BODMAS Rule – Definition, Formula, Examples

What is BODMAS Rule?

The students start to learn mathematics problem solving with simple one operations like subtraction/ multiplication/ addition/ division. These single operations are very simple to do but what about the problems containing more than one operation like addition, subtraction, multiplication, division in the same problem? This is where BODMAS Rule plays a vital role in solving these types of problems with 100% accuracy.

The BODMAS rule is a trick to solve the primary school mathematical questions which stands for

B  –  Bracket
O  –  Orders
D  –  Division
M –  Multiplication
A  –  Addition
S  –  Subtraction

This helps students to remember the order of the operations to be carried out while solving a mathematical numeral problem. Today, it can be commonly seen as BIDMAS in many places but the meaning is the same as BODMAS, I in BIDMAS stands for Indices which is the same as orders.

In some places like the USA, it is also known as PEMDAS

P  –  Parentheses
E  –  Exponents
M –  Multiplication
D  –  Division
A  –  Addition
S  –  Subtraction.

Order of operations of BODMAS Rule

As mathematics is a logic-oriented subject, it requires a set of universal rules about which order in which the operations need to be carried out. BODMAS is itself the order in which the numerical problem has to be solved. Starting from the bracket to the subtraction.

Since modern algebra was introduced, multiplication was given higher precedence than Addition or subtraction. This is the reason we interpret 4+6×3 as 4+ (3×2) = 10, not as (4+3) x2 = 14.

Then in the 16th and 17th centuries, exponents were introduced and they were given precedence on both multiplication and addition. The rule BODMAS is important to eliminate the errors during the solving of problems. To override the above-mentioned precedence, orders and brackets are used to emphasize which operation has to be carried out first. According to the precedence, multiplication has to be done before addition but when the addition is required to be done first, orders or brackets emphasize it. For example: In (3 + 4) x 6 = 42, here, the bracket has emphasise addition to precede multiplication.

Order of operation according to BODMAS Rule

Examples of BODMAS Rule

Example 1: 4 + 2 x 8 =?

Solution: According to the BODMAS Rule, Multiplication needs to be done before addition.
So,
Step 1: 2 x 8 = 16
Step 2: 16 + 4 = 20

The correct answer is 20.
(Common mistake that students make: 4 + 2 = 6, 6 x 8 = 48)

Example 2: 6 – 3 + 8 ÷ 2 =?

Solution: Applying BODMAS Rule,
Step 1: 8 ÷ 2 = 4
Step 2: Mow, We have 6 – 3 + 4
So, 6 – 3 = 3
Step 3: + 4 = 7

7 is the correct answer
(Common errors: 6 – 3 = 3, 3 + 8 = 11, 11 ÷ 2 = 5.5)

Example 3: 4 x (5 + 6) + 5 2 =?

Solution: Apply BODMAS Rule,
Step 1: (5 + 6) = 11
Step 2: 5 2 = 25
Step 3: 4 x 11 = 44
Step 4: 44 + 25 = 69

69 is the correct answer
(Common errors: many students work from left to right and get wrong answer)

Example 4: Find the value of z using BODMAS Rule 33 ÷ 3 + z x 3 -23 = 0

Solution: Apply BODMAS Rule,
Step 1: 33 ÷ 3 = 11
Step 2: z x 3 = 3z
Step 3: now, we have 11 + 3z -23 = 0
Step 4: 11 + 3z = 23
Step 5: 3z = 23 – 11
Step 6: 3z = 12
Step 7: z = 12 ÷ 3
Step 8: z = 4

The value of z is 4.

Example 5: (6/4+2/4) -2 =?

Solution: Applying BODMAS Rule
Step 1: (6/4+2/4) = 2
Step 2: 2 – 2 = 0

0 is the correct answer

Frequently Asked Questions

Q1. What is the need of BODMAS Rule?
Ans. The BODMAS helps students to solve the mathematical problem in the proper order of operations. When students reach the primary classes, they need to solve mathematical problems that require more than one operation. These kinds of problems have more chances of mistakes, BODMAS plays an important role here to eliminate the confusion and errors while solving the problem.

BODMAS instructs that brackets should be solved first, then comes the orders, followed by the division or multiplication and addition or subtraction at the last. It is the most useful rule to make difficult expressions easy to understand. BODMAS is a very easy and simple rule which can be understood easily by the students in primary classes.

Q2. Please give an example of the BODMAS Rule.
Ans. Here is the BODMAS rule example:
4 + 2 x 8 =?
Solution: According to the BODMAS rule, Multiplication needs to be done before addition.
So,
Step 1: 2 x 8 = 16
Step 2: 16 + 4 = 20
The correct answer is 20.
(Common mistake that students make: 4 + 2 = 6, 6 x 8 = 48)
You can find more examples above in the article.

The BODMAS rule is the order of the operations used in solving algebraic problems. First, start with solving the brackets, then orders followed by division and multiplication and addition/subtraction are the last step. If students fail to use the rule properly or ignore the BODMAS rule while solving the question, they will get the wrong answer.

Q3. What is the full form of BODMAS?
Ans. The full form of BODMAS is :
B- Brackets () / {} / []
O- Orders (√)
D- Division (÷)
M- Multiplication (x)
A – Addition (+)
S- Subtraction (-)

Q4. BODMAS and PEMDAS are the same or different?
Ans. BODMAS and PEMDAS are exactly the same things. PEMDAS is usually used in the UK. Although PEMDAS indicates to do multiplication before division but that doesn’t change the calculation. Either way, the answer will be the same.
For example: 5 ÷ 2 x 3 = 7.5 and 5 x 3 ÷ 2 = 7.5. In both cases the answer is same.

Q5. Are Orders, Indices and Exponents the same?
Ans. Orders, Indices, and exponents are the same things which are the subscript numbers representing the powers in Mathematics. These are the half-size numbers we usually see in algebraic expressions as powers. For example: 3 2 +5, Here, 2 is the power of 3. This can be denoted as order, index, or exponent.

Q6. Is BODMAS a universal rule?
Ans. Yes BODMAS is a universal rule. It was introduced by Achilles Reselfelt. This was introduced with the aim of making it easy to solve mathematical problems involving more than one sign or operation. BODMAS tells us the order in which we have to perform the operation.

BODMAS was created according to the rule of mathematics and the precedence of one operation over another. As it is not easy to remember all the rules and precedence, BODMAS is a simple way to solve them. This is accepted universally. Some places call it PEMDAS or BIDMAS also but they are all the same things.

Q7. Is there any chance of getting the wrong answer after using BODMAS?
Ans. Although BODMAS is the rule to solve the problems involving multiple operations but the correct calculations and using it properly is the responsibility of students. If you use the BODMAS rule correctly and make no mistake in calculations, you will surely get the right answer.