Lesson 1.5

Order of Operations (Basic)

Without a universal order, the same expression could produce different answers. PEMDAS gives everyone the same answer every time.

Introduction

Does equal or ? Mathematics has a strict rule set — PEMDAS — that tells us multiplication comes before addition, so the answer is .

Past Knowledge

You can add, subtract, multiply, divide, and evaluate exponents.

Today's Goal

Simplify expressions with no nested grouping symbols using PEMDAS.

Future Success

Every equation you solve in this course relies on correct order of operations.

Key Concepts

1. The PEMDAS Hierarchy

P

Parentheses

Do grouped operations first

E

Exponents

Evaluate powers next

MD

Multiplication & Division

Left to right (same level)

AS

Addition & Subtraction

Left to right (same level)

2. Same-Level Rule

Multiplication & Division are equal. Addition & Subtraction are equal.
When two same-level operations appear, work left to right.

Worked Examples

Example 1: No Parentheses

Basic

Simplify .

1

Multiplication First

2

Then Add

Example 2: Exponents + Mixed Ops

Intermediate

Simplify .

1

Exponents

Expression becomes:

2

Multiplication

Expression becomes:

3

Left to Right

Example 3: Parentheses Change Everything

Advanced

Simplify .

1

Parentheses

2

Exponents

Expression:

3

Multiply, then Subtract

Common Pitfalls

Always Going Left to Right

. Multiplication comes before addition regardless of position.

Multiplication Before Division Always

M and D are same level. In , go left to right: , not .

Real-Life Applications

Spreadsheet formulas (like in Google Sheets or Excel) follow PEMDAS. When you type =10+2*5, the software returns , not . Understanding order of operations is essential for anyone who uses spreadsheets — from accountants to data scientists.

Practice Quiz

Loading...