Order of Operations — PEMDAS and BODMAS Explained

What Is PEMDAS?

PEMDAS is a memory trick used mainly in the US and a few other countries. Each letter stands for one step:

Letter	Stands For	What You Do
P	Parentheses	Anything inside brackets gets solved first
E	Exponents	Powers and square roots come next
M	Multiplication	Work left to right, whichever comes first
D	Division
A	Addition	Work left to right, whichever comes first
S	Subtraction

Some teachers say "Please Excuse My Dear Aunt Sally" as a way to remember the order. A bit corny, but honestly it works.

BODMAS — Is It Different?

Not really. BODMAS (used in the UK, India, Australia and most other countries) stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction. The actual order is the same — just different words. "Orders" means the same thing as Exponents, and Brackets = Parentheses.

So if you've been taught BODMAS and your friend says PEMDAS, you're both doing the same math. Don't let that confuse you.

A Simple Example to Start

Let's go back to that problem: 8 + 2 × 3

The wrong way: 8 + 2 = 10, then 10 × 3 = 30 ✗

The right way: multiplication first, so 2 × 3 = 6, then 8 + 6 = 14 ✓

Simple, but people get this wrong all the time, especially when typing stuff into a basic phone calculator that doesn't respect the order of operations (those older ones just calculate left to right).

Working Through Each Step

Step 1 — Parentheses First

Whatever is inside brackets, you solve that completely before doing anything outside. Nested brackets (brackets inside brackets) get solved from the inside out.

Step 2 — Exponents (Powers and Roots)

After brackets, any powers or roots come next. This catches a lot of people off guard.

Step 3 — Multiplication and Division (Left to Right)

Here's an important thing that trips people up: multiplication doesn't actually "beat" division. They have the same priority. You just work through them left to right, whichever appears first.

This is one of the most common sources of confusion with PEMDAS. The M doesn't come before D in terms of priority — they're equal, and position (left to right) decides it.

Step 4 — Addition and Subtraction (Left to Right)

Same deal here. Addition and subtraction are equal priority. Work left to right.

Worked Examples

Let's try a few complete problems from start to finish:

Problem 1:   5 + 3² × (4 - 1)

Problem 2:   20 ÷ 4 + 6 × 2 - 8

Problem 3:   (2 + 3)² - 4 × 2

Common Mistakes People Make

Mistake	What People Do	Correct Approach
Add before multiply	2 + 3 × 4 = 20 ✗	3 × 4 = 12, then + 2 = 14 ✓
Treat M before D	12 ÷ 2 × 3: do 2 × 3 first = 2 ✗	12 ÷ 2 = 6, then × 3 = 18 ✓
Forget left to right	9 - 4 + 1 = 4 ✗	9 - 4 = 5, then + 1 = 6 ✓
Ignore implied brackets	-3² read as (-3)² = 9 ✗	-(3²) = -9 ✓

Using a Calculator

Modern scientific calculators handle the order of operations automatically — you can type the full expression and it'll give you the right answer. Basic 4-function calculators often don't. If you're unsure whether your calculator respects PEMDAS, test it with 2 + 3 × 4. If it says 20, it's doing left-to-right only. If it says 14, it's following the proper order.

You can use the SolveCalc calculator to check your work — it processes the full expression correctly before giving you a result.

Why the Order of Operations Matters

It's not just a school rule that mathematicians made up to be annoying. Without a standard order, the same expression could mean different things to different people. In engineering, programming, and finance, ambiguous calculations would cause real problems. The order of operations is basically a shared language that makes math consistent globally.

Programming languages also follow it — JavaScript, Python, and basically every language out there follows operator precedence rules that mirror PEMDAS. So if you learn this well, it'll help beyond just math class.

Quick Reference

Priority	Operation	Direction
1st	Parentheses / Brackets	Inside → out
2nd	Exponents / Orders / Roots	Right → left
3rd	Multiplication and Division (equal)	Left → right
4th	Addition and Subtraction (equal)	Left → right

Conclusion

The order of operations isn't complicated — it just needs to become habit. Most people mess it up not because they don't understand the rule, but because they forget multiplication/division trump addition/subtraction, or they forget that M and D are equal priority (same with A and S). Once you've worked through enough problems it becomes second nature.

The big things to remember: parentheses always win, exponents go before everything else except brackets, and multiplication and division are equals — not one before the other.