Multiplying by 9
- Trick / Shortcut
- Multiplying by 9
- Topic
- Multiplication
- How It Works
To multiply any number $n$ by 9, use the identity:
$n \times 9 = n \times (10 - 1) = (n \times 10) - (n \times 1)$
This means you:
- Multiply the number by 10 (add a zero to the end).
- Subtract the original number from the result of step 1.
This is often faster than traditional multiplication for single-digit multipliers like 9.
- Example
$78 \times 9$:
- Multiply by 10: $78 \times 10 = 780$
- Subtract original number: $780 - 78 = \textbf{702}$
$56 \times 9$:
- Multiply by 10: $56 \times 10 = 560$
- Subtract original number: $560 - 56 = \textbf{504}$
$123 \times 9$:
- Multiply by 10: $123 \times 10 = 1230$
- Subtract original number: $1230 - 123 = \textbf{1107}$