Question

In this fill in the blank; ${\displaystyle \frac{3}{7}}$ of a week = ……….. days, the blank space contains the value:
(a) 4
(b) 3
(c) 2
(d) 7

Answer 1

Hint: We know that there are 7 days in a week and we have to find how many days are there in ${\displaystyle \frac{3}{7}}$ of a week so ${\displaystyle \frac{3}{7}}$ of a week means we have to multiply ${\displaystyle \frac{3}{7}}$ by 7 to get the number of days in a week. Now, solve this fraction and then match your answer from the options given in the above question. We have put 1 week in place for 7 days because we want answers in days.

Complete step-by-step answer:
We have to fill in the blank:
${\displaystyle \frac{3}{7}}$ of a week = ……….. days
The above fill in the blank means that we have to find the number of days that ${\displaystyle \frac{3}{7}}$ of a week contains.
We know that there are 7 days in a week. So if we put 7 days in place of “a week” in the given question we get,
${\displaystyle \frac{3}{7}}$ of (7 days)
The mathematical formulation of the above expression we get,
${\displaystyle \frac{3}{7}}\times \left(7days\right)$
As you can see that in the above expression, 7 is written in the numerator and denominator so 7 will be cancelled out and our expression is reduced to:
$\begin{array}{rl}& {\displaystyle \frac{3}{1}}\times \left(1day\right)\\ & =3days\end{array}$
The above solution has given us ${\displaystyle \frac{3}{7}}$ of a week for 3 days so the blank in the above question contains the number 3.

So, the correct answer is “Option b”.

Note: This question demands knowledge about the number of days in a week. If you know the number of days in a week then the question is just a cup of tea.
One more thing, you might get a question which is vice versa of this problem that you have given 3 days and asked you to find which fraction of a week does 3 days contain.
Then you have to divide 3 by 7 to get the fraction of a week that 3 days has:
${\displaystyle \frac{3}{7}}$