As we know Mathematics has become the basic need of human beings. That’s why all the students must learn at least basic mathematical concepts like the BODMAS rule. 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 that 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 (2×4-3+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 the 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;
Ø B → Bracket
It means that firstly, 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 [].
Ø O → Of or Orders
It means that you will have to solve all the numbers which have powers and brackets.
Ø D → Division
It means that you have to perform the division operation.
Ø M → Multiplication
After that, you have to perform the multiplication operation.
Ø A → Addition
After that, you have to add the numbers or terms.
Ø S → Subtraction
At last, you have to subtract the numbers and terms.
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What is the Alternative to the BODMAS rule?
There are also some regions where the PEMDAS rule is used instead of the 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 the BODMAS rule and the PEMDAS rule are two similar rules. It means that either you are using the BODMAS rule or the PEMDAS rule, you will get the same answer. The only difference between the BODMAS rule and the PEMDAS rule is that in the BODMAS rule, you will have to perform a division operation before the multiplication operation. On the other hand, in the PEMDAS rule, you will have to perform a multiplication operation before the division operation.
Who Invented the BODMAS Rule?
Firstly, 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 mathematical signs. When you are going to solve more than one mathematical operation in a mathematical problem, you will have to apply the BODMAS rule.
Use of the 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
i. First Step
In the first step, we should solve the bracket according to the BODMAS rule. After solving the bracket, we get the answer 12.
12 x 5
ii. Second Step
Now, we have to multiply 12 and 5. After multiplication, we get the answer 60.
60
Example 2
15 ÷ 3 × 1 + 5
i. First Step
After getting an idea about the orders of different operations of the BODMAS rule, we try to solve mathematical problems by using this rule.
5 × 1 + 5
ii. Second Step
After that, we have to perform a multiplication operation. After performing this operation, we get the following thing;
5 + 5
iii. 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)}]
i. First Step
In the first step, we have to solve (). After solving it, we get:
4[2+{7×2}]
ii. Second Step
Now, we have to solve {}. After solving it, we get:
4[2+14]
iii. Third Step
Now, we have to solve []. After solving it, we get:
4×16
At last, we have to multiply these two terms. After multiplying 4 and 16, we get the answer 64.
64
Example 4
20 x 2 – (4/2) x 9 x 2^2
i. First Step
20 x 2 – (4/2) x 9 x 2^2
ii. Second Step
20 x 2 – 2 x 9 x 2^2
iii. Third Step
20 x 2 – 2 x 9 x 4
iv. Fourth Step
20 x 2 – 72
v. Fifth Step
40 – 72
vi. Sixth Step
-32
By following these techniques, you will be able to solve any kind of mathematical operation.
Self-Practice Examples Relevant to BODMAS Rule
I think, after reading this article, you have completely learned the order of operations of the BODMAS rule. Moreover, I have also explained the order of operations with the help of examples. Now, it’s time to practice. The reason is that we can’t learn math just by reading the articles or content from the books because math requires practice. Therefore, I am sharing some examples of self-practice. After solving these examples, you should share the answers to these problems in the comment box. I will assign marks after checking your answers.
i. 5 + (4 × 52 + 3)
ii. 2000÷10(12−6) + (60−10)
iii. 30 × 2 − (4/2) × 10 × 2^2 .(Here, ^ is used for power or exponent)
iv. (3^3 – 2 × 2) + (5 × 4 – 2^2)
v. 4/2[{−2(1+3)}20]. Here, / stands for division.
vi. 5 × (6 + 2) x 4
After solving these problems by using the BODMAS rule, you should also solve these problems by using the PEMDAS rule. You should also share your experience either you have got the same answers by using these two rules or you have got different answers.
MCQ’s Relevant to BODMAS Rule and PEMDAS Rule
For a quick assessment of the students, we have arranged an MCQ test. You should participate in this test.
1. Which operation comes after division in the BODMAS rule?
a) Addition b) Multiplication c) Subtraction d) Brackets
2. Which operation comes after parentheses in the PEMDAS rule?
a) Division b) Exponents c) Multiplication d) Subtraction
3. The solution to the question by using the BODMAS rule is 5 + 7 X (1) – 6
a) 5 b) 7 c) 6 d) 8
4. The answer to this question (12 + 8 X 6)/ 5 – 5 is:
a) 7 b) 10 c) 8 d) 9
5. The answer to the question (15/3 + 20/4) of 20 is:
a) 100 b) 300 c) 400 d) 200
6. The answer to the question 4/2 [{3(1 + 3) * 20}/2] is:
a) 120 b) 240 c) 280 d) 320
Correct answers:
1. Multiplication 2. Exponents
3. 6 4. 7 5. 200 6. 240
3. 6 4. 7 5. 200 6. 240
Is bodmas is applicable for non bracket pblms
yes
Give me the perfect answer = 15+6×2=?
15 + 12
27
In the example 3 X 5 -1 + 2=
strictly following BODMAS, add before subtract, gives answer 12. However, working from left to right, the answer is 16.
12