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Time

Units of Time

Choosing the Right Units of Time

Mcq
Which unit is most appropriate for measuring the time it takes to run a 100-meter sprint?








  • A 100-meter sprint is a very fast event.
  • Minutes or hours would be too large as units. We need a small unit to be precise.
  • The most appropriate unit is seconds.

Mcq
Which unit is most appropriate for measuring the time it takes to clean your bedroom?








  • Cleaning a bedroom takes some time, but usually not for many hours.
  • Seconds would be too short, and hours would usually be too long.
  • The most appropriate unit is minutes.

Mcq
Which unit is most appropriate for measuring your age?








  • Age measures all the time since you were born, which is a very long period.
  • We need a large unit to describe this long duration easily.
  • The standard unit for measuring a person’s age is years.

Mcq
Which unit is most appropriate for measuring the time it takes to watch a movie?





  • A movie is a longer activity. It would be many minutes (like 90 or 120), but usually not a full day.
  • The most convenient and appropriate unit is hours.

Mcq
Which unit is most appropriate for measuring the length of a family camping trip?





  • A camping trip lasts much longer than just a few hours.
  • It typically lasts for several full cycles of day and night.
  • The best unit to measure this duration is days.

Converting Units of Time

Converting Units of Time From Bigger to Smaller

Exercise

Convert 2 hours to minutes:
2 h = min

To convert from hours to minutes, we multiply by 60 (since 1 hour = 60 minutes).$$\begin{aligned}2 \, \text{h} &= 2 \times 60 \, \text{min} \\ &= 120 \, \text{min}\end{aligned}$$So, 2 hours is 120 minutes.

Exercise

Convert 3 days to hours:
3 d = h

To convert from days to hours, we multiply by 24 (since 1 day = 24 hours).$$\begin{aligned}3 \, \text{d} &= 3 \times 24 \, \text{h} \\ &= 72 \, \text{h}\end{aligned}$$So, 3 days is 72 hours.

Exercise

Convert 5 minutes to seconds:
5 min = s

To convert from minutes to seconds, we multiply by 60 (since 1 minute = 60 seconds).$$\begin{aligned}5 \, \text{min} &= 5 \times 60 \, \text{s} \\ &= 300 \, \text{s}\end{aligned}$$So, 5 minutes is 300 seconds.

Exercise

Convert 2 weeks to days:
2 wk = d

To convert from weeks to days, we multiply by 7 (since 1 week = 7 days).$$\begin{aligned}2 \, \text{wk} &= 2 \times 7 \, \text{d} \\ &= 14 \, \text{d}\end{aligned}$$So, 2 weeks is 14 days.

Converting Units of Time From Smaller to Bigger

Exercise

Convert 120 seconds to minutes:
120 s = min

To convert from seconds to minutes, we divide by 60 (since there are 60 seconds in 1 minute).$$\begin{aligned}120 \, \text{s} &= 120 \div 60 \\ &= 2 \, \text{min}\end{aligned}$$So, 120 seconds is 2 minutes.

Exercise

Convert 24 hours to days:
24 h = d

To convert from hours to days, we divide by 24 (since there are 24 hours in 1 day).$$\begin{aligned}24 \, \text{h} &= 24 \div 24 \\ &= 1 \, \text{d}\end{aligned}$$So, 24 hours is 1 day.

Exercise

Convert 180 minutes to hours:
180 min = h

To convert from minutes to hours, we divide by 60 (since there are 60 minutes in 1 hour).$$\begin{aligned}180 \, \text{min} &= 180 \div 60 \\ &= 3 \, \text{h}\end{aligned}$$So, 180 minutes is 3 hours.

Exercise

Convert 14 days to weeks:
14 d = wk

To convert from days to weeks, we divide by 7 (since there are 7 days in 1 week).$$\begin{aligned}14 \, \text{d} &= 14 \div 7 \\ &= 2 \, \text{wk}\end{aligned}$$So, 14 days is 2 weeks.

