Question

Take a two digit number and add its digit. Subtract this sum from the number . Find the algebra of this

Answer 1

Answer:

Step-by-step explanation:

A two-digit number can be represented as multiples of 10.

  For example: 21 = 10x2 + 1  and 45 = 10x4 + 5.

  So a number with the left-hand digit of a and the right-hand

  digit of b can be written as 10a + b.

  If you sum the digits you get a + b.

  If you subtract that sum from the original number you get

     (10a + b) - (a + b)

      10a - a + b - b

       9a

  So the value is always 9 times the left-hand digit. And

  anything times nine is a multiple of nine.

This also works with three-digit numbers.

  A three-digit number is 100a + 10b + c.

  The sum of the digits is a + b + c.

  If we subtract them we get:

     (100a + 10b + c) - (a + b + c)

      100a - a + 10b - b + c - c

       99a + 9b

  And that is also evenly divisible by nine.

In fact this works for all numbers of any length.