Question

What fraction of numbers from 1 to 30 is prime?
(a) $\dfrac{1}{3}$
(b) $\dfrac{2}{3}$
(c) $\dfrac{5}{3}$
(d) None of the above

Answer 1

Hint: We will list all the prime numbers that are greater than 1 and smaller than 30. We will count the number of elements in this list. To find the fraction of numbers from 1 to 30 that are prime, we will divide the number of elements in the list by the 30, since there are 30 numbers from 1 to 30.

Complete step by step answer:
We will make a list of prime numbers from 1 to 30. These numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. The number of elements in this list is 10. Next, we have to find the fraction of numbers from 1 to 30 which are prime. For this, we will do the following,
$\text{fraction of numbers that are prime from 1 to 30 =}\dfrac{\text{number of primes from 1 to 30}}{30}$
We will substitute the number of primes from 1 to 30 in the above fraction as follows,
$\text{fraction of numbers that are prime from 1 to 30 =}\dfrac{10}{30}$.
The reduced form of the fraction $\dfrac{10}{30}$ is $\dfrac{1}{3}$.

So, the correct answer is “Option A”.

Note: While finding ratios or fraction of some quantity, it is essential that we understand what quantity is to be placed in the numerator and the denominator. It is important to make the list of primes for such types of questions so that we will notice if we have left out any number from the list. If we are not sure whether a number is prime or not, then we can try to factorize it. For this purpose, the divisibility tests are very useful. If we cannot find the factors upto half of that number, then it is possible that it is a prime number.