BODMAS Questions with Solutions

If there is an equation that includes multiple mathematical operations, which will you solve first? To avoid the confusion, mathematicians came up with the BODMAS rule that will help decide the order in which the signs have to be calculated. 

BODMAS is an acronym that expands to Bracket, Order, Division, Multiplication, Addition and Subtraction. This rule helps while solving a mathematical problem that has more than one mathematical symbol. 

BODMAS Rule

According to the BODMAS rule, if the equation contains brackets, order, division, multiplication, addition and subtraction symbols, exactly the same order has to be followed. It means you first simply the terms inside the bracket. 

• Brackets 

There are three types of brackets: (), [], and {}. If all three are used in the equation like { [ ( ) ] }, the BODMAS rule says that the innermost bracket has to be opened first while the outermost is simplified at the last.

Example: {3+ [2 ÷ (1+1)]}

Solution: Here first, simplify the terms inside the ( ) bracket. We get 1+1 = 2.

Then {3 + [2 ÷ 2]}.

Now solve the equation inside the [] bracket, i.e., 2 ÷ 2 = 1.

We are left with { 3 + 1 } = 4. 

Remember that, even inside the brackets, the ODMAS rule has to be followed.

Order 

The second highest priority should be given to order after brackets. Here, order can mean square root, indices, exponents, and powers in the preferential order. Sometimes the equation uses the word ‘of’. This has to be considered a ‘multiplication sign’ and has to be solved before DMAS.

Example: 

1. 2 + 3 of 3 – 10

As per the BODMAS rule, solve ‘3 of 3’, considering it as multiplication.

           2 + (3 × 3) – 10

           2 + 9 – 10

          Let’s perform addition next, followed by subtraction.

          11- 10 

           =1.

2. (1 / 2 + 3 / 4) of 8

          First priority should be to solve inside the bracket.

          1 / 2 + 3 / 4 = 5 / 4.

         Then the next expression would be 

         (5 / 4) × 8

         =10

Division, Multiplication, Addition and Subtraction

The division, multiplication, addition, and subtraction are performed in the same order of preference. 

Examples: 

1. 10 ÷ 5 – 3 + 2

           Performing the division operation first, we obtain

           2 – 3 + 2

           Now, addition and subtraction have to be solved.

           4 – 3

           =1

2. (9 ÷ 3) + 10 × 2 – (8 ÷ 4)

           Solve the two brackets simultaneously.

           9 ÷ 3 = 3

           8 ÷ 4 = 2

           The expression becomes 3 + 10 × 2 – 2.

           As per the BODMAS rule, multiplication has to be performed next.

           10 × 2 = 20

           3 + 20 – 2

           23 – 2

           =21

Solved problems on BODMAS

Question 1: Simplify the expression 25 + 5 × 3 – 22 ÷ 2.

Solution: 

The division operation is performed first.

22 ÷ 2 = 11

So, the expression reduces to 25 + 5 × 3 – 11.

The multiplication operation is performed next.

5 × 3 = 15

The expression becomes 25 + 15 – 11.

Performing addition,

25 + 15 = 40

Finally, the expression becomes 40 – 11.

= 29.

Question 2: Solve 200 ÷ 10 {(8-3) – (15-11)}

Solution: 

Initially, the first ( ) brackets are simplified,

200 ÷ 10 {(8 – 3) – (15 – 11)}

= 200 ÷ 10 (5 − 4) (solve round bracket)

= 200 ÷ 10 (1) (solve curly bracket)

= 20 (1) (divide 200 by 10 = 20)

= 20 × 1 (if no operator is mentioned behind any given bracket, a multiplication operation can be performed).

= 20

The final answer is 20.

Question 3: Simplify the following expression 3 + 2³ × (25 – 3) using the BODMAS rule.

Solution: 

The expression given is 3 + 2³ × (25 – 3).

The bracket is taken first.

(25 – 3) = 22

Then 3 + 2³ × 5

The calculation is done in order 2³ = 2 × 2 × 2 = 8.

8 × 22 = 176

The addition operation is performed next.

3 + 176 = 179

The final answer is 179.

Question 4: Simplify the expression using BODMAS rule √4 ÷ 2 – 5 × 6 + 1.

Solution: 

The square root is found out first.

√4 = 2

Then 2 ÷ 2 – 5 × 6 + 1

Perform division

2 ÷ 2 = 1

Then, 1 – 5 × 6 + 1

Multiplication is performed.

5 × 6 = 30

We have 1 – 30 + 1

Perform the addition part.

1 + 1 = 2

We get 2 – 30 = -28.

The final answer is -28.

Practice questions

Try to solve more questions ranging from easy to moderate levels to understand its applications.

1. Solve the expression using BODMAS rule {100 – (10 + 5) + 90}.
2. Solve (1 / 4 + 1 / 8) of 64
3. Simplify: 16 + 3 (4 + 2) + 40 – (2 + 3 × 3)
4. Evaluate: [{(90 + 45 ÷ 3 × 3) × 2} ÷ 1 / 2] × 100

Conclusion 

To simplify any given equation, the BODMAS rule is applied. Though the equation may look complicated, if the rules are followed seriously, it becomes very easy to solve any complex expression with ease. Practice more questions and gain perfection.

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Happy practising!

Frequently Asked Questions 

What is the BODMAS Rule of Maths?

It is an acronym for Bracket, Order, Division, Multiplication, Addition and Subtraction. It gives the idea of the sequence to be followed while performing a mathematical equation with many operations. 

Can we Use the BODMAS Rule when there are no Brackets?

Yes, the BODMAS rule can be used when brackets or any other mathematical operation is missing.

Which Arithmetic Operations are Involved in the BODMAS Rule?

Bracket, Order, Division, Multiplication, Addition and Subtraction are used in the BODMAS rule.

What is the Use of the BODMAS Rule?

The BODMAS rule is helpful to solve any mathematical expression that has more than one arithmetic operation. It avoids confusion and is helpful in arriving at the correct solution.

What is the full form of BODMAS?

BODMAS is an acronym for Bracket, Order, Division, Multiplication, Addition and Subtraction.