Bodmas and the Order of Operations

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To solve a mathematical operation in the correct order, the implication of the BODMAS rule is a must. It is one of the operators in the arithmetic field which is very simple and easy to understand. BODMAS stands for Brackets, Orders (powers/indices or roots), Division, Multiplication, Addition, and Subtraction. All the mathematical operations need to be unraveled from left to right in the order of BODMAS which has multiple operators, which implies first solving the expression in brackets, then the exponential terms, moving ahead with divisions and multiplications, and lastly with addition rather than with subtraction.

The BODMAS rule helps in simplifying mathematical expressions, containing many operations like division (/), multiplication(x), addition (+), subtraction (-), and so on. Also, Expressions of multiple brackets can be solved simultaneously. For example, (29+71)/(22-12) = 100/10 = 10. In this article, we will go through the concept of the order of operations and we will also draw out a comparison between PEMDAS and BODMAS along with solving a sum using one of the operators.

What Do You Mean by Order of Operations?

Order of operation simply implies the rules in which certain operations must be solved like BODMAS (from bracket to order of powers to division and multiplication and lastly with addition and subtraction). Operations in mathematics refers to additions (+), subtraction (-), division (/) and multiplication (X). These operations are used to evaluate the mathematical expressions and the set of rules followed in sequence while solving the expression is the order of operations. For example: 3 x (8+7) = 3 x 15= 45  is the correct way of solving the given problem. However, 3 x (8+7) = 24 + 7=31 is not the correct way since it does not follow the rules of BODMAS. From the given example, we understand that first, we have to add the values inside the bracket, then multiply it with the other value that is 3 to get the correct answer using the BODMAS rule.

Various Rules of Order of Operations

  • Rule 1- The first rule is that the values inside the parentheses or brackets should be solved. Order to solve the parentheses i.e. [ { ( ) } ], Round brackets () should be solved first, then curly brackets {} and lastly the box brackets [].
  • Rule 2- Next the exponents should be solved if given any.
  • Rule 3- Now we should solve the operation of multiplication or division, in order from left to right. Division should be considered first. Once the operation of division is solved, we can then proceed to solve the operation of multiplication.
  • Rule 4-Lastly solve the operation with addition and then with subtraction from left to right.

PEMDAS VS BODMAS

PEMDAS OR BODMAS are the two different types of order of operations, both having their own specific rule to solve the mathematical expression using the operators. The comparison for both the operators is given below in the form of a table. 

PPARENTHESIS (), {}, []BBRACKETS (), {}, []
EEXPONENTS (a2)OORDER OF ROOTS
MMULTIPLICATION (X)DDIVISION (/)
DDIVISION (/)MMULTIPLICATION (X)
AADDITION (+)AADDITION (+)
SSUBTRACTION (-)SSUBTRACTION (-)

Solved Example

  1. Solve: { 3 – 7 * 3 (5 + 1) + 3 (30 ÷ 6)}using the rule of BODMAS.

Solution: We know about the rule of BODMAS and thus we will solve brackets first, move on to carrying out the operation of the division followed by multiplication, and then we will move on to carry out the operation of addition and subtraction. 

So, { 3 – 7 * 3 (5 + 1) + 3 (30 ÷ 6)}= { 3 – 7 * 3 (6) + 3 (5)} 

= { 3 – 7 * 18 + 15} = { 3 – 126 + 15 } = { 3 – 141} = -138.

Thus, the required answer using the rule of BODMAS is -138.

If you want to master the concepts of BODMAS and the order of operations in a fun and interactive manner, visit Cuemath.