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:

The Complete Order

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

Example 2: With Parentheses

Solve: (8 + 2) × 5

Example 3: With Exponents

Solve: 3 + 2² × 4

Example 4: Complex Expression

Solve: 24 ÷ 4 × 2 + 3² - (5 - 2)

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:

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.

Why Calculators Sometimes Give Different Answers

Have you ever typed the same calculation into two different calculators and got different results? This is almost always due to how each calculator handles order of operations — particularly whether it evaluates left-to-right or applies mathematical precedence rules.

The Famous ÷ Viral Maths Problem

Consider: 6 ÷ 2(1 + 2)

This expression went viral because different interpretations yield different answers:

• Answer 9: Modern calculators apply BODMAS strictly: 6 ÷ 2 × 3 = 3 × 3 = 9 (division and multiplication left to right)
• Answer 1: Some interpret 2(1+2) as a single grouped term: 6 ÷ (2×3) = 6 ÷ 6 = 1

Both interpretations are mathematically defensible based on convention. In professional mathematics and scientific computing, the expression would be written unambiguously with explicit parentheses.

Order of Operations in Programming vs Mathematics

Most programming languages follow mathematical BODMAS/PEMDAS rules, but there are important differences to be aware of:

Step-by-Step: Worked Examples

Example 1: Mixed Operations

Solve: 3 + 4 × 2 − (8 ÷ 4)²

1. Brackets first: (8 ÷ 4) = 2 → expression becomes 3 + 4 × 2 − 2²
2. Exponents: 2² = 4 → expression becomes 3 + 4 × 2 − 4
3. Multiplication: 4 × 2 = 8 → expression becomes 3 + 8 − 4
4. Left to right addition/subtraction: 3 + 8 = 11, then 11 − 4 = 7

Example 2: Nested Brackets

Solve: 2 × (3 + (4 − 1)²)

1. Innermost brackets: (4 − 1) = 3 → expression becomes 2 × (3 + 3²)
2. Exponent inside brackets: 3² = 9 → expression becomes 2 × (3 + 9)
3. Remaining brackets: (3 + 9) = 12 → expression becomes 2 × 12
4. Multiplication: 2 × 12 = 24

Frequently Asked Questions