Lesson

Think about an analog clock you might see on a wall. The numbers go from $1$1 to $12$12 to show the twelve hours of the "day" (from midnight to midday) and the twelve hours of "night" (from midday to midnight). However, we know that there are $24$24 hours in a day. So now we are going to look at how to use $24$24 hour time. Basically, instead of going from $1$1 to $12$12, we go from $00:00$00:00 to $23:59$23:59 and count how much time has passed since midnight. When we write the time in $24$24-hour time, it looks a bit like a stop watch - there are two numbers that express the hours and two that express the minutes, so it is in the form

**hour hour:minute minute **

$24$24 hour time starts at midnight, which is written as $00:00$00:00, the start of a new day and $12:00$12:00 would be midday. Everything in between is written in the $hh:mm$`h``h`:`m``m` form described above.

$00:15$00:15 would be $12:15$12:15 a.m. or "a quarter past twelve in the morning."

$06:25$06:25 would be $6:25$6:25 a.m. or "twenty-five past six in the morning."

$10:45$10:45 would be $10:45$10:45 a.m. or "a quarter to eleven in the morning."

The afternoon is where things start to get a bit different. $1$1 p.m. is an hour after midday ($12$12 p.m.), so we would write this as $13:00$13:00. Similarly, if we wanted to write $6$6 p.m. in $24$24-hour time, we would add $6$6 hours to midday ($12+6=18$12+6=18), so the time would be $18:00$18:00.

Quick tip

If it's past $12:59$12:59 p.m. simply **add $12$12 hours** to the time to convert it to **$24$24-hour time**. Similarly, if a time is after $12:59$12:59 and written in $24$24-hour time, **subtract $12$12 hours** to convert it back to **$12$12 hour time **- make sure to write whether it's a.m. or p.m.

$18:30$18:30 would be $6:30$6:30 p.m. or "half-past six in the evening."

$23:17$23:17 would be $11:17$11:17 p.m. or "seventeen minutes past eleven in the evening."

Think of time as a timeline like the one below. That will help you convert between $12$12- and $24$24-hour time.

Convert $1$1$0$0:$4$4$4$4 into $12$12-hour time.

$\editable{}$:$\editable{}$ am

Convert $11$11:$26$26 pm into $24$24-hour time.

$\editable{}$$\editable{}$:$\editable{}$$\editable{}$

Convert $2$2$0$0:$5$5$9$9 into $12$12-hour time.

$\editable{}$:$\editable{}$ pm

Solve problems involving the relationship between a 12-hour clock and a 24-hour clock (e.g., 15:00 is 3 hours after 12 noon, so 15:00 is the same as 3:00 p.m.)