 # BODMAS Rule – Definition, Formula, Examples | Order of Operations | How to Apply BODMAS Rule?

BODMAS is a basic rule in mathematics to solve an arithmetic expression simply. BODMAS Rule is very helpful to improve the mathematic operations easily and quickly. Some Mathematical operations where we use BODMAS Rule are given here. Those mathematical operations are addition (+), subtraction (-), multiplication (X), division (÷).

BODMAS stands for
B – Bracket.
O – Of or Order.
D – Division.
M – Multiplication.
S – Subtraction.

### Order of Operations

By following the left to right method on operations, we won’t get the exact solution. We need to follow the order to simplify the mathematical operations. To solve any arithmetic operation, the BODMAS rule provides the order of operations. The operations in mathematics are addition, subtraction, multiplication, and division. While solving an expression we need to follow the below-mentioned order. That is

• Firstly, we have to give priority to the Bracket terms.
• The second priority for Of or Order operation.
• The third priority for division operation.
• Fourth priority for the multiplication operation.
• Next priority for the addition operation.
• Final priority for subtraction operation.

For example: x + (y – z) + a × c ÷ p +a².

1. First priority for bracket operation that is (y – z) = A.
2. Second priority for of or order operation a² = B.
3. Third priority for division operation c ÷ p = C.
4. Fourth priority for multiplication a × C = D.
5. Next priority for addition operation x + A + D + B = E.

Sometimes BODMAS is also called BIDMAS and PEMDAS. BIDMAS stands for Brackets, Indices, Division, Multiplication, Addition, Subtraction. If we have square terms, powers, and exponent terms in an arithmetic operation, then we can use this ‘BIDMAS’ instead of the ‘BODMAS’ rule. PEMDAS stands for Parentheses, Exponent, Multiplication, Division, Addition, and Subtraction.

### Use of Bracket

We have to give the importance for bracket terms first in an expression. In the bracket terms also, we need to follow the division, multiplication, addition, and subtraction order. For example,
2 + 3(2 + 4 × 5) – 1 = 2 + 3(2 + 20) – 1.
= 2 + 3(22) – 1.
= 2 + 66 – 1.
= 68 – 1 = 67.
The brackets will clearly explain the relationship between terms.
1500 ÷ 500 [(12-2) + (10 +5) × (6 + 4)] = 1500 ÷ 500 [10 + 15 × 10].
= 1500 ÷ 500 [10 + 150].
= 1500 ÷ 500 × 160.
= 3 × 160 = 480.
1500 ÷ 500 [(12-2) + (10 +5) × (6 + 4)] = 480.

### BODMAS Rule Questions

1. Simplify the below operations by using the BODMAS Rule.
(i) 8 + 3 × 5.
(ii) 5 × (2 + 6) + 6².
(iii) 4 – 1 + 9 ÷ 3.
(iv) 25 – 8 × 2 + 5.
(v) 50 – 20 + (2 × 4) + 2².

(i) 8 + 3 × 5.
Solution: The given expression is 8 + 3 × 5.
We have only two operations in the above expression. They are addition and multiplication.
As per the BODMAS Rule, we need to simplify the multiplication term first and then additional terms.
Multiplication terms are 3 × 5 = 15.
8 + 3 × 5 = 8 + 15.
Now, simplify the addition term. That is, 8 + 15 = 23.
Therefore, 8 + 3 X 5 is equal to 23.

(ii) 5 × (2 + 6) + 6².
Solution: The given expression is 5 × (2 + 6) + 6².
we have multiplication, bracket terms, and order terms in the above expression.
As per the BODMAS Rule, we need to simplify the bracket term first, next order terms, then multiplication, and finally addition terms.
Bracket terms are (2 × 6) = 12.
So, 5 × 12 + 6².
Next, order terms, 6² = 36.
So, 5 × 12 + 36.
Next, multiplication order. That is, 5 × 12 = 60.
That is 60 + 36.
Finally addition 60 + 36 = 96.
Therefore, 5 × (2 + 6) + 6² is equal to 96.

(iii) 4 – 1 + 9 ÷ 3.
Solution: The given expression is 4 – 1 + 9 ÷ 3.
The order of the BODMAS Rule is
B – Bracket – 1st.
O – Order – 2nd.
D – Division – 3rd.
M – Multiplication – 4th.
S – Subtraction – 6th.
We have only subtraction, addition, and division operations in the above expression. By following the BODMAS Rule, we need to give first priority for division, subtraction, and then addition.
4 – 1 + 9 ÷ 3 = 4 – 1 + 3.
= 3 + 3.
= 6.
Therefore, 4 – 1 + 9 ÷ 3 is equal to 6.

(iv) 25 – 8 × 2 + 5.
Solution: The given expression is 25 – 8 × 2 + 5.
The order of the BODMAS Rule is
B – Bracket – 1st.
O – Order – 2nd.
D – Division – 3rd.
M – Multiplication – 4th.
S – Subtraction – 6th.
We have subtraction, multiplication, and addition operations in the above expression. Based on the BODMAS Rule, the first priority will give for the multiplication, next addition, and then subtraction terms. That is,
25 – 8 × 2 + 5 = 25 – 16 + 5.
= 30 – 16.
= 14.
Therefore, 25 – 8 × 2 + 5 is equal to 14.

(v) 50 – 20 + (2 × 4) + 2².
Solution: The given expression is 50 – 20 + (2 × 4) + 2².
By following the BODMAS Rule,
50 – 20 + (2 × 4) + 2² = 50 – 20 + 8 + 2² (bracket term first).
= 50 – 20 + 8 + 4 (order term).
= 62 – 20 (addition term).
= 42 (subtraction term).
Therefore, 50 – 20 + (2 × 4) + 2² is equal to 42.

### FAQs on BODMAS Rule

1. What is BODMAS Rule?

BODMAS Rule is the order of operations in mathematics to simply solve the arithmetic expression. BODMAS stands for Bracket, Of or Order, Division, Multiplication, Addition, and Subtraction.

2. What is ‘D’ in BODMAS?

D in BODMAS Stands for Division.

3. What is the order of operations in the BODMAS rule?

For better simplification, we have an order of operation in the BODMAS Rule. That is Bracket terms, Order or exponent operation, division operation, multiplication operation, addition operation, and the subtraction operation.

4. Do you Multiply if there are no exponent terms in the expression?

Yes, if there are no bracket terms and exponent terms, then we can do the multiplication operation. If there is a bracket term, then we have to do a bracket term operation and then a multiplication operation.

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