Dividing Time

Exercise
If you divide an hour into two equal parts, how many minutes are in half an hour?
Half an hour = minutes

  • We know that 1 hour has 60 minutes.
  • To find half of something, we divide it by 2.
  • Therefore, half an hour is 30 minutes.
$$\begin{aligned}\text{Half an hour} &= 60 \,\text{minutes} \div 2 \\ &= 30 \,\text{minutes}\end{aligned}$$

Exercise
If you divide an hour into four equal parts, how many minutes are in one quarter of an hour?
One quarter of an hour = minutes

  • We know that 1 hour has 60 minutes.
  • To find a quarter of something, we divide it by 4.
  • Therefore, a quarter of an hour is 15 minutes.
$$\begin{aligned}\text{A quarter of an hour} &= 60 \,\text{minutes} \div 4 \\ &= 15 \,\text{minutes}\end{aligned}$$

Exercise
If you divide a day into two equal parts, how many hours are in half a day?
Half a day = hours

  • We know that 1 full day has 24 hours.
  • To find half of the day, we divide by 2.
  • Therefore, half a day is 12 hours.
$$\begin{aligned}\text{Half a day} &= 24 \,\text{hours} \div 2 \\ &= 12 \,\text{hours}\end{aligned}$$

Converting 1 Unit into 2 Units

Converting 2 Units into 1 Unit

Exercise
A movie lasts 1 hour and 45 minutes. How many minutes is that in total?
1 h 45 min = min

  • Step 1: Convert hours to minutes. We know that \(1 \,\text{h} = 60 \,\text{min}\).
  • Step 2: Add the extra minutes. We add the remaining 45 minutes to this amount.
$$\begin{aligned}1 \, \text{h} \, 45 \, \text{min} &= (1 \times 60 \, \text{min}) + 45 \, \text{min} \\ &= 60 \, \text{min} + 45 \, \text{min} \\ &= 105 \, \text{min}\end{aligned}$$So, the movie lasts 105 minutes.

Exercise
You hold your breath for 2 minutes and 20 seconds. How many seconds is that in total?
2 min 20 s = s

  • Step 1: Convert minutes to seconds. We know that \(1 \,\text{min} = 60 \,\text{s}\).
  • Step 2: Add the extra seconds. We add the remaining 20 seconds.
$$\begin{aligned}2 \, \text{min} \, 20 \, \text{s} &= (2 \times 60 \, \text{s}) + 20 \, \text{s} \\ &= 120 \, \text{s} + 20 \, \text{s} \\ &= 140 \, \text{s}\end{aligned}$$So, you held your breath for 140 seconds.

Exercise
Your soccer practice lasts 1 hour and 30 minutes. How many minutes is that in total?
1 h 30 min = min

  • Step 1: Convert hours to minutes. We know that \(1 \,\text{h} = 60 \,\text{min}\).
  • Step 2: Add the extra minutes. We add the remaining 30 minutes.
$$\begin{aligned}1 \, \text{h} \, 30 \, \text{min} &= (1 \times 60 \, \text{min}) + 30 \, \text{min} \\ &= 60 \, \text{min} + 30 \, \text{min} \\ &= 90 \, \text{min}\end{aligned}$$So, your soccer practice lasts 90 minutes.

Exercise
A trail running race lasts 1 day and 5 hours. How many hours is that in total?
1 d 5 h = h

  • Step 1: Convert days to hours. We know that \(1 \,\text{d} = 24 \,\text{h}\).
  • Step 2: Add the extra hours. We add the remaining 5 hours.
$$\begin{aligned}1 \, \text{d} \, 5 \, \text{h} &= (1 \times 24 \, \text{h}) + 5 \, \text{h} \\ &= 24 \, \text{h} + 5 \, \text{h} \\ &= 29 \, \text{h}\end{aligned}$$So, the race lasts 29 hours.

