What is the BODMAS rule?

    BODMAS rule is an acronym that is used to remember the order of operations to be followed while solving expressions in mathematics. BODMAS stands for B - Brackets, O - Order of powers or roots, (in some cases, 'of'), D - Division, M - Multiplication A - Addition, and S - Subtraction. It means that expressions having multiple operators need to be simplified from left to right in this order only. First, we solve brackets, then powers or roots, then division or multiplication (whichever comes first from the left side of the expression), and then finally, subtraction or addition, whichever comes on the left side.

In this lesson, we will be learning about the BODMAS rule which helps to solve arithmetic expressions, containing multiple operations, like, addition (+), subtraction (-), multiplication (×), division (÷), and brackets ( ).

What is BODMAS?

    BODMAS, which is referred to as the order of operations, is a sequence to perform operations in an arithmetic expression. Math is all about logic and some standard rules that make our calculations easier. So, BODMAS is one of those standard rules for simplifying expressions that have multiple operators.

In arithmetic, an expression or an equation involves two components:

• Numbers
• Operators
• 
  
  
  

• Example 1: Simplify the expression using BODMAS.

  10 + (5 × 3 + 2)

  Solution: Let us solve 10 + (5 × 3 + 2) step by step.

  • Step 1: We need to solve the brackets first. So, this will be 10 + (15 + 2)
  • Step 2: This will result in 10 + 17 = 27

  Example 2: Simplify the expression using BODMAS.

  15 + (30 ÷ 2)

  Solution:

  Let us solve 15 + (30 ÷ 2) step by step.

  • Step 1: We need to solve the brackets first. So, 15 + (30 ÷ 2) = 15 + 15
  • Step 2: This will result in 15 + 15 = 30

1. Example 1: Simplify the expression by using the BODMAS rule:                                [18 - 2(5 + 1)] ÷ 3 + 7

   Solution:

   The given expression is [18 - 2(5 + 1)] ÷ 3 + 7

   • Step 1: We begin with solving the innermost bracket first. Starting with 5 + 1 = 6. Thus, [18 - 2(6)] ÷ 3 + 7
   • Step 2: Next, we work with the order, thereby multiplying 2 (6) or 2 × 6 = 12. Thus, [18 - 12] ÷ 3 + 7
   • Step 3: There is one bracket left, [18 - 12] = 6. So, 6 ÷ 3 + 7
   • Step 4: After B and O comes D, hence, 6 ÷ 3 = 2. So, 2 + 7
   • Step 5: And finally, addition, 2 + 7 = 9

   ∴ The expression is simplified and the answer is 9.