· Multiplying by 9 is really multiplying by 10-1.

So, 9×9 is just 9x (10-1) which is 9×10-9 which is 90-9 or 81.

· Let’s try a harder example: 46×9 = 46×10-46 = 460-46 = 414.

· One more example: 68×9 = 680-68 = 612.

To multiply by 99, you multiply by 100-1.

So, 46×99 = 46x (100-1) = 4600-46 = 4554.

Multiplying by 999 is similar to multiplying by 9 and by 99.

38×999 = 38x(1000-1) = 38000-38 = 37962