## What is Time?

In math, time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through present, and to the future.

Time is used to quantify, measure or compare the duration of events or the intervals between them, and even, sequence events.

### Times of the day

In the image below, a child’s daily routine events have been put in sequence according to the time at which they are done.

We measure time in seconds, minutes, hours, days, weeks, months and years with clocks and calendars.

A day has 24 hours. We use A.M to tell time running from midnight to noon and P.M. for time running from noon to midnight.

We do not write A.M. or P.M. with 12 o’clock in the afternoon and 12 o’clock at midnight.12 o’clock at noon time is written as 12 noon and 12 o’clock at midnight is written as 12 midnight.

Measurement of Time Using Clock

### 1. Analog Clock or the 12-hour clock

We measure and define what time of the day it is using clocks. A clock in general has 12 numbers written on it, from 1 to 12. It has an hour hand, and a minute hand. Some clocks have a third hand as well. It shows time in seconds and is the fastest moving hand. The time is usually based on a 12-hour clock.

The hour hand, the shorter of the two hands, completes 1 rotation ( 360° ) in 12 hours in a normal 12-hour analog. The minute hand, the longer hand, completes 1 rotation through 360° in 60 minutes.

Here’s how the minute hand’s movement shows different times in an hour.

- Time in Half Hours: When the minute hand is at 6, the time is written as half-past.
- Time in Quarter past Hours: When the minute hand is at 3, the time is written as a quarter past the hour.
- Time in Quarter to Hours: When the minute hand is at 9, the time is written as a quarter to the next hour.

**Time in minutes**

There are 12 big divisions on the face of the clock. Each big division has 5 small divisions.

Each small division stands for 1 minute.

So there are 60 small divisions on the face of a clock. There are 12 × 5 = 60 minutes in 1 hour.

1 hour = 60 minutes

1 minute = 60 seconds

When minute hands is at | Number of minutes |

1 | 1 x 5 = 5 |

2 | 2 x 5 = 10 |

3 | 3 x 5 = 15 |

4 | 4 x 5 = 20 |

5 | 5 x 5 = 25 |

6 | 6 x 5 = 30 |

7 | 7 x 5 = 35 |

8 | 8 x 5 = 40 |

9 | 9 x 5 = 45 |

10 | 10 x 5 = 50 |

11 | 11 x 5 = 55 |

12 | 12 x 5 = 60 |

### 2. Digital Clock or the 24-hour clock

Generally, we use the 12 hour clock time. But railways, airlines, armed forces and newspapers use the 24 hour clock time.

In the 24 hour clock time, the hours from midnight to next midnight are marked 0 to 24.

- In 24-hour clock time we use 4-digits.
- The two digits to the right show the minutes past an hour.
- The two digits to the left show the number of hours.

For example:

12:45, its 45 minutes past 12 hours

18:20, its 20 minutes past 18 hours

A day starts at midnight. So time at midnight is expressed as 00:00 hours.

The day ends at midnight. So, midnight is also expressed as 24:00 hours.

**Rules for converting 24 hour clock time to 12 hour clock time:**

We use a.m. if the number of hours is less than 12

**For Example:**

08:00 hours becomes 8:00 a.m.

If the number of hours is more than 12 hours, we subtract 12 from the number of hours and use p.m.

**For Example:**

16:00 hours becomes 4:00 p.m. (16 – 12 = 4)

17:20 hours becomes 5:20 p.m. (17 – 12 = 5)

00:00 hours or 24:00 hours is expressed as 12 midnight.

12:00 hours is expressed as 12 noon.

12:30 is 12:30 p.m.

00:25 hours is 12:25 a.m.

**Rules for converting 12 hour clock time to 24 hour clock time:**

If the time is before 1:00 p.m, we write the same time.

6:20 a.m. is expressed as 06:20 hours

12:25 p.m. is expressed as 12:25 hours

If the time is beyond 1:00 p.m., we add 12 to the number of hours.

4:45 p.m. is expressed as 16:45 hours (4 + 12 = 16)

**Conversion:**

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

1 hour = 3600 seconds

## Solved Examples on Time:

**Example 1: **Fill in the blanks with a.m. or p.m.

- I wake up at 6:30 ______
- Lunch time in school begins at 1:00 ______
- I go to play in evening at 5:00 ______
- I have dinner at 9:00 ______

**Solution:**

- a.m.
- p.m.
- p.m.
- p.m.

**Example 2:** What time will it be 4 hours after 7:45 p.m.

**Solution:** 11:45 p.m.

**Example 3:** Write the number of hours passed between 4:00 p.m. and 8:00 p.m.

**Solution:** 4 hours

**Example 4: **Complete the following table.

12 – Hour clock time | 24 – Hour clock time |
---|---|

1:45 a.m. | _________________ |

_________________ | 14:30 hours |

7:20 p.m. | _________________ |

3:30 a.m. | _________________ |

_________________ | 12:00 hours |

**Solution:**

12 – Hour clock time | 24 – Hour clock time |

1:45 a.m. | 01:45 hours |

2:30 p.m. | 14:30 hours |

7:20 p.m. | 19:20 hours |

3:30 a.m. | 03:30 hours |

12:00 noon | 12:00 hours |

## Practice Problems

## Time

### 1Long hand of a clock is at 11 and the short hand is between 8 and 9, the time (at morning) is written as

Since the hour hand (shorthand) is between 8 and 9 its 8 o’clock and minutes hand (long hand) is at 11 which shows 55 minutes. It's morning before noon so it’s a.m. So, the time is 8:55 a.m.

### 22 hours 10 minutes = _________ minutes

1 hour = 60 minutes So, 2 hours = 2 × 60 minutes = 120 minutes 2 hours 10 minutes = 120 minutes + 10 minutes = 130 minutes

### 313:25 hours is _________ p.m.

13 – 12 = 1 (Subtract 12) So, 13:25 hours is 1:25 p.m. (add p.m. to answer)

## Frequently Asked Questions

**What is the abbreviation for second, minutes and hours ?**

The second can be written as s or sec. The minutes can be written as min and hours as hrs.

**How do you measure time?**

Time can be measured in seconds, minutes, hours, days, weeks, months and years with clocks and calendars.

**What measuring instruments are used to measure time?**

In the past, a common time measuring instrument was the sundial. Today the usual measuring instruments for time are clocks, watches and calendars.

**Why is time measured?**

We need to measure time in order to schedule our work or to plan our day.