Converting 1 Unit into 2 Units

Exercise
You read a book for 100 minutes. How many hours and minutes is that?
100 min = h and min

  • We need to find how many groups of 60 minutes (hours) are in 100 minutes. We divide 100 by 60.
  • The quotient is the number of hours, and the remainder is the number of leftover minutes.
The division shows a quotient of 1 and a remainder of 40.$$\begin{aligned}100 \, \text{min} &= (1 \times 60 \, \text{min}) + 40 \, \text{min} \\ &= 1 \, \text{h} \, 40 \, \text{min}\end{aligned}$$So, 100 minutes is 1 hour and 40 minutes.

Exercise
A race lasts for 140 seconds. How many minutes and seconds is that?
140 s = min and s

  • We need to find how many groups of 60 seconds (minutes) are in 140 seconds. We divide 140 by 60.
The division shows a quotient of 2 (the minutes) and a remainder of 20 (the seconds).$$\begin{aligned}140 \, \text{s} &= (2 \times 60 \, \text{s}) + 20 \, \text{s} \\ &= 2 \, \text{min} \, 20 \, \text{s}\end{aligned}$$So, 140 seconds is 2 minutes and 20 seconds.

Exercise
You study for 150 minutes. How many hours and minutes is that?
150 min = h and min

  • We divide 150 minutes by 60 to find the number of full hours.
The division gives a quotient of 2 (hours) and a remainder of 30 (minutes).$$\begin{aligned}150 \, \text{min} &= (2 \times 60 \, \text{min}) + 30 \, \text{min} \\ &= 2 \, \text{h} \, 30 \, \text{min}\end{aligned}$$So, 150 minutes is 2 hours and 30 minutes.

Exercise
You swim for 200 seconds. How many minutes and seconds is that?
200 s = min and s

  • We divide 200 seconds by 60 to find the number of full minutes.
The division gives a quotient of 3 (minutes) and a remainder of 20 (seconds).$$\begin{aligned}200 \, \text{s} &= (3 \times 60 \, \text{s}) + 20 \, \text{s} \\ &= 3 \, \text{min} \, 20 \, \text{s}\end{aligned}$$So, 200 seconds is 3 minutes and 20 seconds.

24-Hour Time Format

Telling Time the 24-Hour Way

Exercise
Your favorite show starts at 6:15 PM. What time is that in 24-hour format?
:

  • The time is PM, which means it is after noon.
  • To convert PM hours to 24-hour format, we add 12 to the hour.
  • The minutes stay the same.
  • The time is 18:15.
$$ 6 + 12 = 18 $$

Exercise
You wake up at 7:45 AM for school. What time is that in 24-hour format?
:

  • The time is AM, which means it is in the morning (before noon).
  • For AM times, the hour number stays the same.
  • In 24-hour format, we write hours less than 10 with a leading zero.
  • The time is 07:45.

Exercise
Your soccer game starts at 4:30 PM. What time is that in 24-hour format?
:

  • The time is PM (afternoon).
  • We add 12 to the hour.
  • The minutes stay the same.
  • The time is 16:30.
$$ 4 + 12 = 16 $$

Exercise
You eat dinner at 7:00 PM. What time is that in 24-hour format?
:

  • The time is PM (evening).
  • We add 12 to the hour.
  • The time is 19:00.
$$ 7 + 12 = 19 $$

Finding Everyday Time from 24-Hour Clocks

Exercise
You have breakfast at 07:30. What time is this in AM/PM format?
:

  • The hour (07) is less than 12, so it is a morning (AM) time.
  • The hour number stays the same.
  • The time is 7:30 AM.

