Question

What fraction of an hour is $45$minutes?
A) $\dfrac{3}{4}$
B) $\dfrac{5}{6}$
C) $\dfrac{7}{9}$
D) $\dfrac{4}{3}$

Answer 1

Hint: We are given a question in which we have to find the amount of fraction of an hour that will be equal to the particular amount of minute. As we know that there are $60$ minutes in an hour. We can convert any minute into a fraction of an hour by dividing it by $60$. For example, $10$ minutes is $\dfrac{{10}}{{60}} = \dfrac{1}{6}$ of an hour. It’s a good idea to simplify fraction as is done in these examples to make subsequent calculations with the fraction less cumbersome. First we will derive the formula then substitute it.

Complete step-by-step solution:
Step1: We are given $45$ minutes and we have to convert them into a fraction of an hour. For that first we will derive the formula and for that we will assume the number of minutes as $m$.
There are $60$ minutes in an hour. So we can write the number of minutes as a fraction of an hour
By dividing the $m$ by $60$ min/hr.
$ \Rightarrow \dfrac{m}{{\dfrac{{60\min }}{{hr}}}}$
Here by doing so we have derived the general formula for converting the minutes as a fraction of an hour. In the formula $m$ is the no of minutes that is to be converted.
Step2: Minutes we are given are $45$ so we will use the above derived general formula and substitute the value of minutes into it.
$ \Rightarrow \dfrac{m}{{\dfrac{{60\min }}{{hr}}}}$
Putting $m = 45$
$ = \dfrac{{45}}{{60}}$
Reducing the term by 3 we get:
$ = \dfrac{{15}}{{20}}$
Again by reducing the term by $4$ we get:
$ = \dfrac{3}{4}$hour
So fraction of an hour produced is $\dfrac{3}{4}$

Hence option (A) is the correct answer.

Note: In such types of questions students just have to remember to convert the minutes into a fraction of an hour. Just divide by $60$. As there are $60$minutes in an hour. And the number of minutes is fixed. And for doing such types of questions just derive the general formula which is beneficial as it saves time. We don't have to do the same steps again and again just apply the formula directly. It makes the calculation faster and also shows the grip on the concept of the student. Calculation is also quite easy. Unit for the fraction will be hours as minutes get cancelled in division.