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# Simplification on BODMAS Rule

The number series in the aptitude section is a very important topic for competitive exams. This topic is divided into several small topics and one such topic is a simplification. In this, a topic the questions asked is related to the BODMAS rule. This rule is very common in mathematics. It stands for Bracket Of Division Multiplication Addition and Subtraction. Thus, today we are going to cover simplification on BODMAS rule.

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The simplification on BODMAS rule is the topic which is related to the questions asked with brackets. You have solved the question according to the numbers and mathematical signs given in the bracket. There are some simple rules which will help you solve these questions easily.

### Steps to solve BODMAS Question

Step 1: Always remember to solve the expressions that are in the bracket first. Also, while solving these brackets you need to apply the BODMAS rule first.

Step 2: After solving the brackets, you need to solve the mathematical operators ‘order’ and ‘of’ next. Here, ‘of’ means a part of and it is solved by replacing it with a multiplication sign. While ‘order’ is similar to an exponent. After the brackets are solved, powers are solved. This also includes the roots.

Step 3: In the next step, the equations that have multiplication and division sign in it is solved. You need to calculate this after completing the above 2 steps.

Step 4: At the end, you need to solve the equations that contain ‘subtraction’ and ‘addition’. Here you can notice that these steps also followed the BODMAS rule.

### Simplifying the Brackets

The expansion of brackets is known as the simplification of the brackets. To remove the brackets from an expression, you need to expand them by multiplying them. Also, for this step, you can use the distributive law. It is written as

a(b + c) = ab + bc

For brackets also there is a rule that you need to follow while simplifying them. You need to follow the order of (), {}, [ ] for solving the brackets. This means that you solve the equations in the () bracket first and then the other two.

### Example:

320 ÷ 8 x 412 ÷ 4 + 1/2 x {1800 ÷ (8 x 24 ÷ 6 x 4 – 98)^2}

Solution:

As mentioned in the above steps, you need to start solving the equation by solving the brackets first. We will also follow the rules of the bracket in this question where we will solve the round bracket and then solve the curly bracket. Also, there is no ‘ off’ and ‘order’ in the brackets. So, we will directly start by applying the BODMAS rule. Thus, we will start with multiplication and division. Here both the mathematical signs are of the same rank so we will go from left to right to solve this question. So, we will do the multiplication first and then we will do the division.

Here are the steps that we will follow to solve the question:

Thus,  320 ÷ 8 x 412 ÷ 4 + 1/2 x {1800 ÷ (8 x 24 ÷ 6 x 4 – 98)^2}

= 320 ÷ 8 x 412 ÷ 4 + 1/2 x {1800 ÷ (8 x 4 x 4 – 98)^2}

=> 320 ÷ 8 x 412 ÷ 4 + 1/2 x {1800 ÷ (128 – 98)^2}

=> 320 ÷ 8 x 412 ÷ 4 + 1/2 x {1800 ÷ 30^2}

Now we have solved the round bracket. This will be followed by solving the curly bracket.

So, 320 ÷ 8 x 412 ÷ 4 + 1/2 x {1800 ÷ 900}

= 320 ÷ 8 x 412 ÷ 4 + 1/2 x 2

= 320 ÷ 8 x 412 ÷ 4 + 1

Thus, we have solved our brackets entirely. Now we simply have to solve the equation using BODMAS rule. We will start with division and multiplication and this will be followed by addition and subtraction.

320 ÷ 8 x 412 ÷ 4 + 1

= 40 x 103 + 1

=> 4120 + 1

=> 4121

So, the answer required was 4121.

## Practice Questions

Q. Find the number that will come in place of ‘ ?’.

48 + 26 – 10 x 1/2 of 20 – {96 ÷ (34 – 2)} = ?

A. 22                    B. -29                  C. 44                 D. 36

Q. 20 + 12 ÷ 6 + 4 x 16

A. 94                     B. 96                    C. 98                  D. 91

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