How to use BODMAS rule to find the order of operations?

As we know that Mathematics has become the basic need of human being. That’s why it is necessary for all the students to learn at least basic mathematical concepts. While learning mathematics, we have to solve lots of problems. The nature of some problems is such that it is easy for us to solve these problems. On the other hand, there are also some complicated problems which are hard to solve for us. It means that if we are going to solve mathematical problems like (2 x 8), (16/4), (6 – 3) and so on, it is easy for us to solve these kinds of problems. Its reason is that these kinds of problems have only one operation. On another hand, when we are going to solve some arithmetic operations which involve more than one operation like (2x4-3+4), it is hard for us to understand how to solve this problem because we are not able to understand which operation should be solved first. Under such a situation, we have to use a specific rule and that rule is known as BODMAS rule.
What is BODMAS rule?

 What is BODMAS rule?

BODMAS is an acronym and by understanding this acronym, it is easy for us to keep in mind the order of the operations while solving different kinds of mathematical problems or operations. The meanings of different words of this acronym are given below;
B → Bracket
It means that first of all, we have to solve the brackets in the mathematical operation. As there are four different kinds of brackets. First of all, we have to solve “━━━━”. Secondly, we have to solve (). Thirdly, we have to solve {}. At last, we have to solve [].
O → Of or Orders
It means that you will have to solve all the numbers which have powers and brackets.
D → Division
It means that you have to perform the division operation.
M → Multiplication
After that, you have to perform the multiplication operation.
A → Addition
After that, you have to add the numbers or terms.
S → Subtraction
At last, you have to subtract the numbers and terms.

What is the alternative of BODMAS rule?

There are also some regions where PEMDAS rule is used instead of BODMAS rule. The acronym of the PEMDAS rule is given below;
P → Parentheses
E → Exponents
M →Multiplication
D → Division
A →Addition
S → Subtraction
It is considered that BODMAS rule and PEMDAS rule are two similar rules. It means that either you are using BODMAS rule or PEMDAS rule, you will get the same answer. The only difference between BODMAS rule and PEMDAS rule is that in BODMAS rule, you will have to perform division operation before the multiplication operation. On the other hand, in PEMDAS rule, you will have to perform multiplication operation before division operation. 

Who invented the BODMAS rule?

First of all, the BODMAS rule was introduced by Achilles Reselfelt. The main aim of introducing this kind of mathematical rule was to solve those problems which involve the mathematical signs. When you are going to solve more than one mathematical operation in a mathematical problem, you will have to apply BODMAS rule.

Use of BODMAS rule with the help of examples

After getting an idea about the orders of different operations of the BODMAS rule, we try to solve mathematical problems by using this rule.

Example 1

(6 + 6) × 5

First Step

In the first step, we should solve the bracket according to BODMAS rule. After solving the bracket, we get the answer 12.
12 x 5

Second Step

Now, we have to multiply 12 and 5. After multiplication, we get the answer 60.
60

Example 2

15 ÷ 3 × 1 + 5

First Step

First of all, we have to solve the brackets. In this case, we don’t have brackets. Therefore, we should perform other basic operations. It means that we have to divide 15 and 3. After performing the division process, we get the answer 5.
5 × 1 + 5

Second Step

After that, we have to perform a multiplication operation. After performing this operation, we get the following thing;
5 + 5

Third Step

At last, we have to add these two terms. After adding 5 and 5, we get the answer 10.
10

Example 3

4[2+{7(5-3)}]

First Step

In the first step, we have to solve (). After solving it, we get:
4[2+{7x2}]

Second Step

Now, we have to solve {}. After solving it, we get:
4[2+14]

Third Step

Now, we have to solve []. After solving it, we get:
4x16
At last, we have to multiply these two terms. After multiplying 4 and 16, we get answer 64. 
64

Example 4

20 x 2 – (4/2) x 9 x 2^2
First step: 20 x 2 – (4/2) x 9 x 2^2
Second step: 20 x 2 – 2 x 9 x 2^2
Third step: 20 x 2 – 2 x 9 x 4
Fourth step: 20 x 2 – 72
Fifth step: 40 – 72
Fifth step: -32
By following these techniques, you will be able to solve any kind of mathematical operation.
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