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Following The Right Order Of Operations Using Bodmas Rule

Following The Right Order Of Operations Using Bodmas Rule

Mathematics is a challenging subject for most students, and it is the most common subject that students have to struggle with. However, it can become fun and easy for students to solve any math problem with appropriate training, effort, practice, and some tricks up their sleeves. 

So, you might be wondering what these tricks can be? Here, we have the BODMAS rule for you. With the BODMAS rule, students can easily solve any mathematical expression. Interesting, right?

Let us learn more about the rule as we answer your question, “What Is The BODMAS Rule?” 

What Is the Order of Operations? 

The Order of Operations is a method that talks about the sequence in which you can solve mathematical expressions. It states that the expression should be solved by first simplifying the brackets and ending it by simplifying the subtraction at last. And as multiplication and division are of equal rank, they can be solved from left to right in an equation, whichever appears first. The same is applied for addition and subtraction. 

Introduction to the BODMAS Rule

An arithmetic problem that requires multiple operations like division, multiplication, subtraction, and addition is not easy to solve compared to an expression that requires a single or two operations. Therefore naturally, an operation with two numbers can be solved easily, but what happens when you have to solve an arithmetic problem that simplifies brackets, multiplication, addition, and more? Here comes the concept of the BODMAS rule. 

  • The BODMAS rule was introduced by a mathematician called Achilles Reselfelt. 
  • The full form of BODMAS is Bracket, Order, Division, Multiplication, Addition, and Subtraction. 
  • This mnemonic helps determine and remember the order of operations that one needs to follow when solving a mathematical expression. 

As per the BODMAS rule:

  • When you are solving an expression that involves brackets like “(), {}, []”, then you would have to simplify or solve the bracket first.
  • Then you have to follow the order such as the roots, exponents, indices, and powers, followed by division, multiplication, addition, and subtraction. 
  • The expression should be solved from left to right. By solving any complex expression in this order, it prevents the possibility of getting the wrong answer. 

Note: The order in which the brackets need to be solved is (), {}, and lastly []. 

Rules and Conditions For BODMAS 

You need to follow a few rules and conditions during general simplification using the BODMAS rule. These are as follows,

Condition 1: x + (y z) => x y z

Rule: Add the terms after opening the bracket

Condition 2: x-(y z) => x-y-z

Rule: First, open the bracket and multiply the terms inside the bracket with the negative sign. Hence, all positive terms are turned into negative and vice-versa. 

Condition 3: x (y z) => xy xz

Rule: All the terms inside the bracket would be individually multiplied by the term outside the bracket. 

Solving Problems With The Bodmas Rule

Problem 1: 8 + 9 ÷ 9 + 5 x 2 – 7


Now, we will use the BODMAS rule to solve this expression:

First, you have to do the division operation: 9 ÷ 9=1

After that, you would be left with 8 + 1 + 5 x 2 – 7

Now you have to multiply, that is, 5 x 2 = 10

After multiplication, you would have 8 + 1 + 10 – 7

This is the stage where you have to complete the addition, 8 + 1 + 10 = 19

Lastly, perform the subtraction, 19 – 7 = 12

Therefore, the final answer is 12. 

Problem 2: 180÷15{(12–6)–(14–12)}


First you have to start with solving the brackets (),

Now, 180÷15{(12–6)–(14–12)}

=> solve inside the found bracket = 180÷156-2

=> solve inside the curly bracket now = 180÷154

=> divide 180 by 15 = 124

=> when there are no operators before a bracket, consider that has a multiplication operator = 12 x 4

=> multiply 12 x 4 = 48.

Therefore, the answer is 48

Some Common Mistakes That Students Do While Using BODMAS

Here are some common mistakes that students make when using the BODMAS rule. 

  • When multiple brackets are present in a single mathematical expression, students might get confused first about which bracket to solve. When the brackets are not solved in order, one can get the wrong answer. 
  • Sometimes the error occurs when students fail to understand the subtraction and addition of integers. For instance, take the expression 2-5 +6

Now, 2-5 +6 => -3 +6= 3.

However, if you simplify, then, 

2-5 +6 => 2-11= -9. 

In this case, -9 is the wrong answer. 

  • Students may assume that the additional operation has a higher ascendancy than subtraction and that the division operation has a higher ascendancy than multiplication.

Students must remember that both division and multiplication operations are of the same level and should be solved in the sequence left to right. The rule is the same for subtraction and addition and should be performed only after multiplication and division. If one solves division before multiplication that is placed on the left of the division operation as D is before M in terms of BODMAS, they will have the wrong answer. 

Wrapping Up

Hence, you can use the BODMAS rule to evaluate mathematical expressions and apply them to solve any complex calculations that you come across. Usually, a primary school student does not use BODMAS to solve mathematical expressions until the sixth standard. So, if you are facing any difficulty with your maths homework, you now have a cool trick up your sleeve to get an A.

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