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Find the missing digit in each of the following numbers to make them divisible by 11: a) 27...3, b) 1...574, c) 939...?
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4 partsStep-by-step solution
8 stepsTo find the digit in the blank space such that the number is divisible by 11, we use the divisibility rule for 11: a number is divisible by 11 if the alternating sum of its digits (starting from the rightmost digit) is divisible by 11.
Part a· 2 steps
27.......3
Let the missing digit be . The number is .
Calculate the alternating sum of the digits.
For the number to be divisible by 11, the alternating sum must be a multiple of 11 (e.g., 0, 11, -11, etc.).
Since is a single digit (0-9), the only multiple of 11 possible for is 0.
The number is 2783.
Part b
1....... 574
Let the missing digit be . The number is .
Calculate the alternating sum of the digits.
For the number to be divisible by 11, the alternating sum must be a multiple of 11.
Since is a single digit (0-9), the only multiple of 11 possible for is 0.
The number is 13574.
Part c
939.......
Let the missing digit be . The number is .
Calculate the alternating sum of the digits.
For the number to be divisible by 11, the alternating sum must be a multiple of 11.
Since is a single digit (0-9), the only multiple of 11 possible for is -11.
The number is 9394.
Part d
10....... 5
Let the missing digit be . The number is .
Calculate the alternating sum of the digits.
For the number to be divisible by 11, the alternating sum must be a multiple of 11.
Since is a single digit (0-9), the only multiple of 11 possible for is 0.
The number is 1045.
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