Step 2: Now the expression will be (1/2) of 18

Simplifying Brackets

The terms inside the brackets can be simplified directly. That means we can perform the operations inside the bracket in the order of division, multiplication, addition, and subtraction.

Note: The order of brackets to be simplified is (), {}, [].

Example 2:

Simplify: 16 + (10 – 3 × 2)

Solution:

16 + (10 – 3 × 2)

= 16 + (10 – 6)

= 16 + 4

= 20

Therefore, 16 + (10 – 3 × 2) = 20.

Example 3:

Simplify the following.

(i) 2000 ÷ [10{(16−8)+(30−15)}]

(ii) 1/3[{−3(2+3)}10]

Solution:

(i) 2000 ÷ [10{(16−8)+(30−15)}]

Step 1: Simplify the terms inside {}.

Step 2: Simplify {} and operate with terms outside the bracket.

2000 ÷ [10{(16−8)+(30−15)}]

= 2000 ÷ [10{8+15}]

= 2000 ÷ [10{23}]

Step 3: Simplify the terms inside [ ].

= 2000 ÷ 230
= 8.69 (approximately)

(ii) 1/3[{−3(2+3)}10]

Step 1: Simplify the terms inside () followed by {}, then [].

1/3[{−3(2+3)}10]

= 1/3 [{-3(5)} 10]

= 1/3 [{-15} 10]

= 1/3 [-150]

= -50

BODMAS Rule without Brackets

The BODMAS rule can also be applied to solve mathematical expressions without brackets. Let's look at an example to illustrate this.

Example 4:
Simplify: 19 – 30 ÷ 6 × 5 + 10

Solution:
Step 1: According to the BODMAS rule, we solve division and multiplication from left to right.
30 ÷ 6 = 5

Now the expression becomes:
19 – 5 × 5 + 10

Step 2: Next, solve the multiplication:
5 × 5 = 25

Now the expression becomes:
19 – 25 + 10

Step 3: Solve addition and subtraction from left to right:
19 – 25 = -6
-6 + 10 = 4

Example 5:

Simplify the following expression: 1/5 of 50 + 150 ÷ 30 – 15

Solution:

1/5 of 50 + 150 ÷ 30 – 15

= (1/5) × 50 + 150 ÷ 30 – 15

= 10 + 150 ÷ 30 – 15

= 10 + 5 – 15

= 0

Solved Problems On Bodmas

Question 1: Solve 10 + 11 ÷ 11 + 7 × 3 − 9.

Solution:

The problem given is 10 + 11 ÷ 11 + 7 × 3 − 9.

The division operation is performed first.

11 ÷ 11 = 1

So, the expression reduces to 10 + 1 + 7 × 3 − 9

The multiplication operation is taken next,

7 × 3 = 21

So, the expression reduces to 10 + 1 + 21 − 9

The addition operation is

10 + 1 + 21 = 32

The final answer is 32 – 9 = 23.

Question 2: Simplify the expression [30 – 3 (7 + 2)] ÷ 5 + 11.

Solution:

The problem given is [30 – 3 (7 + 2)] ÷ 5 + 11.

The bracket is taken first.

(7 + 2) = 9

Then 30 – 3 * 9 ÷ 5 + 11

Then 30 – 27 ÷ 5 + 11

Then 3 ÷ 5 + 11

Then 0.6 + 11

The final answer is 11.6.

Practice Problems on the BODMAS Rule

Try solving the following problems to practice applying the BODMAS rule.

1. Evaluate 32 – [28 – {3 + 6 × (7 – 2)}]
2. Simplify: 3 + 6(5 + 3) + 4 3 – (2 + 7 × 4)
3. Find the value of 8 + {9 – 4 of (√9 + 3)}.

More Related Links
Surds	Exponent
Index	Expanding brackets

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