Question

Write natural numbers from \[30\] to \[45\]. What fraction of these numbers is odd?

Answer 1

Hint:At first we will find the natural numbers from \[30\] to \[45\] and then we will find the fraction of odd numbers in the given range.

Complete step-by-step answer:
We have to find the natural numbers from \[30\] to \[45\].
In Mathematics, natural numbers are the counting numbers. Natural numbers are the part of the number system including all positive integers from \[1\] to infinity. It does not include zero (\[0\]). More precisely, it is the part of real numbers that includes only the positive integers such as \[1,2,3...\] excluding zero, decimals, fractions and negative integers.
So, by the definition we get, the natural numbers from \[30\] to \[45\] are: \[30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45.\]
Again, we have to find the fraction of odd numbers in this range.
We know that the numbers which are not divisible by \[2\], are known as the odd numbers. For example: \[1,3,5,7,9...\] and so on.
So, by the definition the odd numbers from \[30\] to \[45\]are: \[31,33,35,37,39,41,43,45.\]
Here, numbers of natural numbers from \[30\] to \[45\] is \[16.\]
Numbers of odd numbers from \[30\] to \[45\] is \[8.\]
So, the fraction of these numbers is odd is: (number of odd numbers) \[ \div \](number of natural numbers of these range from \[30\] to \[45\])
So, the required fraction is \[\dfrac{8}{{16}} = \dfrac{1}{2}\]

Note:In Mathematics, natural numbers are the counting numbers. Natural numbers are the part of the number system including all positive integers from \[1\] to infinity. It does not include zero (\[0\]). More precisely, it is the part of real numbers that includes only the positive integers such as \[1,2,3...\] excluding zero, decimals, fractions and negative integers.
We know that the numbers which are not divisible by \[2\], are known as the odd numbers. For example: \[1,3,5,7,9...\] and so on.