BODMAS

BODMAS is an acronym that stands for the bracket, of division, multiplication, addition, and subtraction. It explains the order of operations to solve an operation. According to the BODMAS rule, if any expression contains brackets, then we first need to solve the bracket followed by then, division, multiplication, addition, and subtraction in the order of left to right. If the problem is solved, then the answer obtained will most certainly be wrong. 

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Note- The “of” in BODMAS in its full form stands for ‘order,’ which refers to the numbers which contain powers, square roots, etc.

BODMAS Rule

Let’s understand the BODMAS rule with the help of mathematical operations. Imagine in an equation you have to perform some operations, then how will you decide which operation should be used first and which needs to be done after.

For example: 25×5+46÷2=?

In this expression, the BODMAS rule comes pretty handily. It provides us an understanding of the order of operations. Here, in this case, according to BODMAS rule, first, we need to perform division, followed by Multiplication and then added, which leads to the correct answer that is 48. 

Use of bracket

let’s take a look at the use of brackets first; it is a very vital part of forming and the evaluation of mathematical expressions. Let’s take an example, let’s say you went to one store and decided to buy ten oranges and 2 of them cost Rs 10 each, but the price is not the same for all, 4 of them cost Rs 5 each, and the remaining four cost Rs 20 each. Now, this situation can be shown mathematically as 

2×10+5×4+4×20= 120

But this equation seems to be very confusing, doesn’t it? While you are evaluating this expression, you might be confused about which operation needs to be done first, and you most probably will end up making errors. So to solve this problem, we can use brackets to represent it in an easier way

(2×10) + ( 5×4 ) + ( 4×20 )

This is way easier as compared to the equation written above because this is what we call an organized representation of an expression, now you will have a better understanding of the use of brackets. This also proves that the use of brackets is a must in mathematics. 

BODMAS Full Form

Every single letter of the word BODMAS contains a very important meaning to understand it’s meaning. So to have a better understanding of what is called BODMAS, we will break it down into its constituent letters

  • B– This letter stands for the term ‘bracket’ In the word BODMAS and it is present at the very start of the word because while performing any mathematical operation, the solution of the bracket needs to be found first. 
  • O– This letter stands for the meaning’ order’ which can be regarded as an umbrella term because it contains powers, square roots, etc.
  • D– This letter is in the word BODMAS to make us understand the order of usage of a division operation. 
  • M– Just like division, Multiplication is also a very essential and common mathematical operation, which here in the word BODMAS is shown by the letter M.
  • A-here in the word BODMAS ‘A’ is used to refer to the mathematical operation ‘addition,’ which has its order after the multiplication operation. 
  • S– ‘S’ is used in this word to refer to the mathematical operation’ subtraction’ which is supposed to be solved at last while solving an equation or expression using BODMAS theorem.  

BODMAS Questions

Now I order to understand this rule better we will look at some of the exemplary problems, 

Q– what will come in place of question mark in the question given below?

240÷8 ×512÷4 +1/2 of {1800÷( 11×24÷8×3-69)2}

  1. 4111
  2. 4456
  3. 2424
  4. 3841

Solution– the expression is given to us is 240×8÷512÷4+1/2 of {1800÷(11×24÷8×3-69)2}

According to the rule we are trying to understand, i.e., BODMAS, we first need to solve the problem inside the brackets

Here in the given equation, first, we will solve the curly bracket, and inside the bracket, we will again apply the BODMAS rule. Inside the curly bracket once again, a new bracket has appeared, so we solve this bracket first. Inside of these smaller brackets, nothing like ‘of’ or ‘order’ exists. Hence we proceed with the following order in BODMAS.

We can see multiplication, division, and subtraction signs. Since Multiplication and divisions are of the same rank, we go left to right to solve this. First, we multiply, and then we divide. Then we do the second Multiplication. And it’s only after that we proceed to the subtraction. 

Here are the steps that are given to better understand this process.

  • =240÷8×512÷4+1/2 of {1800÷(11×24÷8×3-69)2}
  • =240÷8×512÷4+1/2 of {1800÷(33×3-69)2}
  • =240÷8×512÷4+1/2 of {1800÷(99-69)2}
  • =240÷8×512÷4+1/2 of {1800÷(30)2}

Now we have solved the small brackets, and here we are welcomed by our first exponent. So we need to solve this ahead of division.

Now solving curly bracket,

  • =240÷8×512÷4+1/2 of {1800÷900}
  • =240÷8×512÷4+1/2 of 2

So far, we have solved all the brackets, and now we can move to the next step where we come across our first ‘of’ which we treat simply as Product or ‘multiplication.’ But keep in mind that ‘of’ should be solved before a regular multiplication.

  • =240÷8×512÷4+1/2×2
  • =240÷8×512÷4+1

Now we are away from our expression of all brackets, exponents, and ‘of.’ We now move to the third step, where we perform all the multiplications and divisions. Remember that these two expressions are of the same rank. So we perform either in the order we came across them in, i.e., from left to right.

  • =30×512÷4+1
  • =15360÷4+1
  • =3840+1
  • =3841

Hence the required answer is 3841. This was one example explained in the most detailed version to help you understand how to use this rule to solve BODMAS questions for competitive exams. This rule can be used to solve as many simplification problems or quant problems. 

