BODMAS Rule

BODMAS Rule Definition and Order of Operations is an abbreviation in which each alphabet has its own identity. In this B is for Brackets, O is for of (also powers and roots), D is for Division, M is for Multiplication, A is for Addition and last alphabet S is for Subtraction. In some regions of the world, it is also known as PEDMAS - Parentheses, Exponents (represents of), Division, Multiplication, Addition and Subtraction. This rule explains the order of operations to solve an expression if more than one arithmetic sign is involved. According to Rule of BODMAS, the brackets have to be solved first followed by powers or roots, then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS is applied very cautiously.

 One must note if there are no brackets or orders then follow DMAS

Here, the BODMAS rule states we should calculate operations which is mentioned inside the Brackets first (7+ 4 = 11), then the Orders (32 = 9), then any Division and Multiplication (3 x 6 (the answer to the brackets) = 18), and lastly any Addition and Subtraction (18 + 25 = 43).

The four basic mathematical operations--additionsubtractionmultiplication, and division--have application even in the most advanced mathematical theories. Thus, mastering them is satisfies the basic need of studying mathematics. It is the root for all the branches of Mathematics The student must understand these basic yet most important concept to progress in Maths and develop interest

In the following videos I have explained in a step by step approach the detailed concepts of BODMAS principles. I have also solved lot of questions of various difficulty levels which will help you to understand the concepts and also how to solve various types of questions which can come in your exams.

 

Introduction to BODMAS

Mathematics has engraved itself as one of the vital structures in the development of science in humanity. In some scientists' theory, all the living activities and the universal activities are based on specific calculations and analysis. To aim for the greatest, we need first to build the foundation. Therefore, mathematics is included in the students' academic curriculum from the beginning of their educational journey.

Students are introduced to numerous formulas and mathematics theories, which helps them learn, analyze, and implement. The BODMAS method is one of the crucial Mathematical formulae, which all of us have come across once in our childhood. So, let dive in to witness the origin of the BODMAS Rule. 

Achilles Reselfelt established the BODMAS theory to standardize an easy and convenient mechanism to solve complex problems, with operational signs in a specific algorithm. The BODMAS Rule applies to any question which involves arithmetic operators' implementation.

It defines the order of operators precedence used throughout mathematics, computer programming languages, science, technology, and many more. Apart from Mathematical grounds, some of the vital computer programming languages, such as Smalltalk, APL, Occam, and Mary, also implements the BODMAS principles to clarify different questions.

So now let's find out what the BODMAS Rule says – 

 

BODMAS Rule 

The BODMAS Rule is one of the concepts of logic-oriented subjects like Mathematics. The order of operation in such subjects defines a bundle of rules that standardize an algorithm declaring the process to initiate first while solving a problem. You can also learn the BODMAS rule in Hindi.

When we operate with one sign or one arithmetical operator, it seems to be a child's play to solve a problem, as we either have to multiply, divide, add, or subtract the numbers. But the tension arises when you need to work with multiple operators in any question. This determines a puzzling situation in which operate to give the first preference.

Here the BODMAS Rule dives in as a rescue. Curious to know the BOSMAS Meaning?

BODMAS stands for B -Brackets, O- Of, D-Division, M- Multiplication, A-Addition, S- Subtraction. A term quoted as PEDMAS – Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction is also famous among some. Both the terms work identically to establish an efficient procedure of which operator to work with in the first step of solving a problem. 

The BODMAS Rule states that we must begin with the brackets followed by of (powers and roots) in a problem that involves multiple operators. We must gradually move from Division towards Multiplication, then addition and at last Subtraction. If you try to solve the question disobeying the BODMAS Rule or the right hand, it will output the wrong answer. 

 

BODMAS Order of Operations

The term Operation portrays things such as addition, multiplication, square, division, Subtraction, etc. But how to work with a set of an operator in the same problem? 

For instance, let's say the question is – 

9+ (7*2)-9

Seems Confusing, right? Here it would be best if you had BODMAS.

BODMAS is a fruitful acronym that defines the order of solving a problem. Now that you are familiar with the BODMAS Meaning, it's quite clear that following the BODMAS Rule's ideologies is extremely vital, or else you get the wrong answers.

BODMAS Order of Operations states that to solve a problem conveniently and efficiently, you need to solve it according to BODMAS moving from left to right.

Let's say, 

9+ (7*2)-9 is the question you need to solve.

Firstly, you need to start working with the brackets. So, after optimizing the terms inside the bracket, the equation turns to 9+14-9 

Now, we need to perform the Addition part, so the equation now turns to 23-9

At last, get your answer by subtracting the terms, and this expression delivers 14 as the correct answer.

 

BODMAS Calculator

BODMAS Calculator is a widely used mathematical software, identical to the traditional calculator we use to perform different mathematical calculations. The only point of difference between the two is the BOMAS Calculator works on the principle defined by the BODMAS Meaning or by the PEDMAS Rule—implying Brackets, Of, Division, Multiplication, Addition, and Subtraction.

Let's take an example if we enter a BODMAS Question: 8*5*(9-5) in the BODMAS calculator.

The calculator will firstly analyze the question and will try to search for the brackets. If the brackets are marked, it will work on the operation inside the brackets to produce: 8*5*4

Now in the second check, it runs to search for any square or root operators. If found, it will function accordingly, and if the search goes in vain. The calculator starts a search for a multiplication operator. If it is found, the calculator produces the respective output, is the search is unsuccessful, then it relies on getting the additional operator to work accordingly. After that, it checks for the multiplication operator to produce the ultimate output to the user. As in this case, the BODMAS Calculator will produce 160 as a result.