Exercise
Your art class starts at 14:45. What time is this in AM/PM format?
:

  • The hour (14) is greater than 12, so it is an afternoon/evening (PM) time.
  • To find the 12-hour clock number, we subtract 12 from the hour.
  • The time is 2:45 PM.
$$ 14 - 12 = 2 $$

Exercise
You go to bed at 20:00. What time is this in AM/PM format?
:

  • The hour (20) is greater than 12, so it is a PM time.
  • We subtract 12 from the hour.
  • The time is 8:00 PM.
$$ 20 - 12 = 8 $$

Exercise
Your music lesson starts at 15:20. What time is this in AM/PM format?
:

  • The hour (15) is greater than 12, so it is a PM time.
  • We subtract 12 from the hour.
  • The time is 3:20 PM.
$$ 15 - 12 = 3 $$

Reading Clock Times

Reading Clocks

Exercise
You leave for school at the time shown on this clock. What time is it?

morning
:

  • Hour Hand: The short hand has passed the 7 but has not yet reached the 8. Therefore, the hour is 7.
  • Minute Hand: The long hand has passed the 3. The 3 represents \(3 \times 5 = 15\) minutes. It is pointing 2 small marks past the 3.
  • Calculation: We add the extra minutes to the base of 15.$$\begin{aligned}15 \,\text{minutes} + 2 \,\text{minutes} = 17 \,\text{minutes}\end{aligned}$$
  • The time is 7:17 AM because it is morning.

Exercise
Your soccer practice starts at the time shown on this clock. What time is it?

afternoon
:

  • Hour Hand: The short hand is past the 4 and is moving towards the 5. The hour is 4.
  • Minute Hand: The long hand has passed the 7. The 7 represents \(7 \times 5 = 35\) minutes. It is pointing 2 small marks past the 7.
  • Calculation:$$\begin{aligned}35 \,\text{minutes} + 2 \,\text{minutes} = 37 \,\text{minutes}\end{aligned}$$
  • The time is 4:37 PM because it is the afternoon.

Exercise
You eat breakfast at the time shown on this clock. What time is it?

morning
:

  • Hour Hand: The short hand has passed the 8. The hour is 8.
  • Minute Hand: The long hand has passed the 4 (\(4 \times 5 = 20\) minutes). It is pointing 3 small marks past the 4.
  • Calculation:$$\begin{aligned}20 \,\text{minutes} + 3 \,\text{minutes} = 23 \,\text{minutes}\end{aligned}$$
  • The time is 8:23 AM because it is morning.

Exercise
You watch a movie at the time shown on this clock. What time is it?

evening
:

  • Hour Hand: The short hand has passed the 6. The hour is 6.
  • Minute Hand: The long hand has passed the 2 (\(2 \times 5 = 10\) minutes). It is pointing 4 small marks past the 2.
  • Calculation:$$\begin{aligned}10 \,\text{minutes} + 4 \,\text{minutes} = 14 \,\text{minutes}\end{aligned}$$
  • The time is 6:14 PM because it is the evening.

Reading Clocks for 24-Hour Time

Exercise
You leave for school at the time shown. What is this time in 24-hour format?

morning
:

  • Step 1: Read the 12-hour time. The hour is 7 and the minutes are 17. Since it's morning, the time is 7:17 AM.
  • Step 2: Convert to 24-hour format. Because it is an AM time, the hour number does not change. We write it with a leading zero.
  • The final time is 07:17.

Exercise
Your soccer practice starts at the time shown. What is this time in 24-hour format?

afternoon
:

  • Step 1: Read the 12-hour time. The hour is 4 and the minutes are 37. Since it's afternoon, the time is 4:37 PM.
  • Step 2: Convert to 24-hour format. Because it is a PM time, we add 12 to the hour.$$\begin{aligned}4 + 12 = 16\end{aligned}$$
  • The final time is 16:37.

Exercise
You eat breakfast at the time shown. What is this time in 24-hour format?

morning
:

  • Step 1: Read the 12-hour time. The hour is 8 and the minutes are 23. The time is 8:23 AM.
  • Step 2: Convert to 24-hour format. Since it is AM, the hour does not change. We write it with a leading zero.
  • The final time is 08:23.

Exercise
You watch a movie at the time shown. What is this time in 24-hour format?

evening
:

  • Step 1: Read the 12-hour time. The hour is 6 and the minutes are 14. The time is 6:14 PM.
  • Step 2: Convert to 24-hour format. Because it is PM, we add 12 to the hour.$$\begin{aligned}6 + 12 = 18\end{aligned}$$
  • The final time is 18:14.

