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[mathematics of grade one] a two digit number, a on the tenth digit and B on the tenth digit. A new two digit number is obtained by exchanging the numbers on the tenth digit and the single digit A new two digit number is obtained by exchanging ten digit numbers with one digit numbers Try to explain that the sum of the original two digits and the new two digits is a multiple of 11, and the difference is a multiple of 9
The original two digit number is 10A + B, now the two digit number is 10B + a
The sum of them is 10A + B + (10b + a) = 11a + 11b = 11 (a + b)
So the sum of them is a multiple of 11
The difference is 10A + B - (10b + a) = 9a-9b = 9 (a-b)
So the difference is a multiple of nine
RELATED INFORMATIONS
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