🧱 See It
A recipe has steps in a set order: crack the eggs, then mix, then bake. Bake before mixing and you don't get a cake — same ingredients, wrong result. Math expressions work the same way: doing the operations in a different order can give a different, wrong answer.
When part of an expression is wrapped in brackets, treat it like a bundle. Everything inside gets dealt with together, first, before it's combined with anything outside.
The dashed box is a bundle — open it and solve what's inside before doing anything else.
✏️ Draw It
Before calculating anything, take a first pass: look at the expression and number each operation in the order it needs to happen. Don't compute yet — just label.
Even though + is written first, × is labelled ① — multiplication happens before addition. Reading order and doing order aren't the same thing.
Only once every operation is numbered do you go back and calculate — one step at a time, in that order.
🔢 Write It
Read left to right like a sentence, and 3 + 4 × 2 looks like it should be 7 × 2. That's the trap — math expressions aren't sentences.
3 + 4 × 2 ≠ 14
Multiplication and division always happen before addition and subtraction, no matter which is written first:
3 + (4 × 2) = 3 + 8 = 11
| Step | Do this |
|---|---|
| 1 | Brackets |
| 2 | Divide / Multiply — left to right |
| 3 | Add / Subtract — left to right |
💡 Worked Examples
Example 1 — No brackets: 3 + 4 × 2
- Scan for brackets: none here.
- Multiply/divide first:
4 × 2 = 8 - Add/subtract what's left:
3 + 8 = 11 - Answer:
11
Example 2 — With brackets: (3 + 4) × 2
- Scan for brackets:
(3 + 4)is a bundle — solve it first:3 + 4 = 7 - Multiply/divide what's left:
7 × 2 = 14 - Answer:
14
🧠 Quick Reference
The "E" (Exponents) joins this list starting at Level 2. For now it's just B, then DM, then AS.