PEMDAS Math Problems- Order of Operations Practice

What PEMDAS Actually Is (And Why It Matters)

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It's the rule that tells you what order to solve math problems when everything isn't just left-to-right.

Here's the brutal truth: if you ignore this order, you'll get the wrong answer every time. There's no exception. 2 + 3 × 4 is not 20. It's 14. The multiplication happens first, then the addition. That's the whole game.

The PEMDAS Breakdown

Each letter represents a step. You work through them in order. Period.

Letter	Stands For	What To Do
P	Parentheses	Solve anything inside ( ) first
E	Exponents	Square roots, powers, anything like 3²
M	Multiplication	Multiply, left to right
D	Division	Divide, left to right (same level as M)
A	Addition	Add, left to right (same level as S)
S	Subtraction	Subtract, left to right

The M and D are at the same level. Same with A and S. You do whichever comes first as you read left to right. This trips up a lot of people.

Common PEMDAS Mistakes

Most errors fall into three categories:

Doing addition before subtraction — people assume A always comes before S. Wrong. It's left to right once you reach that step.
Skipping parentheses entirely — if there's a (3 + 2) inside, you solve that before touching anything else.
Treating M and D as separate steps — they're the same step. 8 ÷ 2 × 4 = 16. Not 0.5. You divide first because it comes first, then multiply.

Practice Problems With Solutions

Work through these. Check your answers only after you've tried.

Problem 1

8 + 2 × 5

Answer: 18 — You multiply first (2 × 5 = 10), then add 8.

Problem 2

(4 + 2) × 3 - 2²

Answer: 16 — Parentheses first (4+2=6), then 6×3=18, exponent 2²=4, finally 18-4=14. Wait, that's 14. Let me fix that.

Actually: (4 + 2) × 3 - 2² = 6 × 3 - 4 = 18 - 4 = 14

Problem 3

20 ÷ 5 × 2 + 1

Answer: 9 — Divide first (20 ÷ 5 = 4), then multiply (4 × 2 = 8), then add (8 + 1 = 9).

Problem 4

3 × (2 + 4) ÷ 2

Answer: 9 — Parentheses first (2+4=6), then 3×6÷2 = 18÷2 = 9.

Problem 5

10 - 3 × 2 + 8 ÷ 4

Answer: 7 — Multiply 3×2=6, divide 8÷4=2, then 10-6+2 = 6. Wait, that's 6.

Correct: 10 - 6 + 2 = 6

How to Practice PEMDAS Effectively

Don't just read problems. Solve them. Here's a method that actually works:

Write out every step — don't do it in your head. Write "multiply first" or "parentheses first" above the problem.
Start with simple problems — if you can't do 5 + 3 × 2 correctly, you won't get further.
Check your work backward — if you got 14 for a problem, plug in different operations to see if any give you 14.
Use flashcards — front: a PEMDAS problem. back: the answer with steps shown.
Set a timer — once you can do basic problems, speed matters. Aim for under 30 seconds per problem.

Tools for Practice

You don't need expensive programs. Here's what's actually useful:

Khan Academy — free, good explanations, tracks progress
Mathway — gives step-by-step solutions if you get stuck
Quizlet — search "PEMDAS flashcards" and you'll find thousands
Your textbook — if you're in a class, the problems at the end of each chapter are gold

Quick Reference Cheat Sheet

Bookmark this. You'll need it.

Always do parentheses first — even nested ones inside parentheses
Exponents come next — 3², √16, anything with a power
Multiplication and Division are the same step — work left to right
Addition and Subtraction are the same step — work left to right
When in doubt, add parentheses to group what should be solved together

The Bottom Line

PEMDAS isn't optional. It's not a suggestion. It's the grammar of math. Get this wrong and every equation you touch will be wrong.

Most people who struggle with order of operations aren't bad at math. They just never learned to slow down and follow the steps in order. You solve what you can, move on, solve what comes next. That's it.

Go practice. Start with the problems above. If you got any wrong, figure out why before moving on. That's the only way this sticks.