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Time - AM and PM

Grade 4ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A full day consists of 2424 hours. On an analog clock face, which shows numbers from 11 to 1212, the hour hand completes two full circles to represent one day. The first cycle covers the morning and night hours (AMAM) and the second cycle covers the afternoon and evening hours (PMPM).

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The term AMAM stands for 'Ante Meridiem', which means 'before midday'. This period begins at 12:0012:00 midnight and ends at 11:5911:59 in the morning. Imagine the sun rising at 6:006:00 AMAM or eating your breakfast at 8:008:00 AMAM.

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The term PMPM stands for 'Post Meridiem', which means 'after midday'. This period starts at 12:0012:00 noon and ends at 11:5911:59 just before midnight. This includes your time at the park at 5:005:00 PMPM or when you go to sleep at 9:009:00 PMPM.

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12:0012:00 noon is exactly the middle of the day and is written as 12:0012:00 PMPM. 12:0012:00 midnight is the start of a new day and is written as 12:0012:00 AMAM. On an analog clock, both the hour hand and the minute hand point exactly at the number 1212 for both noon and midnight.

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On a clock, each number represents a 55-minute interval for the minute hand. To find the minutes, you multiply the number the long hand points to by 55. For example, if the hour hand is past 33 and the minute hand points at 55, the time is 3:253:25 (5times5=255 \\times 5 = 25).

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To calculate the duration or 'elapsed time' between an AMAM and PMPM time, it is easiest to use 12:0012:00 noon as a 'bridge'. For instance, to find the time between 11:0011:00 AMAM and 2:002:00 PMPM, count 11 hour to reach noon and then 22 more hours to reach 2:002:00 PMPM, totaling 33 hours.

📐Formulae

1textday=24texthours1 \\text{ day} = 24 \\text{ hours}

1texthour=60textminutes1 \\text{ hour} = 60 \\text{ minutes}

1textminute=60textseconds1 \\text{ minute} = 60 \\text{ seconds}

text24−hourtime(forPM)=text12−hourhour+12\\text{24-hour time (for PM)} = \\text{12-hour hour} + 12

text12:00Midnight=00:00texthours\\text{12:00 Midnight} = 00:00 \\text{ hours}

text12:00Noon=12:00texthours\\text{12:00 Noon} = 12:00 \\text{ hours}

💡Examples

Problem 1:

Convert 4:304:30 PMPM into the 24-hour clock format.

Solution:

Step 1: Identify that the time is in the PMPM period. Step 2: Add 1212 to the hour part (44). Step 3: 4+12=164 + 12 = 16. Step 4: Keep the minutes (3030) the same. Step 5: Combine the values into the 24-hour format: 16:3016:30 hours.

Explanation:

In the 24-hour system, we continue counting from 1212 for afternoon times. By adding 1212 to the PMPM hour, we find the equivalent time in a 2424-hour cycle.

Problem 2:

A school assembly started at 10:4510:45 AMAM and ended at 12:1512:15 PMPM. How long did the assembly last?

Solution:

Step 1: Find the time from 10:4510:45 AMAM to 12:0012:00 noon. Calculation: 12:00−10:45=1texthourand15textminutes12:00 - 10:45 = 1 \\text{ hour and } 15 \\text{ minutes}. Step 2: Find the time from 12:0012:00 noon to 12:1512:15 PMPM. Calculation: This is simply 15textminutes15 \\text{ minutes}. Step 3: Add the two durations together. Total: 1texthour15textminutes+15textminutes=1texthour30textminutes1 \\text{ hour } 15 \\text{ minutes} + 15 \\text{ minutes} = 1 \\text{ hour } 30 \\text{ minutes}.

Explanation:

We use noon as a middle point to calculate how much time passed before 12:0012:00 and how much passed after 12:0012:00, then add them together.