Multiplication gets a bad reputation because most people only practised it by rote — times tables up to 12, then a long-multiplication algorithm for anything bigger. The result: anything beyond 12×12 triggers a mental blank.
The shortcuts below are taught in mental math competitions and used by expert calculators. Each one converts a "hard" multiplication into two or three easy ones.
Trick 1: Doubling and Halving
If one number is even, halve it and double the other. Repeat until the problem is easy.
16 × 35: halve 16, double 35 → 8 × 70 → 4 × 140 → 2 × 280 = 560.
24 × 25: 12 × 50 → 6 × 100 = 600. Two steps.
This works because halving and doubling preserves the product (a×b = (a/2)×(2b)). Stop when one factor is a power of 10 or a number you know instantly.
Trick 2: Use the Distributive Property
Split one factor into an easy sum, multiply each part, then add.
7 × 84: 7 × (80 + 4) = 560 + 28 = 588.
13 × 47: 13 × (50 − 3) = 650 − 39 = 611.
Choosing to subtract (round up by a small amount) often gives you friendlier intermediate numbers than always splitting at the tens boundary.
Rule of thumb: If the number ends in 7, 8, or 9 — round up and subtract. If it ends in 1, 2, or 3 — round down and add.
Trick 3: Multiplying by 11
For any two-digit number, add the two digits and insert that sum in the middle.
53 × 11: 5_3 → middle digit = 5+3 = 8 → 583.
78 × 11: 7+8 = 15 (two digits!) → write 8, carry 1 → 7+1=8 → 858.
This extends to larger numbers but the two-digit case is the most useful in everyday calculations.
Trick 4: Squaring Numbers Near 50
For numbers close to 50, use the identity: (50+n)² = 2500 + 100n + n².
53² = 2500 + 300 + 9 = 2809.
47² = 2500 − 300 + 9 = 2209.
You only need to square small numbers (n²), which you should have memorised.
Trick 5: The "FOIL in your Head" Method
For two-digit × two-digit, treat it like (a+b)(c+d):
23 × 47:
- 20 × 40 = 800
- 20 × 7 = 140
- 3 × 40 = 120
- 3 × 7 = 21
- 800 + 140 + 120 + 21 = 1081
Four sub-multiplications, all involving round tens or single digits. With practice this takes under five seconds.
Trick 6: Multiply by 5 Instantly
Multiplying by 5 is the same as multiplying by 10 and halving.
84 × 5: 840 ÷ 2 = 420.
137 × 5: 1370 ÷ 2 = 685.
Similarly, × 15 = × 10 + half. × 25 = × 100 ÷ 4. × 125 = × 1000 ÷ 8.
Building Multiplication Speed
These tricks feel clunky at first — that is normal. The goal is to practise each one repeatedly until the transformation feels reflexive. Use MathTrainer for daily timed drills: the adaptive level system will naturally progress you from single-digit recall through two-digit combinations where these shortcuts pay off most.