# Write the smallest digit and the largest digit in the blanks space of each of the following numbers so that the number formed is divisibly by 11.

We will use the divisibility rule of 11 to answer the question.

## Answer: a) The number at _ will be 8

## b) The number at _ will be 6

The number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or divisible by 11.

## Explanation:

a) 92_389

Sum of odd digits = 9 + (blank space) + 8

= 17 + blank space

Sum of even digits = 2 + 3 + 9 = 14

As per Divisibility rule of 11,

The number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or divisible by 11.

If we make the sum of odd digits = 25

Difference between the sum of the digits at odd places and the sum of the digits at even places** **

= Sum of odd digits - Sum of even digits

= 25 - 14 = 11

which is divisible by 11.

To make the sum of odd digits = 25,

The number at black space will be = 25 - 17

### Therefore, the number at blank space will be 8

b) 8 __ 9484

Sum of odd digits = 8 + 9 + 8 = 25

Sum of even digits = blank space + 4 + 4

= blank space + 8

As per Divisibility rule of 11,

The number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is either 0 or divisible by 11.

If we make the sum of even digits = 14

Difference between the sum of the digits at odd places and the sum of the digits at even places** **

= Sum of odd digits - Sum of even digits

= 25 - 14 = 11

which is divisible by 11.

To make the sum of even digits = 14,

The number at black space will be = 14 - 8