askvity

How to Solve Combined Operations?

Published in Order of Operations 2 mins read

To solve combined operations, you must follow a specific order, often referred to as the "order of operations" ([0:12]). This ensures consistency and accuracy in calculations.

Understanding the Order of Operations

The order of operations dictates the sequence in which mathematical operations should be performed. The most common mnemonic to remember this order is PEMDAS or BODMAS.

  • PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
  • BODMAS: Brackets, Orders (powers and square roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

While the acronyms differ slightly, the underlying principle remains the same.

Steps to Solve Combined Operations

Here's a breakdown of the steps involved in solving combined operations:

  1. Parentheses/Brackets: First, solve any expressions inside parentheses ( ) or brackets [ ]. Start with the innermost set if there are nested parentheses.

  2. Exponents/Orders: Evaluate any exponents (powers) or roots (square roots, cube roots, etc.).

  3. Multiplication and Division: Perform multiplication and division operations from left to right. These operations have equal priority, so you proceed in the order they appear.

  4. Addition and Subtraction: Finally, perform addition and subtraction operations from left to right. Similar to multiplication and division, these have equal priority and are done in the order they appear.

Example

Let's consider an example:

10 + 2 * (6 - 3) / 2

  1. Parentheses: Solve (6 - 3) = 3
    10 + 2 * 3 / 2

  2. Multiplication and Division (from left to right):

    • 2 * 3 = 6
      10 + 6 / 2
    • 6 / 2 = 3
      10 + 3

  3. Addition:

    • 10 + 3 = 13

Therefore, the solution to the combined operation is 13.

Importance of Following the Order

Adhering to the order of operations is crucial because performing the operations in a different sequence will lead to an incorrect answer ([0:12], [3:17]). It establishes a standard procedure that everyone follows, ensuring consistency in mathematical problem-solving.

Related Articles