Nines seem to have a lot of magic in mathematics. My seventh grade school teacher in the early 1950s taught us how to prove a multiplication problem answer as correct by casting out nines.
While it seems like a lot of extra hard work to prove an answer, once I got the gist, it came fast and I never had another wrong multiplication problem. I still use it today whenever I dont have a calculator handy.
Multiplying 375 x 725 gives an answer of 271,875.
In the above problem, add the digits of the first number to get 15, then subtract 9 leaving 6.
Add the digits of the second number to get 14, then subtract out 9 leaving 5.
Then multiply the two answers of 6 and 5 to get 30. Subtract out all 9's, in this case 27, to get 3.
Then add the digits in the answer to get 30. Subtract out all 9's, in this case 27, to get 3. Since 3 equals 3, the multiplication is correct. Works every time.
While it seems like a lot of extra hard work to prove an answer, once I got the gist, it came fast and I never had another wrong multiplication problem. I still use it today whenever I dont have a calculator handy.
Multiplying 375 x 725 gives an answer of 271,875.
In the above problem, add the digits of the first number to get 15, then subtract 9 leaving 6.
Add the digits of the second number to get 14, then subtract out 9 leaving 5.
Then multiply the two answers of 6 and 5 to get 30. Subtract out all 9's, in this case 27, to get 3.
Then add the digits in the answer to get 30. Subtract out all 9's, in this case 27, to get 3. Since 3 equals 3, the multiplication is correct. Works every time.