Multiplying by 11
- Trick / Shortcut
- Multiplying by 11
- Topic
- Multiplication
- How It Works
To multiply any number by 11:
- Write the rightmost digit of the original number as the rightmost digit of the answer.
- Add adjacent digits, moving from right to left. Write down the sum.
- If the sum is $\ge 10$, carry over the tens digit to the next sum.
- Write the leftmost digit of the original number (plus any carry) as the leftmost digit of the answer.
For a 2-digit number $ab$: $a \text{ | } (a+b) \text{ | } b$ (digits separated visually)
- Example
$23 \times 11$:
- Rightmost digit: $3$
- Sum of digits: $2+3 = 5$
- Leftmost digit: $2$ Result: $\textbf{253}$
$47 \times 11$:
- Rightmost digit: $7$
- Sum of digits: $4+7 = 11$. Write $1$, carry $1$.
- Leftmost digit: $4 + \text{carry } 1 = 5$. Result: $\textbf{517}$
$63 \times 11$:
- Rightmost digit: $3$
- Sum of digits: $6+3 = 9$
- Leftmost digit: $6$ Result: $\textbf{693}$