Order of Operations (PEMDAS)

Using PEMDAS to evaluate expressions

Order of Operations (PEMDAS)

PEMDAS

P - Parentheses (and other grouping symbols) E - Exponents M/D - Multiplication and Division (left to right) A/S - Addition and Subtraction (left to right)

Memory aid: "Please Excuse My Dear Aunt Sally"

Important Notes

Multiplication and Division have the SAME priority - do them left to right
Addition and Subtraction have the SAME priority - do them left to right
Always work from inside out with parentheses

Grouping Symbols

All mean "do this first":

Parentheses: $( )$
Brackets: $[ ]$
Braces: $\{ \}$
Fraction bar: $\frac{a + b}{c - d}$

Nested Parentheses

Work from innermost to outermost: $3 + [2 \times (5 - 1)]$

Common Mistakes

❌ $6 + 2 \times 3 = 8 \times 3 = 24$ (Wrong!) ✅ $6 + 2 \times 3 = 6 + 6 = 12$ (Correct: multiply first)

❌ $12 \div 3 \times 2 = 12 \div 6 = 2$ (Wrong!) ✅ $12 \div 3 \times 2 = 4 \times 2 = 8$ (Correct: left to right)

📚 Practice Problems

1Problem 1easy

❓ Question:

Evaluate: $5 + 3 \times 4$

💡 Show Solution

Follow PEMDAS: Multiplication before Addition

Step 1: Multiply first $3 \times 4 = 12$

Step 2: Add $5 + 12 = 17$

Answer: $17$

2Problem 2medium

❓ Question:

Evaluate: $20 \div 4 \times 2 + 3$

💡 Show Solution

Step 1: Division and multiplication (left to right) $20 \div 4 = 5$ $5 \times 2 = 10$

Step 2: Addition $10 + 3 = 13$

Answer: $13$

3Problem 3hard

❓ Question:

Evaluate: $6 + 2[5 - (3 + 1)]$

💡 Show Solution

Step 1: Innermost parentheses $3 + 1 = 4$ $6 + 2[5 - 4]$

Step 2: Brackets $5 - 4 = 1$ $6 + 2[1]$

Step 3: Multiply $2 \times 1 = 2$ $6 + 2$

Step 4: Add $6 + 2 = 8$

Answer: $8$

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