Question

Ayesha has a theory about two digits numbers that have a larger tens digit then ones digit.she says that reversing the digits and subtracting the reversed number from the original number will always generate a number that is multiple of 9.is ayesha right?if so why do you think this works?if not,why not?

Answer 1

Answer:

Yes she is right

Step-by-step explanation:

Given that Ayesha has a theory about two digits numbers that have a larger tens digit then ones digit.she says that reversing the digits and subtracting the reversed number from the original number will always generate a number that is multiple of 9.

The reason is as follows: Let x be in 10th digit and y be in unit digit.

x>y

10x+y will be the place value.

If reversed we have 10y+x would be the value of the number

Difference would be

$10x+y-(10y+x)\\=9x-9y\\=9(x-y)$

Hence this has to be a multiple of 9.

Answer 2

Yes she is right. It works because the sum of the individual digits of the difference is divisible by nine.