Question

I.What fraction of an hour is 24 minutes?
II.How many natural numbers are there from 2 to 10. What fraction of them are prime numbers?

Answer 1

Hint: There are two main questions in the given problem. We have to find fractions in both the cases. The first part can be solved by taking the given minutes and dividing it by total minutes of one hour. The second part requires us to find total natural numbers present between \[2\]to \[10\]and the finding out the fraction of the prime numbers to the total numbers.

Complete step-by-step answer:
I.We are given the fraction to be found in minutes. So we will take them in minutes.
Thus, \[1hr = 60\min \]
So the fraction of an hour is minutes. Thus we will take 24 in numerator and 60 in denominator.
\[ = \dfrac{{24}}{{60}}\]
This is not the simplified fraction. We will find the HCF of these numbers and we will divide them by it to get a simplified fraction.
Factors of 24 are \[1,2,3,4,6,8,12,24\]
Factors of 36 are \[1,2,3,4,5,6,10,12,15,20,30,60\]
HCF is 12.
Thus on dividing by 12 we get,
\[ = \dfrac{2}{5}\]
This is the answer for the first question.

II.Natural numbers are a subset of the number system that encompasses all positive integers from \[1\] to infinity and are used for counting.
Natural numbers from 2 to 10 are 2,3,4,5,6,7,8,9,10. Thus there are a total of 9 numbers.
Now the numbers that are prime are 2,3,5,7. That is only 3.
Thus the fraction will be, in numerator the numbers that are prime and in denominator total numbers.
\[ = \dfrac{4}{9}\]
This is the correct answer.

Note: In the second part of the question, we had to find the prime numbers and natural numbers.
Natural numbers do not include negative numbers or zero.
Positive integers with just two factors, 1 and the integer itself, are known as prime numbers. The prime numbers are also known as the numbers that are only divisible by one or the number itself.