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Question 666248: Pick a two digit number with the digits different. Reverse the digits. Subtract the small number from the larger number. Add the digits in the difference. Why is the sum of the digits always nine?
Example: 27. 72-27 = 45. 4+5=9
Found 3 solutions by Alan3354, lynnlo, MathTherapy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Pick a two digit number with the digits different. Reverse the digits. Subtract the small number from the larger number. Add the digits in the difference. Why is the sum of the digits always nine?
Example: 27. 72-27 = 45. 4+5=9
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t = 10's
u = 1's
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Number = 10t + u
Reversed = 10u + t
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10t + u - (10u + t) = 9t - 9u
It's divisible by 9
Answer by lynnlo(4176)  (Show Source):
You can put this solution on YOUR website! pick two digits============reverse the digits==subtract==add=
25=========== 52 27 2+7=9
18 81 63 6+3=9
30 03 27 2+7=9
23 32 9 0+9=9
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Pick a two digit number with the digits different. Reverse the digits. Subtract the small number from the larger number. Add the digits in the difference. Why is the sum of the digits always nine?
Example: 27. 72-27 = 45. 4+5=9
Every two-digit number - even those not considered to be 2-digit numbers, such as 01, 02, 03, etc. – when transposed (switching of their digits-place) has a difference that is a multiple of 9. Now, ALL multiples of 9 contain digits that sum to 9, and this is why the sum of the digits will ALWAYS sum to 9.
For example, 01 reversed or transposed gives us 10. Their difference is 9 (multiple of 9), and as seen, the sum of the digits of their difference (9 & 0) is 9.
Sixty-three (63) reversed or transposed gives us 36. Their difference is 27 (multiple of 9), and as seen, the sum of the digits of their difference (2 & 7) is 9.
Try any 2-digit number and after transposing them, you'll have the same result as above.
Send comments and “thank-yous” to “D” at MathMadEzy@aol.com
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