askvity

What is the order of operations on integers?

Published in Order of Operations 2 mins read

The order of operations on integers, often remembered by the acronym PEMDAS, dictates the sequence in which mathematical operations must be performed to correctly evaluate an expression.

Understanding PEMDAS

PEMDAS stands for:

  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

This order ensures that everyone arrives at the same correct answer when simplifying mathematical expressions. As the reference "Performing Arithmetic Operations with Integers - Order of Operations" states, PEMDAS is the order we follow to simplify algebraic expressions.

The Order Explained

Let's break down each step of PEMDAS:

  1. Parentheses: First, simplify any expressions inside parentheses or other grouping symbols (like brackets and braces). Start with the innermost set of parentheses if there are nested ones.

  2. Exponents: Next, evaluate any exponents (powers) in the expression.

  3. Multiplication and Division: Perform multiplication and division operations from left to right, in the order they appear.

  4. Addition and Subtraction: Finally, perform addition and subtraction operations from left to right, in the order they appear.

Example

Let's evaluate the following expression:

2 + 3 * (4 - 1)^2 / 3

  1. Parentheses: (4 - 1) = 3
    So the expression becomes: 2 + 3 * 3^2 / 3

  2. Exponents: 3^2 = 9
    So the expression becomes: 2 + 3 * 9 / 3

  3. Multiplication and Division:

    • 3 * 9 = 27
      So the expression becomes: 2 + 27 / 3
    • 27 / 3 = 9
      So the expression becomes: 2 + 9

  4. Addition: 2 + 9 = 11

Therefore, the answer is 11.

Summary Table

Order Operation Example
1 Parentheses (2 + 1) = 3
2 Exponents 32 = 9
3 Multiplication 2 * 3 = 6
4 Division 6 / 2 = 3
5 Addition 2 + 3 = 5
6 Subtraction 5 - 2 = 3

Related Articles