Add and Subtract Time

Adding Time

Exercise
You watch a movie for 1 hour 20 minutes and do homework for 1 hour 15 minutes.
How long is that altogether?
h min

Method: Add the minutes and the hours separately, starting from the right.$$\begin{aligned} & 1 \, \text{h} \, 20 \, \text{min} \\ + \, & 1 \, \text{h} \, 15 \, \text{min} \\ \hline & 2 \, \text{h} \, 35 \, \text{min}\end{aligned}$$The total time is 2 hours and 35 minutes. Since the minutes (35) are less than 60, no regrouping is needed.

Exercise
You ride your bike for 1 hour 25 minutes and play soccer for 1 hour 30 minutes.
How long is that altogether?
h min

Method: Add the minutes and the hours separately.$$\begin{aligned} & 1 \, \text{h} \, 25 \, \text{min} \\ + \, & 1 \, \text{h} \, 30 \, \text{min} \\ \hline & 2 \, \text{h} \, 55 \, \text{min}\end{aligned}$$The total time is 2 hours and 55 minutes.

Exercise
You spend 1 hour 15 minutes on Math homework and 55 minutes on Science homework.
How long is that altogether?
h min

Method: Add the minutes and hours, then regroup the minutes.$$\begin{aligned} & 1 \, \text{h} \, 15 \, \text{min} \\ + \, & 0 \, \text{h} \, 55 \, \text{min} \\ \hline & 1 \, \text{h} \, 70 \, \text{min}\end{aligned}$$Since 70 minutes is more than 60, we regroup: \(70 \, \text{min} = 1 \, \text{h} \, 10 \, \text{min}\). We add this to our result:$$ 1 \, \text{h} + (1 \, \text{h} \, 10 \, \text{min}) = 2 \, \text{h} \, 10 \, \text{min} $$The total time is 2 hours and 10 minutes.

Exercise
You play a game for 2 hours 30 minutes and read a book for 1 hour 45 minutes.
How long is that altogether?
h min

Method: Add the minutes and hours, then regroup.$$\begin{aligned} & 2 \, \text{h} \, 30 \, \text{min} \\ + \, & 1 \, \text{h} \, 45 \, \text{min} \\ \hline & 3 \, \text{h} \, 75 \, \text{min}\end{aligned}$$Regroup the 75 minutes: \(75 \, \text{min} = 1 \, \text{h} \, 15 \, \text{min}\).$$ 3 \, \text{h} + (1 \, \text{h} \, 15 \, \text{min}) = 4 \, \text{h} \, 15 \, \text{min} $$The total time is 4 hours and 15 minutes.

Subtracting Time

Exercise
You have 3 hours 40 minutes to finish your chores. You spend 1 hour 25 minutes cleaning your room.
How much time is left?
h min

Method: Subtract the minutes and the hours separately.$$\begin{aligned} & 3 \, \text{h} \, 40 \, \text{min} \\ - \, & 1 \, \text{h} \, 25 \, \text{min} \\ \hline & 2 \, \text{h} \, 15 \, \text{min}\end{aligned}$$You have 2 hours and 15 minutes left.

Exercise
You have 2 hours 35 minutes before dinner. You spend 1 hour 20 minutes practicing piano.
How much time is left?
h min

Method: Subtract the minutes and hours.$$\begin{aligned} & 2 \, \text{h} \, 35 \, \text{min} \\ - \, & 1 \, \text{h} \, 20 \, \text{min} \\ \hline & 1 \, \text{h} \, 15 \, \text{min}\end{aligned}$$You have 1 hour and 15 minutes left.

