I am having issues determining the correct average for the question below:

**Question:**

1/2

1/2

1/2

1/2

1/100

I think the answer should be one of these two::

Average = (0.5+0.5+0.5+0.5+0.01)/5 = 0.402

Average = Sum of numerator/sum of denominator

Average = (1+1+1+1+1)/(2+2+2+2+100) = 0.04629

Which of these two answers is mathematically correct/right? **And why?**
> Sum of numerator/sum of denominator

This is a meaningless operation,

Consider:

1/2 and 1/100 => (1+1)/(2+100) = 2/102 = 1/51

2/4 and 5/500 => (2+5)/(4+500) = 7/504 = 1/72

These two should have the same result.
The first way. 1/2 and 1/100 are numbers on a number line. Not sure why you would add denominators? The values in decimal form are as you have.

The average of all those 1/2s would have to be closer to 0.5 than 0.01

If you had 4 piles of 50 cents (1/2 dollars) and 1 pile of a sole penny, the sum is the total all mushed together (so 201 cents). The average (there are more than one average-others being median and mode, so the mean in this case) 'means' sharing out the 201 cents into 5 piles. Or 40.2 cents each. (0.402).
The first one is consistent with the actual definition of the average. When you get stuck like this, it's always good to look up the relevant definitions so you know you're working from a good foundation.

If your intuition is telling you that the two expressions should be equivalent, then your intuition was wrong. Honestly I'm not sure how you even came with the second expression, so it's hard to explain *why* it's wrong.