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How do you solve using the BODMAS rule?

Published in Math Operations 2 mins read

The BODMAS rule is a specific order of operations used to solve mathematical expressions, ensuring everyone arrives at the same correct answer. Here's how to apply it:

Understanding BODMAS

BODMAS is an acronym that stands for:

  • B - Brackets
  • O - Orders (powers, square roots, etc.)
  • D - Division
  • M - Multiplication
  • A - Addition
  • S - Subtraction

This order dictates the sequence in which you perform mathematical operations within an expression.

Steps to Solve Using BODMAS

  1. Brackets (B): First, solve all operations within any type of brackets (parentheses, square brackets, curly braces).
  2. Orders (O): Next, handle any powers, roots, or "of" operations. Note: "of" in a mathematical context usually means multiplication (e.g., "1/2 of 10" is the same as "1/2 * 10").
  3. Division (D) and Multiplication (M): Perform division and multiplication from left to right as they appear in the expression. These have equal priority, so complete them in the order encountered.
  4. Addition (A) and Subtraction (S): Finally, perform addition and subtraction from left to right. These also have equal priority, so complete them in the order encountered.

BODMAS Order of Operations Summarized

Order Operation Symbol(s) Example
1 Brackets ( ), [ ], { } (2 + 3) * 4
2 Orders ², √, etc. "of" 2³ + 10 or 1/2 of 10
3 Division / , ÷ 10 / 2 + 5
4 Multiplication * , x 2 * 5 - 1
5 Addition + 10 + 5 - 2
6 Subtraction - 10 - 2 + 1

BODMAS in Practice

Let's see how to solve using BODMAS with some examples:

Example 1:

10 + 2 * (8 - 3)

  1. Brackets: 8 - 3 = 5. Expression now is 10 + 2 * 5
  2. Multiplication: 2 * 5 = 10. Expression now is 10 + 10
  3. Addition: 10 + 10 = 20.

Therefore, the answer is 20.

Example 2:

(15 / 3) + 4² - 1

  1. Brackets: 15 / 3 = 5. Expression is now 5 + 4² - 1
  2. Orders: 4² = 16. Expression is now 5 + 16 - 1
  3. Addition: 5 + 16 = 21. Expression is now 21 - 1
  4. Subtraction: 21 - 1 = 20.

Therefore, the answer is 20.

Key Insight: Following the BODMAS rule step-by-step guarantees accurate and consistent calculations for any mathematical expression.

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