Multiplying by 11

The Multiply by 11 Trick

Multiplying any two-digit number by 11 is one of the easiest mental math shortcuts. Simply split the digits apart, add them together, and place the sum in the middle. For 35 × 11: split into 3 _ 5, add 3 + 5 = 8, place in middle → 385. The entire calculation takes under two seconds.

When Digits Sum to 10 or More

If the middle sum is 10 or greater, carry the extra digit. For 57 × 11: 5 + 7 = 12. Write 2 in the middle, carry 1 to the first digit: 5 + 1 = 6. Result: 627. This carry rule is the only complication, and it follows the same logic as standard addition carries.

Why This Works

Multiplying by 11 is equivalent to multiplying by (10 + 1). For a two-digit number ab: ab × 11 = ab × 10 + ab = ab0 + ab. This expands to a hundreds digit (a), a tens digit (a + b), and a ones digit (b) — exactly what the trick computes. Understanding the why makes the trick memorable and extendable.

Extending to Three Digits

For three-digit numbers, add adjacent digit pairs from right to left, carrying as needed. For 253 × 11: (2)(2+5)(5+3)(3) = 2, 7, 8, 3 → 2,783. Practice the two-digit version until automatic before attempting three digits.

Practice Examples

Example 1: 35 × 11 = ?

1. Split digits: 3 _ 5
2. Add them: 3 + 5 = 8
3. Place in middle: 385

Answer: 385

Example 2: 72 × 11 = ?

1. Split: 7 _ 2
2. Add: 7 + 2 = 9
3. Result: 792

Answer: 792

Example 3: 57 × 11 = ?

1. Split: 5 _ 7
2. Add: 5 + 7 = 12
3. Carry: write 2 in middle, add 1 to 5 → 627

Answer: 627