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Order of Operations PEMDAS Practice: Free Worksheet

August 10, 2026

Order of Operations (PEMDAS) Practice: Free Step-by-Step Worksheet

A person using order of operations as they write mathematical equations by hand on grid paper using a pencil. — Image by kaboompics.com via Pexels

Why do we get different answers if we solve a math problem from left to right versus following a set of rules? That is the exact trap students fall into when learning Order of Operations (PEMDAS)! Without a standardized set of rules, an expression like 15 + 18 ÷ 3² could produce multiple different answers. PEMDAS gives students a reliable “roadmap” to solve every multi-step problem correctly, every single time. In this post, we’re breaking down the most common PEMDAS pitfalls — plus providing a free downloadable practice worksheet complete with calculation drills and real-world word problems!

💡 The PEMDAS Hierarchy: Memory Tricks & Golden Rules

To help your student master the sequence, keep this classic memory phrase in mind: Please Excuse My Dear Aunt Sally!

Parentheses & Grouping Symbols: Always solve inside parentheses () and brackets [] first. Work from the innermost set outward!

Exponents: Simplify powers and roots next (e.g., 3² = 9 or 2³ = 8).

Multiplication & Division: Crucial Rule! These two operations have equal priority. Solve them in order from left to right as you encounter them in the problem.

Addition & Subtraction: Crucial Rule! These two also have equal priority. Solve them in order from left to right.

⚠️ The #1 Student Misconception:

Students often assume Multiplication must come before Division, or Addition must come before Subtraction! Remind them that M/D and A/S are tied pairs played strictly from left to right.

✏️ Step-by-Step Example Problem

Let’s solve a practice question:[4 · (12 – 3)] ÷ 6 + 5

Step 1 (Inner Parentheses): 12 – 3 = 9

[4 • 9] ÷ 6 + 5

Step 2 (Outer Brackets): 4 • 9 = 36

36 ÷ 6 + 5

Step 3 (Division): 36 ÷ 6 = 6

6 + 5

Step 4 (Addition): 6 + 5 = 11 (Final Answer!)

Inside Your Free Printable PDF:

8 Calculation Drills:

Multi-step problems including nested brackets, exponents, and strict left-to-right division.

2 Real-World Modeling Problems:

Practice writing and evaluating original PEMDAS expressions for practical scenarios (School Carnival & Flower Boxes)!

Full Teacher Answer Key:

Includes full step-by-step breakdowns for quick grading and tutoring.

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