It is known that positive integers, N, K satisfy the inequality 6 / 11 ＜ n / K ＜ 5 / 9, then when n and K take the minimum value, the value of N + k is?

It is known that positive integers, N, K satisfy the inequality 6 / 11 ＜ n / K ＜ 5 / 9, then when n and K take the minimum value, the value of N + k is?

6 / 11 & lt; n / K & lt; 5 / 9 according to a / b ＜ C / D, then a / b ＜ (a + C) / (B + D) ＜ C / D, 6 + 5 = 119 + 11 = 206 / 11 ＜ 11 / 20 ＜ 5 / 9N = 11, k = 20 & nbsp; so n + k = 11 + 20 = 31

All of them are equal to 7 / 18

7/18＜N/6＜8/9
7/3＜N＜16/3
Because n is a natural number
So n can be 3, 4, 5
The sum is 3 + 4 + 5 = 12

How many different solutions can you come up with

（15）（2）
（22）（3）
（23）（3）
（31）（4）
（29）（4）
（39）（5）
（38）（5）
（37）（5）
（36）（5）
（47）（6）
. countless

Find the minimum natural number n, so that 8 / 15 is less than N + K, N / 13 is less than 7 / 13 for a unique integer K

8/1513/7
7/8>k/n>6/7
14/16>k/n>12/14
k=13,n=15