Question

find the smallest number that must be added to 128 so that it becomes exactly divisible by 9 . why only that number? ​

Answer 1

Answer:

The smallest number that must be added to 128 so that it becomes exactly divided by 9 is 7.

The other numbers which when added to 128 to make it exactly divided by 9 are multiples of 9 added to 7 and all of them are greater than 7.  Also, adding negative numbers is equivalent to subtracting negative number.  And greater the number subtracted is smaller the number added.  Hence, there is no limit how small a number can be.  Therefore, we are to limit the result to positive numbers only.

Step-by-step explanation:

$\frac{128}{9}$

$=\frac{99+27+2}{9}$

$= 11 + 3 + \frac{2}{9}$

$= 14 + \frac{9-7}{9}$

$= 14 + \frac{9-7}{9}$

$= 14 + \frac{9}{9} - \frac{7}{9}$

$= 14 + 1 - \frac{7}{9}$

$= 15 - \frac{7}{9}$

Therefore. the smallest number that must be added to 128 so that it becomes exactly divided by 9 is 7.

The other numbers which when added to 128 to make it exactly divided by 9 are multiples of 9 added to 7 and all of them are greater than 7.  Also, adding negative numbers is equivalent to subtracting negative number.  And greater the number subtracted is smaller the number added.  Hence, there is no limit how small a number can be.  Therefore, we are to limit the result to positive numbers only.