The natural numbers from 102 to 113 can be written as: 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113.

To determine which of these numbers are prime numbers, we need to recall the definition of prime numbers. A prime number is a number greater than 1 that is divisible only by 1 and itself.

Let's analyze each of the numbers from 102 to 113:

1. 102: This number is divisible by 2, so it is not a prime number.
2. 103: This number is only divisible by 1 and itself, so it is a prime number.
3. 104: This number is divisible by 2, so it is not a prime number.
4. 105: This number is divisible by 3 and 5, so it is not a prime number.
5. 106: This number is divisible by 2 and 53, so it is not a prime number.
6. 107: This number is only divisible by 1 and itself, so it is a prime number.
7. 108: This number is divisible by 2, 3, 4, 6, 9, 12, 18, 27, 36, and 54, so it is not a prime number.
8. 109: This number is only divisible by 1 and itself, so it is a prime number.
9. 110: This number is divisible by 2, 5, and 11, so it is not a prime number.
10. 111: This number is divisible by 3, so it is not a prime number.
11. 112: This number is divisible by 2, 4, 7, 8, 14, 16, 28, 56, and 112, so it is not a prime number.
12. 113: This number is only divisible by 1 and itself, so it is a prime number.

Out of the 12 numbers from 102 to 113, we can see that 4 of them are prime numbers: 103, 107, 109, and 113.

To calculate the fraction of prime numbers, we need to divide the number of prime numbers by the total number of numbers:

Fraction of prime numbers = Number of prime numbers / Total number of numbers

Fraction of prime numbers = 4 / 12 = 1/3

Therefore, the fraction of prime numbers among the natural numbers from 102 to 113 is 1/3, which corresponds to option A.

The natural numbers from 102 to 113 are102, 103,104,105,106,107,108,109,110,111,112,113

the prime numbers are 103,107,109,113

thus the fraction is 4/12 =the simplest form is 1/3

therfore, the answer is 1/3 which is proved