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To find out which fraction will have the minimum change in value, we need to compare the differences between the original fraction and the new fraction after adding s to both the numerator and denominator.

Let's start with the fraction 2/3. After adding s, the new fraction becomes (2+s)/(3+s). To find the difference in value, we can subtract the original fraction from the new fraction:

(2+s)/(3+s) - 2/3

Simplifying this expression, we get:

(6+3s-2s-2(3+s))/(3(3+s))

= (4-s)/(3+s)

Similarly, we can find the differences for the other fractions:

- For 3/4, the difference is (3+s)/(4+s) - 3/4 = (s)/(4+s)
- For 4/5, the difference is (4+s)/(5+s) - 4/5 = (s)/(5+s)
- For 5/6, the difference is (5+s)/(6+s) - 5/6 = (s)/(6+s)

Now we need to compare these expressions to see which one has the smallest absolute value. We can ignore the sign since we're only interested in the magnitude of the change.

- For 2/3, the absolute value of the difference is |(4-s)/(3+s)|
- For 3/4, the absolute value of the difference is |s/(4+s)|
- For 4/5, the absolute value of the difference is |s/(5+s)|
- For 5/6, the absolute value of the difference is |s/(6+s)|

To find the minimum, we need to find the value of s that minimizes each expression.

- For (4-s)/(3+s), the minimum occurs when s = 4, resulting in a minimum value of 0.
- For s/(4+s), the minimum occurs when s = 0, resulting in a minimum value of 0.
- For s/(5+s), the minimum occurs when s = 0, resulting in a minimum value of 0.
- For s/(6+s), the minimum occurs when s = 0, resulting in a minimum value of 0.

Therefore, the fraction with the minimum change in value is 5/6. Adding s to both the numerator and denominator of this fraction has no effect on its value when compared to the other fractions.