分钟 <--> 天

Sometimes in order to convert one unit to another, there are intermediate conversion steps. For example, if we want to convert minutes into days, we must first convert minutes into hours, and then the number of hours that we found from that into days.

What units might we be dealing with? A minute is a unit of time, as are second, hour, and day. There are others, but these are the most commonly used.

As an example, let's convert $2{,}500 \text{ minutes}$ into $\text{days}$.

We know that an hour is equal to $60$ minutes, so we set up our minutes to hour conversion like this. $$2{,}500 \text{ minutes} \times \frac{1 \text{ hour}}{60 \text{ minutes}} \approx 42.667 \text{ hours}$$

We then want to convert the number of hours into days, by another unit conversion: $$42.667 \text{ hours} \times \frac{1 \text{ day}}{24 \text{ hours}} \approx 1.736 \text{ days}$$

We could have also done this more concisely in one line like so: $$2{,}500 \text{ minutes} \times \frac{1 \text{ hour}}{60 \text{ minutes}} \times \frac{1 \text{ day}}{24 \text{ hours}} \approx 1.736 \text{ days}$$

The correct answer is $\approx3.615 \text{ days}$. We see the conversion is: $$5{,}205 \text{ minutes} \times \frac{1\text{ hour}}{60\text{ minutes}}\times \frac{1\text{ day}}{24\text{ hours}}\approx3.615 \text{ days}$$

The correct answer is $6{,}192 \text{ minutes}$. We see the conversion is: $$4.3 \text{ days} \times \frac{24\text{ hour}}{1\text{ day}}\times \frac{60\text{ minutes}}{1\text{ hour}}=\boxed{6{,}192 \text{ minutes}}$$

When converting different units of measurements, in this case minutes to days, it is important to set up the ratios correctly. A trick to knowing if you set up the ratios correctly is by checking if your units cancel each other out. Treat the ratios exactly how you treat fractions. If you have the same thing in the numerator (top) and the denominator (bottom), they can cancel each other out.

When setting up the ratios begin with what you are being asked to convert. In this case we will find the amount of minutes in a day. $$1{\color{#8925AE}{\text{ day}}}\cdot\frac{24{\color{#29A603}{\text{ hours}}}}{1 {\color{#8925AE}{\text{ day}}}}\cdot\frac{60\text{ minutes}}{1 {\color{#29A603}{\text{ hour}}}}=\,??? \text{ minutes}$$ Notice the units! Because there are days and hours in the top and the bottom of the fractions, they cancel each other out. Since the only unit remaining in the left side of the equation is minutes, we know we set the problem up correctly and can solve for the number of minutes in a day.

$$1\,\cancel{{\color{#8925AE}{\text{day}}}}\cdot\frac{24\,\cancel{\color{#29A603}{\text{hours}}}}{1\,\cancel{\color{#8925AE}{\text{day}}}}\cdot\frac{60\text{ minutes}}{1\,\cancel{\color{#29A603}{\text{hour}}}}=1{,}440\text{ minutes}$$

Now that we know there are $1{,}440 \text{ minutes}$ in a $\text{day}$, we can use that as a conversion factor instead of converting days to hours then to minutes.

Suppose we wanted to convert $3 \text{ days}$ into $\text{minutes}$. We now know that $1 \text{ day} = 1{,}440 \text{ minutes}$ so we can use that information to solve this problem. Remember to check if your units cancel when setting up the equation. $$3{\color{#8925AE}{\text{ days}}}\cdot\frac{1{,}440\text{ minutes}}{1{\color{#8925AE}{\text{ day}}}}=4{,}320\text{ minutes}$$

There is another unit between minutes and days—hours. We know there are $60 \text{ minutes}$ in an hour and $24 \text{ hours}$ in a $\text{day}$.

First, let's convert days to minutes. Recall that when going from bigger units to smaller units, we multiply. There are $1\times24\times60=1{,}440 \text{ minutes}$.

Now, let's convert, for example, $2{,}000\text{ minutes}$ to $\text{days}$. Going from smaller units to bigger units we divide. There are $2{,}000\div60\div24\approx1.39 \text{ days}$.

Here are the unit rates for minutes and days:

$$\frac{1 \text{ day}}{1440 \text{ minutes}}$$ $$\frac{1440 \text{ minutes}}{1 \text{ day}}$$

These are actually equal to each other. That means we get to call them proportions.