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. a) 92_389 b) 8 __ 9484
Solution:
We will use the divisibility rule of 11 to answer the question.
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.
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
Therefore, the number at blank space will be 6
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. a) 92_389 b) 8 __ 9484
Summary:
a) The number at blank space 92_389 will be 8, b) The number at blank space 8 __ 9484 will be 6.
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