分钟 <--> 秒

(Video) Converting Units of Time: Minutes to Seconds

by Reenu Math

Here is a Youtube video, by Reenu Math, that covers Converting Minutes to Seconds.

$\large{\text{Summary}}$

There are $60 \text{ seconds}$ in $1 \text{ minute}$. In other words, a second is $\frac{1}{60}$ of a minute. The second is called the base unit of time. That means scientists defined one minute to be $60$ seconds.

Let’s take a look at the example he used.

How many seconds are there in $5 \text{ minutes}$?

Since we know that $1 \text{ minute} = 60 \text{ seconds}$, we can use this information to solve. $$\begin{align} 5 \text{ minutes} \times \frac{60 \text{ seconds}}{1 \text{ minute}} &= 5 \cancel{\text{ minutes}} \times \frac{60 \text{ seconds}}{1 \cancel{\text{ minute}}} \\ &= 5 \times 60 \text{ seconds} \\ &= 300 \text{ seconds} \\ \end{align}$$

Next, he explains how to convert seconds to minutes. Since there is $1 \text{ minute}$ in $60 \text{ seconds}$, there are $\frac{1}{60} \text{ minutes}$ in $1 \text{ second}$.

Let’s take a look at the example he used.

How many minutes are there in $400 \text{ seconds}$?

Since we know that there are $\frac{1}{60} \text{ minutes}$ in $1 \text{ second}$, we can use this information to solve. $$\begin{align} 400 \text{ seconds} \times \frac{1 \text{ minute}}{60 \text{ seconds}} &= 400 \cancel{\text{ seconds}} \times \frac{1 \text{ minute}}{60 \cancel{\text{ seconds}}}\\ &= \frac{400}{60} \text{ minutes}\\ &= \frac{20}{3} \text{ minutes} \end{align}$$

In the last step we reduced the fraction. The numerator and denominator had a common factor of $20$. After dividing that away, the denominator is a prime number. Let's take a look at some of the types of problems you might encounter about converting minutes to seconds.

$$\begin{align} 1.5 \text{ minutes} \times \frac{60 \text{ seconds}}{1 \text{ minute}} &= 1.5 \cancel{\text{ minutes}} \times \frac{60 \text{ seconds}}{1 \cancel{\text{ minute}}}\\ &= 1.5 \times 60 \text{ seconds} \\ &= 90 \text{ seconds} \\ \end{align}$$

$$\begin{align} 600 \text{ seconds} \times \frac{1 \text{ minute}}{60 \text{ seconds}} &= 600 \cancel{\text{ seconds}} \times \frac{1 \text{ minute}}{60 \cancel{\text{ seconds}}}\\ &= \frac{600}{60} \text{ minutes}\\ &= \boxed{10 \text{ minutes}} \end{align}$$

Seconds to Minutes

One day, Ally decided to time how long she could hold her breath. She counts up to $150 \text{ seconds}$. If Ally wants to know how long she can hold her breath for in minutes, how can she change seconds into minutes?

Let's use the fact that there are $60 \text{ seconds}$ in a $\text{minute}$. These are the unit rates:

$$\frac{60 \text{ seconds}}{1 \text{ minute}}$$ $$\frac{1 \text { minute}}{60 \text{ seconds}}$$

Better yet, they are equal, and we call them proportions.

Now we can find out how long Ally can hold her breath.

When converting different units of measurement, in this case seconds to minutes, 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 $\text{minutes}$ that are in $150\text{ seconds}$. $$150{\color{#29A603}{\text{ seconds}}}\times \frac{1 \text{ minute}}{60 {\color{#29A603}{\text{ seconds}}}}=\,??? \text{ minutes}$$ Notice the units! Because there are seconds in the top and the bottom of the fractions, they cancel each other out. Since the only unit remaining on the left side of the equation is minutes, we know we set the problem up correctly and can solve for the number of minutes Ally can hold her breath.

$$150\,\cancel{\color{#29A603}{\text{ seconds}}}\times\frac{1\text{ minute}}{60\,\cancel{\color{#29A603}{\text{seconds}}}}=2.5\text{ minutes}$$

Thus, Ally can hold her breath for $2.5 \text{ minutes}$ or $2 \text{ minutes}$ and $30 \text{ seconds}$.

If we wished, we could also convert between minutes and hours or minutes and days. We can use the same procedure to convert between any units.

There are $60 \text{ seconds}$ in $1 \text{ minute.}$

The goal is to correctly convert seconds to minutes and vice versa. There are different ways people come up with to remember when to multiply and when to divide.

Below is a graph illustrating conversions between the two units.

Generally, we divide for converting smaller units to bigger units; we multiply for converting bigger units to smaller units. Test your understanding with the question below:

How many $\text{seconds}$ are there in $1.25 \text{ minutes}$?

Let's convert. $$\begin{array}{c|c} 1.25\text{ minutes}&60\text{ seconds}\\ \hline &1\text{ minute} \end{array}$$ $$\begin{array}{c|c} 1.25\cancel{\text{ minutes}}&60\text{ seconds}\\ \hline &1\cancel{\text{ minute}} \end{array}=75\text{ seconds}$$