Fast Multiplication Without a Calculator: Techniques & Drills
Published October 2, 2025 • 9 min read
Multiplication is often the bottleneck in mental math. Addition and subtraction feel manageable, but the moment you need 47 × 8 or 23 × 17, things slow down. The good news: a handful of techniques—used by mental math champions and seasoned consultants alike—can make these calculations fast and reliable.
This post covers the most useful shortcuts and shows you how to practice them. If you’re training for interviews, pair this with Mental Math for Interviews and use Focused training to drill multiplication-only sets.
1. The distributive (break-apart) method
This is the workhorse technique for most two-digit multiplications.
Idea: Split one number into tens and ones, multiply each part, then add.
Example: 47 × 6
- 40 × 6 = 240
- 7 × 6 = 42
- 240 + 42 = 282
With practice, steps 1–3 happen almost simultaneously.
2. The 11 trick
Multiplying any two-digit number by 11 is almost instant once you know the pattern.
Rule: Separate the digits, add them, put the sum in the middle.
Example: 34 × 11
- Separate: 3 _ 4
- Add: 3 + 4 = 7
- Insert: 3 7 4 = 374
With a carry: 57 × 11
- 5 + 7 = 12 (≥ 10, so carry the 1)
- Result: (5 + 1) 2 7 = 627
3. Squaring numbers ending in 5
Any number ending in 5 can be squared in two steps.
Rule: Multiply the tens digit by (tens digit + 1), then append 25.
Example: 35²
- 3 × 4 = 12
- Append 25 → 1225
Example: 85²
- 8 × 9 = 72
- Append 25 → 7225
4. The "round and adjust" method
When one factor is close to a round number, exploit that.
Example: 49 × 7
- 50 × 7 = 350
- Subtract 1 × 7 = 7
- 350 − 7 = 343
This also works for addition/subtraction-heavy scenarios (e.g., 98 + 47 → 100 + 47 − 2 = 145).
5. Multiplying numbers close together
When both numbers share the same tens digit, there's a slick shortcut.
Example: 23 × 27 (both in the 20s)
- Base = 20
- Add ones of one number to the other: 23 + 7 = 30
- Multiply by base: 30 × 20 = 600
- Multiply the ones: 3 × 7 = 21
- Add: 600 + 21 = 621
6. Multiply by 5 (halve then ×10)
Example: 48 × 5
- 48 ÷ 2 = 24
- 24 × 10 = 240
7. Multiply by 9 (×10 minus original)
Example: 37 × 9
- 37 × 10 = 370
- 370 − 37 = 333
Putting it into practice
Knowing these tricks is one thing; making them automatic is another. Here's a drill plan:
| Week | Focus | Suggested thetamac settings |
|---|---|---|
| 1 | Distributive method | Medium difficulty, × only, Practice mode (10 s/problem) |
| 2 | 11 trick + squaring 5s | Learning mode with tips, × only |
| 3 | Round-and-adjust, multiply by 5/9 | Medium, mixed + / − / × |
| 4 | Speed test | Timed mode (2 min), all operations |
Mini-drills (great for daily practice):
- 10× distributive reps: do 10 problems like 46×7, 58×6, 73×8. Say the breakdown out loud.
- 11-trick sprint: do 15 problems of two-digit × 11. Track accuracy—carry errors are common.
- Round-and-adjust set: do 10 problems with “almost-round” numbers: 49×6, 98×7, 199×4.
Try it now
Open thetamac and run a quick multiplication-only session. Start in Learning mode to see step-by-step breakdowns, then graduate to Timed mode once the techniques feel natural. When you’re ready to benchmark, compare your score on the Leaderboard.