Why Order of Operations Matters

Without agreed-upon rules for the order of operations, the expression 2 + 3 × 4 could mean two different things. Do you add first (5 × 4 = 20) or multiply first (2 + 12 = 14)? The answer is 14, because multiplication comes before addition. These rules ensure everyone evaluates expressions the same way — and they're essential for algebra, programming, science, and any field that uses formulas.

PEMDAS: The Order

P - Parentheses first. Evaluate anything inside parentheses (or brackets) before anything else. If there are nested parentheses, work from the inside out.

E - Exponents next. Calculate powers and square roots.

M/D - Multiplication and Division. These have equal priority. Work left to right, doing whichever comes first.

A/S - Addition and Subtraction. These also have equal priority. Work left to right.

The critical thing most students miss: multiplication and division are at the SAME level, not "multiplication before division." Same for addition and subtraction. Within each level, you go left to right.

Examples That Trip Students Up

Example 1: 8 ÷ 2 × 4

Wrong approach: "Division before multiplication" → 8 ÷ 8 = 1 Right approach: Left to right → 8 ÷ 2 = 4, then 4 × 4 = 16

Example 2: 12 - 3 + 5

Wrong approach: "Subtraction after addition" → 12 - 8 = 4 Right approach: Left to right → 12 - 3 = 9, then 9 + 5 = 14

Example 3: 2 + 3 × (4 + 1)²

Step 1 - Parentheses: 4 + 1 = 5 Step 2 - Exponents: 5² = 25 Step 3 - Multiplication: 3 × 25 = 75 Step 4 - Addition: 2 + 75 = 77

The Most Common Mistakes

Mistake 1: Doing all multiplication before all division. Remember, they're at the same level — go left to right.

Mistake 2: Forgetting that the fraction bar acts as parentheses. In (6 + 2)/(4 - 2), evaluate the top and bottom separately before dividing.

Mistake 3: Not completing parentheses fully. In 3(2 + 4)², the parentheses say to add first (getting 6), THEN apply the exponent (36), THEN multiply by 3 (108).

Mistake 4: Confusing negative signs with subtraction. -3² means -(3²) = -9, not (-3)² = 9. The negative sign is applied after the exponent unless parentheses say otherwise.

How to Practice Effectively

Start with simple expressions (two operations) and gradually increase complexity. When your child gets one wrong, don't just correct the answer — walk through the order of operations step by step and identify exactly where they went off track.

Our practice tools generate unlimited order of operations problems appropriate for each grade level:

Grade 5 Order of Operations — Two to three operations
Grade 6 Order of Operations — Including exponents
Grade 7 Order of Operations — Complex expressions
Grade 8 Order of Operations — With integers and decimals

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Master PEMDAS with unlimited practice at Order of Operations Practice. Instant feedback and AI explanations help students learn from every mistake.

Order of Operations Explained for Middle Schoolers (PEMDAS)