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What is the Bodmas rule?

Published in Math Rules 2 mins read

The BODMAS rule is a mnemonic used to remember the order of operations in mathematical calculations. It dictates the sequence in which operations should be performed to arrive at the correct answer. According to the reference provided, the BODMAS acronym stands for:

  • B - Brackets
  • O - Order of powers or roots
  • D - Division
  • M - Multiplication
  • A - Addition
  • S - Subtraction

Mathematical expressions containing multiple operators must be solved from left to right following this exact order.

Understanding the BODMAS Order

The BODMAS rule ensures consistency and accuracy in mathematical problem-solving. Let's break down each component with examples:

  1. Brackets (B): Solve everything inside the brackets first. This includes any operation within the brackets following the BODMAS rule itself.

    • Example: 2 x (3 + 5) = 2 x 8 = 16

  2. Orders (O): This refers to powers (exponents) and roots (square roots, cube roots, etc.).

    • Example: 5 + 23 = 5 + 8 = 13
    • Example: √9 + 4 = 3 + 4 = 7

  3. Division (D): Perform all division operations from left to right.

    • Example: 10 / 2 + 3 = 5 + 3 = 8

  4. Multiplication (M): Perform all multiplication operations from left to right.

    • Example: 4 x 2 + 7 = 8 + 7 = 15

  5. Addition (A): Perform all addition operations from left to right.

    • Example: 6 + 3 - 2 = 9 - 2 = 7

  6. Subtraction (S): Perform all subtraction operations from left to right.

    • Example: 10 - 4 + 1 = 6 + 1 = 7

Practical Application of BODMAS

Let's consider a more complex example to illustrate how the BODMAS rule works:

Example: 10 + (6 - 2) x 3 / 22

  1. Brackets: (6 - 2) = 4. The expression becomes: 10 + 4 x 3 / 22
  2. Orders: 22 = 4. The expression becomes: 10 + 4 x 3 / 4
  3. Division: 3 / 4 = 0.75. The expression becomes: 10 + 4 x 0.75
  4. Multiplication: 4 x 0.75 = 3. The expression becomes: 10 + 3
  5. Addition: 10 + 3 = 13

Therefore, the final answer is 13.

BODMAS vs. PEMDAS

It's worth noting that the BODMAS rule is also known as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) in some regions, particularly in the United States. Both acronyms represent the same order of operations.

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