Multiplying any number by 9 easily

Rule: 

• Subtract the digits of multiplicand 'ALL FROM 9 AND THE LAST FROM 10'. 

• Add the neighbor.   

• For the leading zero, subtract 1 from the neighbor.

For rules 9, 8, 4, and 3 only the first digit is subtracted from 10. After that each digit is subtracted from nine instead.

Example: 2,130 × 9 =?

Working from right to left:

• (10 - 0) + 0 = 10. Write 0, carry 1.
• (9 - 3) + 0 (neighbor) + 1 (carried) = 7. Write 7.
• (9 - 1) + 3 (neighbor) = 11. Write 1, carry 1.
• (9 - 2) + 1 (neighbor) + 1 (carried) = 9. Write 9.
• 2 - 1 = 1. Write 1.

So, 2,130 × 9 = 19,170

45,612 × 9 =?

Working from right to left:

• (10 - 2) + 0 = 8. Write 8.
• (9 - 1) + 2= 10. Write 0, carry 1.
• (9 - 6) + 1 +1 = 5. Write 5.
• (9 - 5) + 6 = 10. Write 0, carry 1.
• (9 - 4) + 5 +1 = 11. Write 1, carry 1.
• 4 - 1 +1 = 4. Write 4.

So, 45612 × 9 = 410,508