Question

Write the natural numbers from \[102\] to\[113\]. What fraction of them are prime numbers?

Answer 1

Hint:Write the set of natural numbers from \[102\] to \[113\] and we have to choose a set of prime numbers from \[102\] to \[113\] and calculate what fraction of them are prime numbers.

Complete step-by-step answer:
Natural numbers start with \[1\] and \[2,{\text{ }}3,{\text{ }}4\]…etc., are called natural numbers
Here we have to write from \[102\] to \[113\] and prime numbers from \[102\] to\[113\].
The number is said to be a prime number, it has only two divisors one is \[1\] and another is itself.
E.g. \[2,3,5,7,11,..\] etc., these are the prime number, it has only two divisors.
The number which is not prime is called composite numbers (except \[1,{\text{ }}1\] is neither prime nor composite).

First the set of natural numbers from \[102\] to \[113\] is
 \[\{ 102,103,104,105,106,107,108,109,110,111,112,113\} \]
Then we split into two sets, they are composite and prime numbers.
Composite numbers\[ = \{ 102,104,105,106,108,110,111,112\} \]
Prime number\[ = \{ 103,107,109,113\} \]
Consider the prime numbers set, it has \[4\] elements (numbers)
Also, the set of natural number from \[102\] to \[113\] has \[12\] elements (numbers)
Then, we get there are\[\;4\] numbers are prime numbers out of \[12\] numbers.
Fraction of prime numbers is equal to the total number of prime numbers from \[102\] to \[113\] divided by the total numbers of natural numbers.
Number of prime numbers is \[4\]; total number of numbers is \[12\]
Then, we get fraction of prime number \[ = \dfrac{4}{{12}}\]
On Simplification,
 We get fraction of prime number \[ = \dfrac{1}{3}\]
Hence, \[\dfrac{1}{3}\] fraction of them is prime numbers.

Note:Sometimes, we may think every odd number is a prime number, and every number ending with \[1\] or \[7\] are prime numbers but it is not true. Every odd number is not a prime number but every prime number is odd except the number \[2\]. Also, \[2\] is only a prime number which is an even number, all other even numbers are divisible by \[2\].