Understanding PEMDAS: The Order of Operations in Mathematics

Athena
2 min readSep 27, 2023

Introduction

Mathematics is a field that thrives on rules and structures. One such set of rules that almost every student learns early on is the order of operations, often remembered by the acronym PEMDAS. It is a vital guide to ensure that mathematical expressions are evaluated in a consistent manner. In this blog post, we will delve into the meaning and significance of PEMDAS, examine examples, and explore how this rule enables us to maintain uniformity in mathematical calculations.

What is PEMDAS?

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This mnemonic helps us remember the sequence in which to perform operations when evaluating mathematical expressions.

- Parentheses: Perform all calculations inside parentheses first.
- Exponents: Next, handle all exponents (or powers).
- Multiplication and Division: Multiply and divide in the order that they appear, from left to right.
- Addition and Subtraction: Finally, add and subtract in the order that they appear, from left to right.

Importance of PEMDAS

Without a standardized order of operations, even simple equations would be open to interpretation. For example, consider the expression \(2 + 3 \times 4\). Without PEMDAS, one could argue for either of the following evaluations:

1. (2 + 3) x 4 = 20
2. 2 + (3 x 4) = 14

PEMDAS tells us that multiplication comes before addition, so the correct answer is 14.

## Examples

### Example 1: Simple Operations
3 + 4 x 2
According to PEMDAS:
3 + 8 = 11

### Example 2: Involving Parentheses and Exponents
(2 + 3) x
According to PEMDAS:
5 x 8 = 40

### Example 3: Division and Multiplication
16 \ 4 x 2
According to PEMDAS:
4 x 2 = 8

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Athena

Mom of three boys. Computer programmer living in the country with my husband focusing on my hobbies and youngest son. https://ko-fi.com/athenaandrew