Question

What fraction of a day is 8 hours?

Answer 1

Hint: In this question, we need to find what the fraction of a day is 8 hours. For this, we will first convert the day into the number of hours. Given hours will be in the numerator and total hours will be in the denominator. After that, we will simplify the fraction to get our required answer.

Complete step by step answer:
Here we need to find what the fraction of a day is 8 hours. For this, we need to find the fraction in which 8 hours is in the numerator and day is in the denominator. But we know we cannot solve a fraction unless the units are the same. So we need to convert a day into hours. We know that 24 hours comprises 1 day.
Therefore, 1 day = 24 hours.
Now we can write numerator as 8 hours and denominator as the number of hours in a day i.e. 24 hours. Hence our fraction looks like this $ \dfrac{8\text{ hours}}{\text{24 hours}}=\dfrac{8}{24} $ .
Now we need to simplify the fraction as much as possible. Since both the numerator and denominator are even numbers so dividing them by 2 we get, $ \dfrac{8\div 2}{24\div 2}=\dfrac{4}{12} $ .
Again dividing the numerator and the denominator by 2 we get, $ \dfrac{4\div 2}{12\div 2}=\dfrac{2}{6} $ .
Again dividing the numerator and the denominator by 2 we get, $ \dfrac{2\div 2}{6\div 2}=\dfrac{1}{3} $ .
It cannot be simplified further, therefore, the required fraction is $ \dfrac{1}{3} $ .
Hence $ \dfrac{1}{3} $ of a day is 8 hours.

Note:
Students should note that 8 hours should always be in the numerator and 24 hours in the denominator. Students can also check the answer as following,
 $ \dfrac{1}{3} $ of the day is 8 hours, we can say, $ \dfrac{1}{3} $ of 24 hours = 8 hours.
 $ \dfrac{1}{3}\times 24\text{ hours}=8\text{ hours} $ .
8 hours = 8 hours. Hence our answer is verified.
Make sure to divide both numerator and denominator by the same number to find the reduced fraction.