Fundamentals

When evaluating mathematical expressions, operations must be performed in a specific order:

1. Parentheses: Solve operations inside grouping symbols first.
2. Exponents: Evaluate powers and roots.
3. Multiplication and Division: Perform these from left to right.
4. Addition and Subtraction: Perform these from left to right.

Mnemonic: Please Excuse My Dear Aunt Sally

For any real numbers $a$, $b$, and $c$:

• Commutative Property: $a + b = b + a$ and $ab = ba$.
• Associative Property: $(a + b) + c = a + (b + c)$ and $(ab)c = a(bc)$.
• Distributive Property: $a(b + c) = ab + ac$.
• Identity Property: $a + 0 = a$ and $a \cdot 1 = a$.
• Inverse Property: $a + (-a) = 0$ and $a \cdot \frac{1}{a} = 1$ (for $a \neq 0$).