 

BODMAS Problems

Please scroll down to find some of the BODMAS Questions and their solutions with an increasing difficulty level.

Some of the BODMAS Problems are as follows –

 

Question 1-

1800÷10 {(12−6) + (24−12)}

1800÷10 {6+12} (performing calculations in bracket first)

=1800÷10 {18}

= 1800÷10×18 (performing division first)

 = 180×18

 Output = 3,240

 

Question 2 - 

1/2[{−2 (1+2)}10] (performing calculations in bracket first)

= 1/2 [{-2(3)} 10]

= 1/2 [{-6} 10]

= 1/2 [-60] (performing division first)

  Output= -30

 

Question 3 – 

(−40) × (−1) + (−28) ÷ 7 (performing division first)

(− 40) × (− 1) + (− 28) ÷ 7 (performing multiplication first)

 = 40 + (− 4)   

Output = 36

 

Question 4 – 

(−3) × (−4) ÷ (−2) + (−1) (performing division first)

= (−3) × 2 + (−1) (performing multiplication first) = −6 − 1 

Output = -7

 

Question 5 – 

3 x (4 x 5²) ÷ 6 + 7 – 8 (performing bracket calculations first)

 = 3 x (4 x 25) ÷ 6 + 7 – 8(perform squaring first)

 = 3 x 100 ÷ 6 + 7 – 8 (perform division followed by multiplication)

= 50 + 7 – 8

Output = 49

So, are some examples of BODMAS Rule in the form of BODMAS Problems along with their solutions.

Some people demand explanations in their native language. Let's say they want BODMAS Hindi. If you have a good grasp of Hindi and want to learn BODMAS Hindi, you can visit Hindi websites and YouTube channels.

 

Frequently Asked Questions

Q1: What are BODMAS Rule examples?

Ans – For instance, take 3+ (8-1)*5 as a BODMAS Question. Here, the first thing we need to do according to the BODMAS principles is to start working with the expression inside the brackets, so here 8-1 is the expression, solving it we get 7. So now, the equation stands as 3+7*5. Next, we must look for the operator, followed by division, multiplication, addition, and then subtraction operators. Here on apply BODMAS, Meaning we first must do the multiplication part to construct the equation as 3+35. Now we can add the terms to generate 38 as the output.

The BODMAS Rule suggests that we must follow the strict guidelines to grasp the correct answer.

 

Q2: Why is BODMAS Rule important?

Ans – Calculations using one operator are easy, but when multiple operators enter in an equation is produced the tide of confusion on which operator to work first. The logically disciplined subject Mathematics thus introduced the BODMAS System in the scene.

BODMAS Rule is one of the fruitful descriptors that determines the order within which we can solve a mathematical issue. And one must strictly follow these guidelines to produce the correct result.

The BODMAS description is given below –

  1. Brackets (parts of a calculation inside brackets always performed first).
  2. Orders (numbers including powers or square roots).
  3. Division.
  4. Multiplication.
  5. Addition.
  6. Subtraction.

 

Q3: Why do we implement BODMAS?

Ans – BODMAS Rule helps us remember the exact mechanism to solve any diplomatic problem that involves multiple operators. Moreover, it's one of the easy methods to remember for young children or students. The BODMAS Rule guides them to organize an equation and solve it systemically following a proper algorithm.

We can use the rule to simplify the tough questions using the proper guidelines. Any expression that remains in the brackets must be handled first, following the OF operator (square and roots). We must proceed with the Division Operator, and simplify the equation to generate the correct output by conveniently solving the Multiplication, Addition, and Subtraction Operator one by one.

 

Q4: How does the BODMAS Rule work?

Ans – The easy to follow guidelines portrayed by the BODMAS Rule made it one of the most convenient formulas to grasp. It simply explains the order of precedence of the operators. The BODMAS Rule or the PEDMAS Rule states that –  

The expression inside the parenthesis or brackets must be handled first.

Then you must work on the squaring or roots part of the equation.

Now, you can solve the multiplication part.

Following this, we must look to simplify the division parts of the equation.

Then, it would help if you simplified the Multiplication section of the expression.

Now it's turn for the Addition part of the equation.

And at last, simplify the Subtraction part to generate the output.

 

Q5: How can you calculate BODMAS?

Ans – If you work following the BODMAS Rule, you must begin to solve the expressions in the brackets or parenthesis of the given equation, followed by squaring, division multiplication, addition, and at the end subtraction. BODMAS Rule, or PEMDAS, is the key to solve complex equations that involve more than one operator to generate perfect results.

When you are stuck with a mathematical equation that involves multiple operator BODMAS, ease the pressure. Everything inside the parenthesis must be solved first, followed by the squaring, multiplication, division, addition, and subtraction parts. BODMAS here turns to be the portal to the right answer, so your output may come wrong if you disobey these guidelines.

 

Q6: How to solve the BODMAS Problems easily?

Ans – To solve the BODMAS Questions with ease, you need to establish a strong understanding of the rule's methodologies. A thorough understanding of the guidelines will simplify complex problems to easy equations using the BODMAS Rule. The next step that you must turn to is Practise.

As you know, Practise is the key to perfection; you need to practice solving various problems implementing BODMAS. Start from the lower level of difficulty and try to conquer the apex of complex BODMAS Questions. You can also use different books and online platforms like YouTube to learn BODMAS Hindi to grasp the theory with ease.

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