Exercise
You have 4 hours 10 minutes to complete your tasks. You spend 2 hours 45 minutes organizing your books.
How much time is left?
h min

Method: Since we cannot subtract 45 from 10, we must regroup first.
  1. Regroup: Borrow 1 hour from the 4 hours, leaving 3 hours. Add the borrowed 60 minutes to the 10 minutes (\(10 + 60 = 70\) min). The starting time becomes 3 h 70 min.
  2. Subtract: Now subtract the hours and the new minutes.
$$\begin{aligned} & \phantom{0}\text{4 h 10 min} \quad \rightarrow \quad 3 \, \text{h} \, 70 \, \text{min} \\ - \, & \phantom{0}\text{2 h 45 min} \quad \rightarrow \quad 2 \, \text{h} \, 45 \, \text{min} \\ \hline & \phantom{0}\quad\quad\quad\quad\quad\quad\quad 1 \, \text{h} \, 25 \, \text{min}\end{aligned}$$You have 1 hour and 25 minutes left.

Exercise
You have 3 hours 15 minutes to work on a project. You spend 1 hour 40 minutes writing a story.
How much time is left?
h min

Method: Regrouping is needed because 15 is less than 40.
  1. Regroup: Borrow 1 hour from 3 hours, leaving 2 hours. Add 60 minutes to 15 minutes (\(15 + 60 = 75\) min). The starting time is now 2 h 75 min.
  2. Subtract.
$$\begin{aligned} & \phantom{0}\text{3 h 15 min} \quad \rightarrow \quad 2 \, \text{h} \, 75 \, \text{min} \\ - \, & \phantom{0}\text{1 h 40 min} \quad \rightarrow \quad 1 \, \text{h} \, 40 \, \text{min} \\ \hline & \phantom{0}\quad\quad\quad\quad\quad\quad\quad 1 \, \text{h} \, 35 \, \text{min}\end{aligned}$$You have 1 hour and 35 minutes left.

Exercise
You have 4 hours 15 minutes of free time. You play a game for 1 hour 45 minutes.
How much time is left?
h min

Method: Regrouping is needed because 15 is less than 45.
  1. Regroup: Borrow 1 hour from 4 hours, leaving 3 hours. Add 60 minutes to 15 minutes (\(15 + 60 = 75\) min). The starting time is now 3 h 75 min.
  2. Subtract.
$$\begin{aligned} & \phantom{0}\text{4 h 15 min} \quad \rightarrow \quad 3 \, \text{h} \, 75 \, \text{min} \\ - \, & \phantom{0}\text{1 h 45 min} \quad \rightarrow \quad 1 \, \text{h} \, 45 \, \text{min} \\ \hline & \phantom{0}\quad\quad\quad\quad\quad\quad\quad 2 \, \text{h} \, 30 \, \text{min}\end{aligned}$$You have 2 hours and 30 minutes left.

Time Problems

Figuring Out Time

Exercise
You work 2 hours 30 minutes on Saturday and 1 hour 20 minutes on Sunday.
How much time do you work altogether?
h min

Analysis: The word "altogether" tells us to find a total, so the operation is addition.$$\begin{aligned} & 2 \, \text{h} \, 30 \, \text{min} \\ + \, & 1 \, \text{h} \, 20 \, \text{min} \\ \hline & 3 \, \text{h} \, 50 \, \text{min}\end{aligned}$$You work 3 hours and 50 minutes altogether.

Exercise
A train starts at 8:20 AM and arrives at 1:30 PM.
How long is the train journey?
h min

Analysis: To find the duration between a start and end time, we subtract. To make subtraction easier, first convert the PM time to 24-hour format.
  • Step 1: Convert. 1:30 PM becomes \(1 + 12 = 13:30\). The start time is 8:20.
  • Step 2: Subtract.
$$\begin{aligned} & 13 \, \text{h} \, 30 \, \text{min} \\ - \, & 8 \, \text{h} \, 20 \, \text{min} \\ \hline & 5 \, \text{h} \, 10 \, \text{min}\end{aligned}$$The train journey takes 5 hours and 10 minutes.

