🧱 See It
Multiplication is just counting equal groups. 3 × 4 means "3 groups of 4":
4
4
4
3 groups of 4. Skip-count to check: 4, 8, 12.
If you don't instantly know a fact, skip-counting like this always gets you there — it's slower than instant recall, but it never fails.
✏️ Draw It
For a bigger fact like 7 × 8, split it into two smaller facts you already know, then add the pieces back together. 8 = 4 + 4, so:
7×4 (28) + 7×4 (28) = 56. Two easier facts instead of one hard one.
🔢 Write It
7 × 8 = 7 × (4 + 4) = (7 × 4) + (7 × 4) = 28 + 28 = 56
Division is just multiplication in reverse — one multiplication fact always gives you two division facts for free:
7 × 8 = 56 ⇒ 56 ÷ 8 = 7 and 56 ÷ 7 = 8
Learn one fact, get three more for free: 7×8, 8×7, 56÷7, and 56÷8 are all the same fact family.
💡 Worked Examples
Example 1 — The ×9 shortcut: 9 × 6
- 9 is just 10 minus 1, so multiply by 10 first:
10 × 6 = 60 - Then subtract one group of 6:
60 − 6 = 54 - Answer:
9 × 6 = 54
Example 2 — Division by bridging: 42 ÷ 6
- Start from a known anchor:
6 × 5 = 30 - How much further to 42?
42 − 30 = 12 - 12 is 2 more groups of 6:
12 ÷ 6 = 2 - Total groups:
5 + 2 = 7 - Answer:
42 ÷ 6 = 7
🧠 Quick Reference
| Anchor | Shortcut |
|---|---|
| ×1 | same number |
| ×2 | double it |
| ×5 | half of ×10 |
| ×10 | add a zero |
Don't know a fact instantly? Bridge from the nearest anchor (×1, ×2, ×5, or ×10) and adjust. It's always faster than starting from zero, and a calculator is always fine too.