What is BODMAS?

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BODMAS rule is a rule in mathematics used to solve the arithmetic expression involving more operators in mathematics. BODMAS helps us to solve an equation involving more operators. It tells us the order to decode the mathematical expression. 


What is the Full Form of BODMAS?

The full form of BODMAS is

  • Brackets (Numbers inside the Bracket always comes first)

  • Precedence of brackets are : [{(bar)}]

  • Orders (the power)

  • Division

  • Multiplication

  • Addition

  • Subtraction

Each letter in BODMAS signifies a mathematical operation. 

It works with an expression having two or more similar mathematical operators that come in succession, and then the precedence is from left to right. By using BODMAS, we can solve an expression based on the precedence. 


The first thing to solve is Anything inside the Bracket. Followed by the evaluation of any powers or roots. Then, do any division or Multiplication in an expression working, but that has to be left to right and then finally complete it by addition and subtraction, which is again from left to right. Hence, division and Multiplication have the same priority, and addition and subtraction have the same priority when solving an expression according to the BODMAS. 

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History of BODMAS

Achilles Reselfelt is a mathematician who invented BODMAS. It is a mnemonic that helps us remember how to evaluate mathematical operators in a mathematical statement involving more than one mathematical operation.


BODMAS Rules

The meaning of BODMAS – 

  • BO- Identify the Bracket and open it – Solve the mathematical operation inside it.

  • D- Division – Solve the numbers involving the division operation. 

  • M- Multiplication- Solve the numbers involving multiplication operation

  • A- Addition – Solve the numbers involving addition operation

  • S-Subtraction- Solve the numbers involving subtraction operations

Example, 

Given, 5 – [2 + 5 of (4 – 3 x 1)]

By using BODMAS Rule,

First simplify the value inside the brackets ()

= 5 – [2 + 5 x (4– 3 x 1 )] “Multiply 3 x 1

= 5 – [2 + 5 x 1 ] “Subtract 1.313 from 2.1”

Simplify the value inside the brackets [ ]

= 5 – [2 + 5 ] “Multiply 5 x1

= 5 – 7 “Add two values inside the brackets [ ]”

Finally, Subtract the values

= - 2

Therefore, the value of 5 – [2 + 5 of (4 – 3 x 1)] is -2. 


BODMAS without Bracket

Yes, it does. If no brackets, the next step is Indices, then Multiplication and Division, then Addition and Subtraction. It says to do Multiplication first and then division, and the other says the reverse.

For example , 

3+ 4 x 2 + 4. -1 

BOD MAS says Multiplication first, so multiply, 4 x 2 

3+ 8 + 4 -1 

BODMAS says addition next, 

3+ 8 +4 = 15 

BODMAS Says subtraction at last 

15 -1 = 14 

The correct answer is 14 using BODMAS. 


What is BODMAS RULE in Maths? 

Mathematics is a logic-based discipline which is applied in various aspects of our life. In arithmetic, an equation or an expression involves two components, which are,

  • Numbers 

A number represents a mathematical value representing a specific quantity and often utilized in counting and many calculations. We use symbols to describe a particular number, which is called a numeral. For example, 3, 4, 8, etc. Numbers can be classified as

1. Natural Numbers

2. Whole Numbers

3. Rational Numbers

4. Irrational Numbers

5. Integers

5. Real Numbers

6. Complex Numbers

7. Imaginary Numbers

The numbers are treated according to mathematical operations. 

  • Operators or Operations: 

A character that combines two numbers, resulting in an expression or equation. The most commonly used operators used in mathematics are as follows :

1. Addition (+)

2. Subtraction (-)

3. Division (÷)

4. Multiplication (x)

In mathematics, the order of operations has defined the rule of BODMAS. A bar is a symbol that is used for grouping the value. The characters which are grouped are treated as a single expression.


Steps for Using BODMAS 

Let’s take this example, 2 x (5 x 5²) ÷ 6 + 7 – 8 =?


Steps:

I. Brackets 

Solve the brackets first.

If you have, 5 x 5² 

5² = 25 

So 5 x 25 = 125


II. ÷× Division and Multiplication 

In the second step, we have both division and Multiplication both. 

This calculation has to be done from left to right

2 x 125 = 375

2 ÷ 250 = 125

Our calculation now becomes 125 + 7 – 8 = ?


III. +- Addition and Subtraction- 

In the third step, we have both addition and subtraction.

This has to be followed the calculation left to right

125 + 7 = 131

 131– 8 = 123

Answer: 123!

FAQ (Frequently Asked Questions)

1. Solve the Following 

a). 1800÷10{(12−6)+(24−12)}


1800 ÷10{16+8}


1800 ÷10{ 24}


1800÷240 = 7.5 


b). 3×(32+4)−8


3X (36) -8 


108- 8 = 100 

2. Simplify the Expression

Ans. 


3 X 4-5 + {(4+5) X (6-2)}


3 X 4-5 + { 9 X 4} 

 

3 X 4 -5 + 36


12 -5 + 36


48 - 5 


43

3. Verify the Expressions

Ans. 


2 + 6 - 3 ( 3 x1) = (2+ 6) -3 x 3 x1 


2 + 6 - 3 (3) = 8 -3 x3 x1 


2 + 6 -9 = 8 - 9  


8-9 = 8-9 


True, LHS = RHS

4. Can we use BODMAS in an Expression without the Bracket. For Example, 

 5 + 3 - 2 - 8 -2 x 2 

Ans. Yes, we can use 


5 + 3-2 -8 - 4


8 - 14 = -6