BODMAS Formula

BODMAS is a useful acronym that lets us know in which order to solve mathematical problems or let’s say sums. It’s very important that one follows the rules of BODMAS as without doing that, the answers obtained will certainly be wrong. 

  • Brackets– start with anything inside brackets going from left to right.
  • Orders– The next step is solving anything involving power or square root, now again go from left to right if there are more than one.
  • Division and Multiplication– once you have finished the parts involving brackets of the question, the next step is division and Multiplication. Multiplication and division rank equally so you can go from left to right in the sum, doing all the operations in the order in which they appear. 
  • Addition and subtraction– The final and last step is to calculate any sort of addition or subtraction. Just like Multiplication and division, addition and subtraction also rank equally, so one can simply move from left to right.

BODMAS Meaning

In mathematics and computer programming, the order of operations is a set of rules which reflect conventions about which procedures should be performed first to evaluate a given mathematical equation or operation.

For instance, in mathematics and most computer languages, Multiplication is given higher precedence than addition, and this has been the way since the introduction of modern algebraic notation. Hence the expression 2+3×4 is interpreted to have a value 14 and not 20. With the introduction of exponents in the 16th century, they have been taking precedence over both the addition as well as Multiplication. And they could oy be placed as a superscript to the right of there base. 

These conversations exist only to eliminate ambiguity while allowing notation to be as brief as possible. Where these are desired to override the precedence conventions or even simply to emphasize them, parenthesis or braces can give the indication of alternate order or reinforce the default order to avoid the confusion. 

BODMAS problems and examples- 

Question- 25-48÷6+12×2=

Solution

  • 25-8+12×2
  • =25-8+24
  • =17+24
  • =41

Question- 78-[5+3 of (25-2×10)]

Solution-

  • 8-[5+3 of (25-20)]
  • 78-[5+3 of 5]
  • 78-[5+3×5]
  • 78-20
  • 48

BODMAS Rule in Mathematics

The BODMAS rule is an acronym to help the kids remember about the order of mathematical operations, the right order in which the problems should be solved. Some kids also use it as a mnemonic.

One might have also heard of referred to it as BIDMAS, but other than the letter difference, there is no difference in the meaning of these two terms.

Mathematical operations are what you do to the numbers given-

The four main operations are-

  1. Addition
  2. Subtraction
  3. Multiplication
  4. Division

Orders mean square roots or indices. 

BIDMAS stands for-

  1. Brackets
  2. Indices
  3. Division/Multiplication
  4. Addition/subtraction

Here indices are used instead of orders as done in the BODMAS.

This is the order in which the mathematical operations are supposed to be done, from brackets first to addition and subtraction last.

Division and Multiplication must be shown alongside each other as they are of equal importance, which is also the case of addition and subtraction.

As a parent and a guide to your children, to support them in solving order of operations questions, you will find that most calculators and also computers nowadays are good enough to complete calculations according to BODMAS. However, it’s worth testing the calculators just to be sure. And for your utter convenience, there are also plenty of calculators available online.

BODMAS or PEMDAS

Both are mnemonics for the order of operations of binary infix operations in arithmetic. BODMAS, BIDMAS, and PEMDAS are all acronyms for remembering the order of operations in mathematics. BODMAS stands for brackets, orders, division, multiplication, addition, and subtraction. 

BIDMAS and PEMDAS do the same work but just use different words. BODMAS explains the order of operations in mathematics, and BIDMAS and PEMDAS do the same thing but using different words for that.

In the case of the mathematical acronyms BODMAS, BIDMAS, and PEMDAS, they all mean the same thing, and all servy the same purpose. Now going deeper into the concept, orders, indices, and exponents are the little superscript numbers which represent power in mathematics. 

Brackets, Multiplication, division, addition, and division, are the words with which we are very familiar, but what of the second element of the acronyms-orders, indices, or exponents? These are the half-size numbers that many times occur in mathematical expressions. 

A mathematical operation can be thought of as one of the symbols which make something occur, or let’s say happen in mathematics. A multiplication sign means that two numbers need multiplying together while an addition sign shows that the two numbers between which it is present need to be added. These types of activities in mathematics are together called operations. 

The correct order of these operations in mathematics is brackets, orders, division, multiplication, addition, and subtraction. But while using BODMAS, one should remember to replace the word orders with indices even when they perform almost the same function. The whole point of BODMAS and BIDMAS is to make a guy remember which operations need to be done in which order. Not to be very fortunate, mathematics dictates that this is not the order from left to right as a person looking at it might expect. These are all the things one needs to know to have enough knowledge to perform any operation, which is mathematical using BODMAS, BIDMAS, or PEMDAS. These rules are very important to solve the questions which are there in the curriculum textbooks. Not only textbooks require knowledge of these rules and terms but almost all the competitive exams which are there in the country in which basic mathematics has even the smallest weightage, these rules and terms will turn out to be very useful.

To remember these rules, try learning them alongside the regular practice of questions, which will help you understand how these terms or more precisely rules work. The importance of these questions can only be understood after solving the questions based on these.

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About the Author

Piyush values education and has studied from the top institutes of IIT Roorkee, IIM Bangalore, KTH Sweden and Tsinghua University in China. Post completing his MBA, he has worked with the world’s # 1 consulting firm, The Boston Consulting Group and focused on building sales and marketing verticals for top MNCs and Indian business houses.

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