# 3.04 12 and 24 hour time

Lesson

### Representing time

There are two main ways we represent time over a day. $24$24 hour time represents time as one block of $24$24 hours.$12$12 hour time represents a day as two blocks of $12$12 hours each. The hours before midday add an "am" to show it's the morning and the hours after midday add on a "pm" so we know it's the afternoon.

There is also variation in how $12$12 and $24$24 hour time is displayed.$12$12 hour time may use "am", "a.m.", "AM" or similar variations, while $24$24 hour time could represent $03:15$03:15 as $3:15$3:15or $0315$0315 which is more common in the military

Below is a diagram showing the conversion between $12$12 and $24$24 time. In all cases the number of minutes will be the same.

### Calculating time

The conversions between the different units of time are:

Time calculations are similar to our normal addition and subtraction so we can use similar strategies. However, we will also use these time unit conversions, such as $60$60 minutes in an hour and $24$24 hours in a day.

#### Worked Example

What will the time be $2$2 hours and $40$40 minutes after $10:45$10:45 am?

Think: We can approach this problem in a few ways. We can add the number of minutes on first and then the number of hours.

Do: If we add $40$40 minutes onto $10:45$10:45 we can only add $15$15 minutes on before we get to $11:00$11:00 am. We then can add the remaining $\left(40-15\right)=25$(4015)=25 minutes to get to $11:25$11:25 am.

We can then add $2$2 hours on, which is $13:25$13:25 which would be correct in $24$24 hour time, but we know this is $12$12 hour time because the time has "am". So, the time will be $1:25$1:25 pm.

Reflect: There are many different strategies we can take to get to this answer, just like regular addition and subtraction.

Use the clock applet above to play around with adding or subtracting different amounts of time. We can also change the starting time using input box.

#### Practice questions

##### Question 1

Write $9$9 days in hours.

##### Question 2

Which of the following represents $30$30 minutes after $11$11$:$:$40$40 pm?

1. $12$12$:$:$10$10am

A

$11$11$:$:$10$10 pm

B

$11$11$:$:$70$70 pm

C

$12$12$:$:$10$10 pm

D

$12$12$:$:$10$10am

A

$11$11$:$:$10$10 pm

B

$11$11$:$:$70$70 pm

C

$12$12$:$:$10$10 pm

D
##### Question 3

Kate leaves her home at $11$11$:$:$15$15 am to visit her grandmother in a different state. She arrives at her grandmother's house at $5$5$:$:$15$15 pm.

1. How long was Kate's trip in hours?

### Outcomes

#### MA4-7NA

operates with ratios and rates, and explores their graphical representation

#### MA4-15MG

performs calculations of time that involve mixed units, and interprets time zones