What fraction of numbers from 1 to 30 is prime?(a) 1/3 (b) 2/3 (c) 5/3 (d) None of the above

To solve this problem, we need to determine the fraction of numbers from 1 to 30 that are prime. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Step 1: List the numbers from 1 to 30
The numbers from 1 to 30 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

Step 2: Identify the prime numbers
Prime numbers between 1 and 30 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

There are 10 prime numbers in total.

Step 3: Calculate the total number of numbers from 1 to 30
There are 30 numbers in total from 1 to 30.

Step 4: Calculate the fraction of prime numbers
The fraction of prime numbers is the number of prime numbers divided by the total number of numbers: Fraction of prime numbers = 10 / 30 = 1 / 3.

Step 5: Conclusion
The correct answer is (a) 1/3.