To determine the fraction of prime numbers among the natural numbers from 2 to 12, we first need to identify which of these numbers are prime.
The natural numbers between 2 and 12 are: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
Next, we identify the prime numbers in this range. A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. The prime numbers from 2 to 12 are:
- 2
- 3
- 5
- 7
- 11
Thus, the prime numbers between 2 and 12 are: 2, 3, 5, 7, and 11. This gives us a total of 5 prime numbers.
Now, let’s count the total numbers we considered, starting from 2 to 12:
- Total numbers: 11 (which includes every number from 2 to 12)
To find the fraction of prime numbers, we take the number of prime numbers and divide it by the total count of numbers. Therefore, the fraction of prime numbers in this range is:
Fraction of prime numbers = Number of prime numbers / Total numbers = 5 / 11
In conclusion, the fraction of the natural numbers from 2 to 12 that are prime is 5/11.