### Instruction: What is the smallest possible average of four distinct positive even integers?### Response: I want to find four even numbers that are as small as possible, but also distinct, meaning they are different from each other.
The smallest even number is 2, so I can use that as one of the numbers.
The next smallest even number is 4, so I can use that as another number.
But I can't use 2 or 4 again, because they have to be distinct.
The next smallest even number is 6, so I can use that as a third number.
The next smallest even number is 8, so I can use that as the fourth number.
Now I have four distinct positive even numbers: 2, 4, 6, and 8.
To find their average, I need to add them up and divide by 4.
2 + 4 + 6 + 8 = 20.
20 divided by 4 is 5.