What is BODMAS Rule? Definition, Explanation, Examples

BODMAS Rule:- Solving arithmetic expressions with multiple operations—like addition, subtraction, multiplication, and division—can be challenging compared to working with just two numbers. When an expression includes brackets and several different operations, it’s crucial to follow a specific order to simplify it correctly. 

To tackle such problems efficiently, we use the BODMAS rule. BODMAS stands for Brackets, Orders (exponents and roots), Division, Multiplication, Addition, and Subtraction. By following this rule, we can simplify expressions with brackets and multiple operations systematically. Check out the BODMAS Rule details along with BODMAS Rule questions from the below article. 

Check out: School Books

What is the BODMAS Rule?

The BODMAS rule helps you solve math problems correctly by showing you the order in which to do calculations. BODMAS stands for:

• Brackets: First, calculate inside brackets (like (2 + 3)).

• Orders: Next, handle any exponents or roots (like 2² or √9).

• Division and Multiplication: Then, any division or multiplication from left to right can be performed.

• Addition and Subtraction: Finally, do addition and subtraction from left to right

BODMAS Full Form 

As previously mentioned, BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. When applying the BODMAS rule, it's important to follow this specific order of operations.

Check out: Class 7th Books

BODMAS Rule Definition 

The BODMAS rule helps you solve math problems by showing the order of operations. First, simplify anything inside brackets ((), {}, []). Next, handle any exponents or roots. Then, do division and multiplication from left to right. 

Finally, perform addition and subtraction from left to right. Following this order is crucial to getting the right answer. For expressions with multiple operators, start with the innermost brackets and work outward, then tackle exponents, followed by division and multiplication, and end with addition and subtraction.

BODMAS Conditions and Rules

1. For the expression x+(y+z)
To simplify, first remove the brackets and simply add the terms inside. The result is x+y+z. This means you just combine xxx with the sum of y and z.

2. For the expression x−(y+z)
When subtracting a bracketed expression, distribute the negative sign to each term inside the bracket. This turns y and z into −y and −z. So, the expression becomes x−y−z. Here, you subtract each term inside the bracket from x.

3. For the expression x(y+z)
To simplify this, you need to multiply the term outside the bracket by each term inside. So, x is multiplied by both y and z. The result is xy+xz. This means you distribute x to both y and z, and then add the products together.

Check out: Class 8th Books

Tips To Remember BODMAS

1. Use the Acronym: Remember the acronym BODMAS which stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. This helps you recall the order of operations.

2. Brackets First: Always start by simplifying expressions within brackets. This step is crucial for setting up the rest of the calculation.

3. Orders Next: After brackets, deal with orders, including exponents and roots. This step deals with powers and roots before moving to the next operations.

4. Left to Right: For Division and Multiplication, as well as Addition and Subtraction, work from left to right. They have equal priority within their group, so perform them in the order they appear.

5. Practice with Examples: Work through various problems to get comfortable with applying BODMAS. Practice will help reinforce the rule and make it second nature.

6. Use Mnemonics: Create a mnemonic to remember the order. For example, “Big Ogres Dive, Munch Apples, Swallow” for Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

7. Check Your Work: After solving, double-check your results to ensure you followed the BODMAS order correctly. Mistakes are often due to skipping steps or improper order.

8. Interactive Tools: Use online calculators or educational tools that follow BODMAS to verify your answers and understand how the rule is applied.

Check out: Class 9th Books

BODMAS Questions

Evaluate the expression: 8+(5×2)

Solution:

• Perform the multiplication inside the brackets: 5×2=10

• Then add: 8+10=18
  Answer: 18

Simplify: 12−[3+(2×4)]

Solution:

• Calculate inside the inner brackets first: 2×4=8

• Then simplify the expression inside the outer brackets: 3+8=11

• Finally, subtract from 12: 12−11=1
  Answer: 1

Calculate: 7×[3+(8−5)]
Solution:

• Solve inside the inner brackets first: 8−5=3

• Then simplify inside the outer brackets: 3+3=6

• Finally, multiply: 7×6=42
  Answer: 42

Find the result of: 9−(2×3)+5
Solution:

• Perform the multiplication inside the brackets: 2×3=6

• Then simplify: 9−6+5

• First subtract: 9−6=3

• Then add: 3+5=8
  Answer: 8

Evaluate: 15÷[3+(2×4)]

Solution:

• Calculate inside the inner brackets first: 2×4=8

• Then simplify inside the outer brackets: 3+8=11

• Finally, divide: 15÷11≈1.36
  Answer: Approximately 1.36

Simplify: (5+3)×2−4
Solution:

• Solve inside the brackets: 5 + 3 = 8

• Then multiply: 8×2=16

• Finally, subtract: 16−4=12
  Answer: 12

Solve the expression: 10+[4×(6−3)]

Solution:

• Calculate inside the inner brackets first: 6−3=3

• Then perform the multiplication: 4×3=12

• Finally, add: 10+12=22
  Answer: 22

Calculate: (8−3)×(2+4)÷2
Solution:

• Solve inside the brackets: 8−3=5 and 2+4=6

• Multiply the results: 5×6=30

• Finally, divide by 2: 30÷2=15

Answer: 15

Check out: CBSE Class 10th Books

BODMAS Questions Without Bracket

Question 1: 6 + 2 x 7

The correct answer is 20. According to the BODMAS rule, multiplication should be done before addition. 

So, first, multiply 2×7 to get 14, and then add 6 to 14, resulting in 20. A common mistake is to work from left to right, which might lead to the incorrect answer of 56: first adding 6+2 to get 8, and then multiplying 8 by 7 to get 56.

Question 2: 3 x (2 + 4) + 52

The correct answer is 43. According to the BODMAS rule, start by solving the brackets first: 2+4=6. Next, handle the orders (exponents): Then, perform the multiplication using the result from the brackets: 3×6=18. Finally, add the results: 18+25=43. A common mistake is to work from left to right, which might lead to the incorrect answer of 35.

Question 3: 5 – 2 + 6 ÷ 3

The correct answer is 5. According to the BODMAS rule, start by performing the division first: 6÷3=2. Then, handle the addition and subtraction from left to right since they are of equal priority. 

So, you compute 5−2+2 (where 2 is the result of the division), which gives you 5. Common mistakes include getting 3 by working from left to right without following BODMAS, or getting 1 by incorrectly assuming that addition should be done before subtraction."

Check out: PW Stationery

BODMAS Rule FAQs

Q1. What is the BODMAS rule?

Ans. BODMAS stands for Brackets, Orders (i.e., powers and roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). It is a rule used to determine the order of operations in mathematical expressions.

Q2. Why is the BODMAS rule important?

Ans. It ensures that mathematical expressions are interpreted correctly and consistently. Without it, different people might solve the same problem in different ways.

Q3. How do you apply the BODMAS rule in calculations?

Ans. First, solve expressions inside brackets. Then, handle orders (exponents and roots). Next, perform division and multiplication from left to right. Finally, perform addition and subtraction from left to right.

Q4. What if there are multiple brackets?

Ans. Solve the innermost bracket first and then move outward.

Q5. How do you handle division and multiplication together?

Ans. Perform division and multiplication from left to right, as they appear in the expression.