Order of Operations Explained: PEMDAS, BODMAS, and BEDMAS

Have you ever seen a math problem go viral on social media because people couldn't agree on the answer? Usually, the confusion stems from not understanding the order of operations — the fundamental rules that dictate how mathematical expressions should be evaluated. This guide will make you an expert.

What is the Order of Operations?

The order of operations is a set of rules that tells us the sequence in which mathematical operations should be performed. Without these rules, the same expression could yield different results depending on which operation you do first.

Consider: 2 + 3 × 4

If you calculate left to right: (2 + 3) × 4 = 5 × 4 = 20
Using order of operations: 2 + (3 × 4) = 2 + 12 = 14

The correct answer is 14, because multiplication comes before addition in the order of operations.

PEMDAS, BODMAS, and BEDMAS

Different countries use different acronyms to remember the order, but they all mean the same thing:

PEMDAS (USA)

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

BODMAS (UK, India)

Brackets
Orders (powers/roots)
Division
Multiplication
Addition
Subtraction

BEDMAS (Canada)

Brackets
Exponents
Division
Multiplication
Addition
Subtraction

The Complete Order

Parentheses/Brackets: Solve everything inside parentheses first, starting with the innermost.
Exponents/Orders: Calculate powers and roots.
Multiplication and Division: From left to right (equal priority).
Addition and Subtraction: From left to right (equal priority).

Important: Multiplication and Division have equal priority — perform them left to right. Same for Addition and Subtraction.

Step-by-Step Examples

Example 1: Basic

Solve: 8 + 2 × 5

Step 1: Multiplication first → 2 × 5 = 10

Step 2: Addition → 8 + 10 = 18

Example 2: With Parentheses

Solve: (8 + 2) × 5

Step 1: Parentheses first → 8 + 2 = 10

Step 2: Multiplication → 10 × 5 = 50

Example 3: With Exponents

Solve: 3 + 2² × 4

Step 1: Exponent first → 2² = 4

Step 2: Multiplication → 4 × 4 = 16

Step 3: Addition → 3 + 16 = 19

Example 4: Complex Expression

Solve: 24 ÷ 4 × 2 + 3² - (5 - 2)

Step 1: Parentheses → (5 - 2) = 3

Expression: 24 ÷ 4 × 2 + 3² - 3

Step 2: Exponent → 3² = 9

Expression: 24 ÷ 4 × 2 + 9 - 3

Step 3: Division (left to right) → 24 ÷ 4 = 6

Expression: 6 × 2 + 9 - 3

Step 4: Multiplication → 6 × 2 = 12

Expression: 12 + 9 - 3

Step 5: Addition and subtraction (left to right) → 12 + 9 = 21, then 21 - 3 = 18

Common Mistakes to Avoid

Treating MD and AS as separate levels: Multiplication doesn't always come before division. They have equal priority — go left to right.
Forgetting implicit multiplication: In expressions like 2(3+4), multiply after the parentheses.
Nested parentheses: Always work from innermost to outermost.
Negative exponents: Calculate the exponent first, then apply the negative sign if outside the parentheses.

The Viral Math Problem Explained

Remember that viral problem: 8 ÷ 2(2+2) = ?

This causes debate because of ambiguous notation. Strictly following PEMDAS:

Step 1: Parentheses → 2 + 2 = 4

Expression: 8 ÷ 2 × 4

Step 2: Left to right → 8 ÷ 2 = 4

Step 3: 4 × 4 = 16

However, some argue that 2(4) should be treated as a single term, giving 8 ÷ 8 = 1. This is why mathematicians prefer clearer notation using fractions or additional parentheses to avoid ambiguity.

Practice with Our Calculator

Our calculator correctly applies the order of operations. Try it yourself!

Use Calculator →

Frequently Asked Questions

Do calculators follow order of operations?

Scientific calculators and computer programs typically follow order of operations automatically. Simple four-function calculators may not — they often calculate left to right as you enter operations.

Why was this convention created?

The order of operations evolved to create consistency in mathematical notation. It became standardized in the 1800s as mathematics became more formalized.

Does the order apply in programming?

Yes! Programming languages follow similar rules, called "operator precedence." However, specific details may vary slightly between languages.