Question

How many minutes are in $$9{\displaystyle \frac{1}{4}}$$ 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 $$9{\displaystyle \frac{1}{4}}$$ hour.
Now, we will convert the mixed fraction into an improper fraction. So, we get
$$\Rightarrow 9{\displaystyle \frac{1}{4}}\mathrm{H}\mathrm{o}\mathrm{u}\mathrm{r}={\displaystyle \frac{9\times 4+1}{4}}\mathrm{H}\mathrm{o}\mathrm{u}\mathrm{r}$$
Now, by simplifying the expression, we get
$$\Rightarrow 9{\displaystyle \frac{1}{4}}\mathrm{H}\mathrm{o}\mathrm{u}\mathrm{r}={\displaystyle \frac{37}{4}}\mathrm{H}\mathrm{o}\mathrm{u}\mathrm{r}$$
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.
$$\Rightarrow {\displaystyle \frac{37}{4}}\mathrm{H}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s}={\displaystyle \frac{37}{4}}\times 60min$$
Dividing 60 by 4, we get
$$\Rightarrow {\displaystyle \frac{37}{4}}\mathrm{H}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s}=37\times 15min$$
Now, multiplying the terms, we get
$$\Rightarrow {\displaystyle \frac{37}{4}}\mathrm{H}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s}=555min$$

Therefore, the minutes in $$9{\displaystyle \frac{1}{4}}$$ hour is 555 minutes.

Note:
We know that an hour is defined as a unit of time of $${\displaystyle \frac{1}{24}}$$ of a day. A minute is defined as a unit of time of $${\displaystyle \frac{1}{60}}$$ 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
$$9{\displaystyle \frac{1}{4}}\mathrm{h}\mathrm{r}\mathrm{s}=\left(9+{\displaystyle \frac{1}{4}}\right)\mathrm{h}\mathrm{r}\mathrm{s}$$
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.
$$\Rightarrow 9{\displaystyle \frac{1}{4}}\mathrm{h}\mathrm{r}\mathrm{s}=\left(9+{\displaystyle \frac{1}{4}}\right)\times 60min$$
Now, by using the distributive property of multiplication, we get
$$\Rightarrow 9{\displaystyle \frac{1}{4}}\mathrm{h}\mathrm{r}\mathrm{s}=\left(9\times 60+{\displaystyle \frac{1}{4}}\times 60\right)min$$
Now, by simplifying the terms, we get
$$\Rightarrow 9{\displaystyle \frac{1}{4}}\mathrm{h}\mathrm{r}\mathrm{s}=\left(540+15\right)min$$
$$\Rightarrow 9{\displaystyle \frac{1}{4}}\mathrm{h}\mathrm{r}\mathrm{s}=555min$$
Therefore, the minutes in $$9{\displaystyle \frac{1}{4}}$$ hour is 555 minutes.