**Definition**

Time can be defined as the dimension based on which the evolution of any system takes place. We measure time in seconds, minutes, hours, days, weeks, months and years with clocks and calendars. We can observe that there are 12 numbers written on the face of a clock. We also know that a day has 24 hours. Therefore, the hour hand of the clock completes 1 round in 12 hours. So, we divide 24 hours of a day in two periods:

- From 12:00 midnight to 12:00 noon
- From 12:00 noon to 12:00 midnight

**The time between 12:00 midnight to 12:00 noon is written as a.m. Here a.m. means ante meridiem which means before midday.**

**The time between 12:00 noon and 12:00 midnight is known as p.m. Here p.m. means post meridiem which means after midday. **

Another thing that should be noticed is that at times we see time written in a.m. or p.m. while at times it is written as, say, 16:00 with no mention of a.m. and p.m.

**Converting Hours into Minutes**

Time is measured in hours, minutes and seconds. How are these three related to each other?

**1 minute = 60 seconds**

**1 hour = 60 minutes**

This means that 1 hour = 60 x 60 = 3600 seconds

**This means that to convert hours into minutes, we will have to multiply the value of hours by 60. **Let us understand it through an example.

**Example**

How many minutes are there in 3 hours?

**Solution**

We need to convert 3 hours into minutes.

Now, we know that 1 hour = 60 minutes

So, 3 hours = 3 x 60 = 180 minutes

**So, there are 180 minutes in 3 hours**

Also, a second is a very short period of time, say the time that is taken to blink your eye, to snap your fingers etc. it is a smaller unit of time than a minute.

To understand how to convert hours into minutes, let us consider an example.

Suppose Victor and his sister Alice were going to school. When they started from home, the following time was shown by the clock –

Victor asked her to read the time. She read it easily as 7:30. Then they reached the school and the time shown by the clock in the school is

Victor again asked her to read the time. But, she was not able to read the time to the exact minutes. Now, Victor told her it was 8: 10. Let us understand how to read time to exact minutes.

If you see carefully, there are 12 numbers and 60 divisions on the face of a clock. Therefore, we have,

1 hour = 60 minutes.

Hence, the number of divisions between two consecutive numbers is 60 ÷ 12 = 5 divisions or 5 minutes.

We will read the time on the given clock as 2 :07 if,

- The hour hand of the clock is at 2
- The minute hand of the clock is at the 2nd division after the 1
^{st}number, i..e 7 minutes ( 1 x 5 = 5) + 2 minutes = 7 minutes.

Hence, we can say that the numbers on the clock actually represent hours and the divisions between them represent the minutes.

It is important to know here that –

**Quarter of an hour = 60 ÷ 4 = 15 minutes**

**Half of an hour = 60 ÷ 2 = 30 minutes.**

**12 :00 o’clock in the night is 12:00 midnight**

**12 :00 o’clock at the daytime is 12:00 noon**

**We do not write a.m. or p.m. with 12:00 o’clock time.**

**In what time to the hour, minute and second hands complete one round or one revolution of the clock? **

- The hour hand of the clock goes round the clock in 12 hours.
- The minute hand completes one round in 1 hour.
- The second’s hand completes one round in 1 minute

Now, what is we want to convert minutes into hours?

Converting minutes into hours

We know that 1 hour = 60 minutes. This means that

**1 minute = **$\frac{1}{60}$** hours**

From above, we can see that in order to convert minutes into hours, we will have to divide minutes by 60.

Let us understand it through an example.

**Example**

Convert 540 minutes into hours

**Solution**

We know that 1 minute = $\frac{1}{60}$ hours. This means that for converting 540 minutes into hours we will have to divide 540 by 60.

So, 540 ÷ 60 = 9

**Hence, 540 minutes when converted into hours is 9 hours.**

**Solved Examples**

**Example 1** Convert 9 hours 35 minutes into minutes

**Solution** We are required to convert 9 hours 35 minutes into minutes. Now, we know that

1 hour = 60 minutes

This means that 9 hours = 9 x 60 = 540 minutes . . . . . . . . . . . . . . . . . . . . . . ( 1 )

So, 9 hours 35 minutes = 540 minutes + 35 minutes ( From equation ( 1 ) )

⇒ 9 hours 35 minutes = 575 minutes

**Hence, we can say that 9 hours 35 minutes is equal to 575 minutes.**

**Example 2** Alicia’s family is travelling from Atlanta, Georgia to New York by plane. Their flight leaves at 9:15 a.m. and should take 135 minutes. What time will their plane arrive in New York?

**Solution** We have been given that Alicia’s family is travelling from Atlanta, Georgia to New York by plane. Their flight leaves at 9:15 a.m. and should take 135 minutes. We need to find the time at which their plane arrives at New York.

The first thing that we would do when solving for elapsed time is to figure out our start time and end time. Here, our start time is 9:15 a.m. and the end time is 135 minutes after the start time.

Next, we are going to count to the nearest hour after the start time, i.e. 9:15 a.m. Looking at the clock, we know that the next hour after 9:15 a.m. would be 10:15 a.m. So counting from 9:15 a.m. to 10:15 a.m.. we see that there is one hour from 9:15 a.m. and 10:15 a.m. Since we are required to find the time 135 minutes after 9:15 a.m., therefore we shall now jump another 1 hour from 10:15 a.m. Looking at the clock, we know that the next hour after 10:15 a.m. would be 11:15 a.m. So counting from 10:15 a.m. to 11:15 a.m. . We see that there is one hour from 10:15 a.m. and 11:15 a.m.

So, we have now counted 2 hours from 9:15 a.m. and reached at 11:15 a.m. we are left to count 15 minutes now. Looking at the clock again, we can see that 15 minutes after 11:15 a.m. would be 11:30 a.m. So, what would be the time 15 minutes after 11:15 a.m? It would be 11:30 a.m. Hence, the plane would arrive in New York at 11:30 a.m. which is 2 hours and 15 minutes after it left Atlanta.

**Key Facts and Summary**

- Time can be defined as the dimension based on which the evolution of any system takes place.
- 1 minute = 60 seconds
- 1 hour = 60 minutes
- Quarter of an hour = 60 ÷ 4 = 15 minutes
- Half of an hour = 60 ÷ 2 = 30 minutes.
- 1 minute = $\frac{1}{60}$ hours

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