Question

Find the ratio of 10 hours to a day.

Answer 1

Hint: We have to find the ratio of 10 hours to a day so first of all to solve this problem we have to convert a day into the number of hours to make the units of the numerator and the denominator in the ratio or fraction to be same. Without the same units, we cannot solve the fraction. We will convert a day to hours according to this unit criteria i.e. 1 day = 24 hours. After that, we will simplify the ratio by canceling out any common factors from the numerator or denominator if they have any. And we will get the answer.

Complete step-by-step solution:
We have to find the ratio of 10 hours to a day,
This can be represented as,
10 hours: 1 day
Now by converting it to fractional form we get,
= $\dfrac{10\,hours}{1\,day}$
We know that to simplify any fraction we need to first make the units of numerator and denominator same,
We can do this using the universal fact that 1 day = 24 hours,
So applying the above fact in our equation, we get
= $\dfrac{10\,hours}{24\,hours}$
Now we can cancel out the unit hour from numerator and denominator, so we get
= $\dfrac{10}{24}$
Now we can also write the above equation as,
= $\dfrac{2\times 5}{2\times 12}$
Now dividing both numerator and denominator by 2, we get
$=\dfrac{5}{12}$
As 5 and 12 do not have any common factor so this fraction cannot be solved further, so by converting the fraction form again into ratio we will get the answer, i.e.
5: 12
Hence our answer is 5: 12

Note: Remember whenever you are given a fraction of a ratio to simplify then always first make sure that the units of the numerator and denominator are same, otherwise, you may get the wrong answer and also in this problem remember to convert the fractional form back into the ratio else you may lose marks for that.