Question

What fraction of a week is $3$ days?

Answer 1

Hint: In this question, we have to find the fraction that represents three days out of a whole week. So, we will first find the number of parts of a week that corresponds to the given number of days and then form a fraction on that basis. We will also simplify the fraction by cancelling the common factors in numerator and denominator. When the numerator and the denominator are in the form of prime factors and don’t have any common factor, the fraction is said to be simplified. We can find whether the given fraction is simplified or not by writing both the numerator and the denominator as a product of their prime factors, and thus simplify the fraction if it is not in the simplified form.

Complete step-by-step solution:
Now, we have to find the fraction that represents three days out of a whole week.
So, we know that a whole week consists of seven days.
So, we have to find the fraction that corresponds to three out of seven days.
Fraction represents a part of whole. The numerator of the fraction represents the part and the denominator represents the whole quantity.
So, three will be the numerator and seven will be the denominator in the required fraction. So, we get the fraction as $\left( {\dfrac{3}{7}} \right)$.
Now, the numerator and the denominator in the fraction are both prime numbers and don’t have any common factor, so it cannot be simplified further.
Hence, the fraction is in the simplified form.
Therefore, $\left( {\dfrac{3}{7}} \right)$ fraction of a week is $3$ days.

Note: When a horizontal line divides a term into two parts such that there is one number above the horizontal line and one below it, the part above the horizontal line is called the numerator and the denominator is the lower part. Following the information and the steps mentioned in the above solution, we can solve similar questions. We must check the common factors between numerator and denominator before getting to the final answer.