Order of Operations.

Two people compute $3 + 4 \times 2$ and get different answers — one says $14$, the other $11$. Math has a fixed rule for who's right: PEMDAS.

PEMDAS

1. P — Parentheses (grouping symbols) — anything inside ( ), [ ], or { } first.
2. E — Exponents — like $3^2$ or $\sqrt{9}$ — next.
3. MD — Multiplication & Division — left to right, same priority.
4. AS — Addition & Subtraction — left to right, same priority.

The trick most people miss: M and D are equal priority — you do them in left-to-right order. Same for A and S. There's no "multiplication before division."

$8 \div 4 \times 2 \;=\; 2 \times 2 \;=\; 4 \quad\text{(left to right — NOT } 8 \div 8 = 1\text{)}$

Worked example — the classic trap

$3 + 4 \times 2 \;=\; 3 + 8 \;=\; 11 \quad\checkmark$ Multiplication has higher priority than addition, so $4 \times 2$ runs first.

If you wanted addition to go first, you'd need parens: $(3+4) \times 2 = 14$.

With negatives

$-3 + 4 \times (-2) \;=\; -3 + (-8) \;=\; -11$

Multiplication first ($4 \cdot -2 = -8$), then add to $-3$.

With exponents

$2 + 3^2 \;=\; 2 + 9 \;=\; 11$ $(2 + 3)^2 \;=\; 5^2 \;=\; 25$