The sum and the difference of the largest and the smallest four digit numbers is {fill regular} and ____.

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Detailed Solution

Concept-The sum and the difference of the largest and the smallest four digit numbers is 10999 and 8999.
There are a total of 10 basic digits that help form each digit: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The smallest possible 4-digit number should start at 1 and be as high as possible. The number must start with 9. Use this concept to get the sum and difference.
Possible numbers are (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9).
Next, you need to create the minimum and maximum 4-digit numbers.
We found that we couldn't start a number from zero, so if not, for example, the number would be converted to a three-digit number (0123 = 123).
Therefore, the smallest four digits start at 1 and the rest of the terms are padded with the smallest digit, zero.
Hence, the smallest 4-digit number

.
Then create the maximum 4-digit number. As you know, with the maximum 4-digit number, you can fill the maximum number 9 in every position.
Therefore, the maximum 4-digit number is

.
Next, we need to calculate the sum and difference between these two numbers.
(i) Total (S)

Therefore, the sum of the maximum and minimum 4-digit numbers is 10999.
(ii) Difference (D)

Therefore, the difference between the maximum and minimum 4-digit numbers is 8999.
Hence, the correct answers are sum= 10999 and difference= 8999

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