Question

Express one day as the fraction of $1$ week.

Answer 1

Hint: We know that $1$ day contains $24$ hours. Similarly $1$ week contains $7$ days. So $1$ week contains $7 \times 24$ hours. How we can easily find the fraction $1$ day of $1$ week.

Complete step-by-step answer:
So according to the question we are given to express one day as the fraction of $1$ week. Now for fraction, we need to change both into the same units like days, seconds, hours any one of them.
So, if we consider hours then we need to change $1$ day as well as $1$ week in hours. So as we know that $1$ day contains $24$ hours. So we can write that
$1$ day $ = $$24$ hours
Similarly we know that $1$ week contains seven days and each day contains $24$ hours.
So one week contains $(24 \times 7)$ hours.
Thus we can write it as
$\begin{gathered}
  1{\text{ week}} = 7{\text{ days}} \\
  {\text{1 week}} = 7(24){\text{ hours}} = {\text{168hours}} \\
\end{gathered} $
Now we are asked to find $1$ day as the fraction of $1$ week and we know that $1$ week is equivalent to $24$ hours and also we know that $1$ week is equivalent to $168{\text{ hours}}$.
So if we need to find \[1\] day as the fraction of $1$ week, then as $1$ day is equivalent to $24$ hours and $1$ week is equivalent to $168$ hours. So we can say that to express $1$ day as a fraction of $1$ week = fraction of $24$ hours and $168$ hours.
So $1$ day as the fraction of $1$ week$ = \dfrac{{24}}{{168}} = \dfrac{1}{7}$
So $1$ day is equal to ${\dfrac{1}{7}}^{th}$ week.

Note: We can also express both in terms of day, like we know that $1{\text{ week}} = 7{\text{ days}}$
So $1{\text{ day}} = \dfrac{1}{7}{\text{ week}}$