Dividing by 9 Trick

This trick extends the remainder rule for 9 to find the full quotient. When dividing a number $abcd$ by 9, you can find the digits of the answer sequentially.

• Hundreds digit: $a$
• Tens digit: $a+b$ (carry if sum > 9)
• Ones digit: $a+b+c$ (carry if sum > 9)
• Remainder: $a+b+c+d$ (find remainder when this sum is divided by 9)

For $3211 \div 9$: Hundreds is 3. Tens is $3+2=5$. Ones is $3+2+1=6$. Remainder is $3+2+1+1=7$. Answer: $356\frac{7}{9}$.