Question

How many minutes are in \[9\dfrac{1}{4}\] hour?

Answer 1

Hint: Here, we will first convert the given time in a mixed fraction into an improper fraction. We will use the fact that hour is a larger unit than a minute, so we will multiply the conversion factor and not divide it to the given dimension. So, we will find the required minutes by multiplying the given hour by 60.

Formula Used:
1 Hour is equal to 60 minutes i.e., 1 Hour \[ = \] 60 Minutes.

Complete Step by Step Solution:
We are given that \[9\dfrac{1}{4}\] hour.
Now, we will convert the mixed fraction into an improper fraction. So, we get
\[ \Rightarrow 9\dfrac{1}{4}{\rm{Hour}} = \dfrac{{9 \times 4 + 1}}{4}{\rm{Hour}}\]
Now, by simplifying the expression, we get
\[ \Rightarrow 9\dfrac{1}{4}{\rm{Hour}} = \dfrac{{37}}{4}{\rm{Hour}}\]
We know that 1 Hour is equal to 60 minutes i.e., 1 Hour \[ = \] 60 Minutes.
Now, we will find the minutes in the given hour by multiplying the given hour with 60 to convert into minutes.
\[ \Rightarrow \dfrac{{37}}{4}{\rm{Hours}} = \dfrac{{37}}{4} \times 60\min \]
Dividing 60 by 4, we get
\[ \Rightarrow \dfrac{{37}}{4}{\rm{Hours}} = 37 \times 15\min \]
Now, multiplying the terms, we get
\[ \Rightarrow \dfrac{{37}}{4}{\rm{Hours}} = 555\min \]

Therefore, the minutes in \[9\dfrac{1}{4}\] hour is 555 minutes.

Note:
We know that an hour is defined as a unit of time of \[\dfrac{1}{{24}}\] of a day. A minute is defined as a unit of time of \[\dfrac{1}{{60}}\] of an hour. We can calculate the minutes in the given hour by rewriting the given hours.
Now, we will rewrite the given hours, we get
\[9\dfrac{1}{4}{\rm{hrs}} = \left( {9 + \dfrac{1}{4}} \right){\rm{hrs}}\]
We know that 1 Hour is equal to 60 minutes i.e., 1 Hour \[ = \] 60 Minutes.
Now, we will find the minutes in the given hour by multiplying the given hour with 60 to convert into minutes.
\[ \Rightarrow 9\dfrac{1}{4}{\rm{hrs}} = \left( {9 + \dfrac{1}{4}} \right) \times 60\min \]
Now, by using the distributive property of multiplication, we get
\[ \Rightarrow 9\dfrac{1}{4}{\rm{hrs}} = \left( {9 \times 60 + \dfrac{1}{4} \times 60} \right)\min \]
Now, by simplifying the terms, we get
\[ \Rightarrow 9\dfrac{1}{4}{\rm{hrs}} = \left( {540 + 15} \right)\min \]
\[ \Rightarrow 9\dfrac{1}{4}{\rm{hrs}} = 555\min \]
Therefore, the minutes in \[9\dfrac{1}{4}\] hour is 555 minutes.