Learn: Order of Operations

The idea

Worked example

Every step explained — why we do it, and what happens.

1. 1
   $3 + 6 \times 2^2 - 8 \div 4$

   Why: Before touching the numbers, scan the whole expression: no brackets, one power (2²), then × and ÷, then + and −. That scan decides the order.

   What happens: One expression, four operations — the rules pick the order, not left to right.

2. 2
   $2^2 = 4$

   Why: Powers come first — before ×, ÷, +, and −. Only brackets would go ahead of them.

   What happens: The power collapses to 4.

3. 3
   $\begin{aligned} 6 \times 4 = 24 \\ 8 \div 4 = 2 \end{aligned}$

   Why: × and ÷ are the express lane: do all of them before any + or −, moving left to right.

   What happens: Only + and − are left standing.

4. 4
   $3 + 24 - 2$

   Why: Now the remaining + and − are the same level, so walk left to right.

   What happens: Evaluate left to right: 3 + 24 = 27, then 27 − 2.

5. 5
   $= 25$

   Why: Check by re-reading the original: 3 + 24 − 2 = 25. The rules give one answer, and only one.

   What happens: 25 ✓ — order matters, and we kept it.