4 distinct integers p, q, r and s are chosen from the set {1,2,3,…,16,17}. The minimum possible value of (p/q)+(r/s) can be written as a/b, where a and b are positive, coprime integers. What is the value of a+b?
To find the minimum possible value of (p/q) + (r/s), we need to find the smallest values for p, q, r, and s from the given set {1,2,3,…,16,17}.
Let's start by choosing the smallest values for p and q. We can select 1 as the smallest value for p, and 2 as the smallest value for q.
Next, let's choose the smallest values for r and s. Since we need distinct integers, we cannot choose 1 again. So, we choose the next smallest value, 3, for r. For s, we can choose either 4 or any value greater than 4 since 4 is already chosen for q. Let's choose 4 as the smallest value for s.
Now, we can substitute these values into the expression (p/q) + (r/s):
(1/2) + (3/4)
To add fractions, we need to find a common denominator. In this case, the common denominator is 4. Let's convert both fractions:
(2/2)*(1/2) + (3/4)
= 2/4 + 3/4
= 5/4
So, the minimum value of (p/q) + (r/s) is 5/4.
Since 5 and 4 are coprime, the value of a+b is 5+4 = 9.
Therefore, the answer is 9.