Multiplying any 2 or 3-digit number by 111 mentally

You likely know the technique of multiplying any number by 11. Here is the trick to multiply a 2-digit and 3-digit number by 111.

Multiplying a 2-digit number by 111

Example: 111 × 58

1. Write down the ones digit. > 8

2. Add the tens and ones; carry, if any. > 38 (5 + 8 = 13)

3. Repeat the previous step (and add carry, if any) > 438 (5 + 8 + 1 = 14)

4. Write the tens digit (add carry, if any) > 6438 (5 + 1 = 6)

So, 111 × 58 = 6,438

Multiplying a 3-digit number by 111

Use right-to-left "sweeps" of 1, 2, 3, 2, and 1 digit.

Example: 111 × 234

1. Write down the right most digit. > 4

2. Add the 2 right most digits (carry, if any) > 74 (3 + 4 = 7)

3. Add all the 3 digits (and carry, if any) > 974 (2 + 3 + 4 = 9)

4. Add the 2 left most digits (and carry, if any) > 5974 (2 + 3 = 5)

5. Write down the left most digit (add carry) > 25974

So, 111 × 234 = 25,974

Edited January 27, 201213 yr by swansont
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