Order of Operations

When an expression has multiple operations, follow PEMDAS:

The Order

Parentheses first Exponents second Multiplication and Division (left to right) Addition and Subtraction (left to right)

Mnemonic

"Please Excuse My Dear Aunt Sally"

Examples

Example 1

$3 + 4 \times 2$

Multiplication first: $= 3 + 8 = 11$

NOT $(3 + 4) \times 2 = 14$ ❌

Example 2

$(5 + 3) \times 2^2$

1. Parentheses: $(5 + 3) = 8$
2. Exponents: $2^2 = 4$
3. Multiplication: $8 \times 4 = 32$

Example 3

$24 \div 4 \times 2$

Left to right (same level): $= 6 \times 2 = 12$

Example 4

$10 - 3 + 7$

Left to right (same level): $= 7 + 7 = 14$

Example 5 (Complex)

$2 + 3 \times (4 + 1)^2 - 6 \div 2$

1. Parentheses: $(4 + 1) = 5$
2. Exponents: $5^2 = 25$
3. Multiply: $3 \times 25 = 75$
4. Divide: $6 \div 2 = 3$
5. Add/Subtract: $2 + 75 - 3 = 74$

Common Mistakes

❌ Forgetting that M/D and A/S go left to right ❌ Doing addition before multiplication ❌ Forgetting to apply exponents before multiplication