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Rick890
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It seems that if the number 9 is multiplied by a number, the resulting digits of that number will sum to 9. Does this always hold true? Is there a simple proof for this, or at least a proof up to some finite number?
Rick890 said:It seems that if the number 9 is multiplied by a number, the resulting digits of that number will sum to 9. Does this always hold true? Is there a simple proof for this, or at least a proof up to some finite number?
robert Ihnot said:This fact was often used by bookkeepers in the old days as a check on figures. After calculating the answer, they would go through the problem again "casting out nines," to get a check.
For example: 125x275 = 34375== 4 Mod 9. and 125==8 Mod 9, 275 ==5 Mod 9. So that 125 x 275 ==8x5=40==4 Mod 9.
Hmmm...I think this sentence could have been better constructed, wot?Dodo said:This is a consequence of the behavior of modular arithmetic, plus the fact that 10 = 1 (mod 9).
Chris Hillman said:For another amusing and instructive fact about grade school arithmetic, see https://www.physicsforums.com/showthread.php?p=1413810#post1413810
The "Number 9 multiplication trick" is a mental calculation technique that helps simplify the process of multiplying a number by 9.
The trick involves multiplying the number by 10 and then subtracting the original number from the result. For example, to multiply 9 by 6, you would multiply 6 by 10 to get 60, and then subtract 6 from 60 to get the answer 54.
The trick can be helpful in situations where you need to do quick mental calculations, such as in exams or in daily life. It can also help improve mental math skills and make multiplication easier to understand.
The trick only works for numbers that are multiples of 9. It also may not be as accurate as using traditional multiplication methods, so it is important to double-check the answer.
You can practice by using the trick with different numbers and trying to calculate the answers mentally. You can also try using the trick in everyday situations, such as calculating tips or grocery prices, to become more comfortable with it.