Exercise
Liam has to wrap 12 gift boxes for a charity event. It takes him 3 minutes to wrap each box.
How long will it take to wrap all the gift boxes?
min

Analysis: The same action (wrapping for 3 minutes) is repeated 12 times. For repeated addition, we multiply.$$\begin{aligned}12 \, \text{boxes} \times 3 \, \text{minutes per box} = 36 \, \text{minutes}\end{aligned}$$It will take Liam 36 minutes to wrap all the boxes.

Exercise
A teacher has 36 minutes to grade tests. Each test takes 3 minutes to grade.
How many tests can the teacher grade?
tests

Analysis: We need to find how many equal groups of 3 minutes fit into a total of 36 minutes. This is a division problem.$$\begin{aligned}36 \, \text{minutes} \div 3 \, \text{minutes per test} = 12 \, \text{tests}\end{aligned}$$The teacher can grade 12 tests.

Exercise
You spend 1 hour 40 minutes mixing cookie dough and 1 hour 25 minutes decorating the cookies.
How long do you spend baking altogether?
h min

Analysis: The word "altogether" tells us to find a total, so we add.$$\begin{aligned} & 1 \, \text{h} \, 40 \, \text{min} \\ + \, & 1 \, \text{h} \, 25 \, \text{min} \\ \hline & 2 \, \text{h} \, 65 \, \text{min}\end{aligned}$$Since 65 minutes is more than an hour, we regroup: \(65 \, \text{min} = 1 \, \text{h} \, 5 \, \text{min}\).$$ 2 \, \text{h} + (1 \, \text{h} \, 5 \, \text{min}) = 3 \, \text{h} \, 5 \, \text{min} $$You spend 3 hours and 5 minutes baking.

Exercise
Sofia needs to bake 15 cupcakes for a school event. Each cupcake takes 5 minutes to prepare.
How long will it take to prepare all the cupcakes?
h min

Analysis: This is a two-step problem. First, we find the total minutes by multiplying, then we convert the minutes to hours and minutes.
  • Step 1: Multiply. $$ \begin{aligned} 15 \, \text{cupcakes} \times 5 \, \text{minutes per cupcake} = 75 \, \text{minutes} \end{aligned} $$
  • Step 2: Convert. 75 minutes is more than one hour. $$ \begin{aligned} 75 \, \text{min} &= 60 \, \text{min} + 15 \, \text{min} \\ &= 1 \, \text{h} \, 15 \, \text{min} \end{aligned} $$
It will take Sofia 1 hour and 15 minutes.

Exercise
To plant the vegetables, it takes you 20 hours. You work over 4 days.
How many hours do you work per day?
hours per day

Analysis: We are sharing a total amount of time (20 hours) equally over 4 days. This is a division problem.$$\begin{aligned}20 \, \text{hours} \div 4 \, \text{days} = 5 \, \text{hours per day}\end{aligned}$$You work 5 hours per day.

Exercise
In a library, you begin to work at 8:30 AM. You finish at 10:20 AM.
How much time do you work?
h min

Analysis: To find the duration between a start and end time, we subtract. We need to regroup because 20 is less than 30.
  1. Regroup: Borrow 1 hour from 10 hours, leaving 9 hours. Add 60 minutes to 20 minutes (\(20 + 60 = 80\) min). The end time becomes 9 h 80 min.
  2. Subtract.
$$\begin{aligned} & \phantom{0}\text{10 h 20 min} \quad \rightarrow \quad& 9 \, \text{h} \, 80 \, \text{min} \\ - \, & \phantom{0}\text{8 h 30 min} \quad \rightarrow \quad& 8 \, \text{h} \, 30 \, \text{min} \\ \hline & & 1 \, \text{h} \, 50 \, \text{min}\end{aligned}$$You work for 1 hour and 50 minutes.

Timelines

Reading Dates on a Timeline

Exercise
This timeline shows monarchs of France in the 17th century:
When did Louis XIII begin his reign?
In the year

  • Look at the timeline: Louis XIII’s name points to 1610.
  • This marks the start of his reign.
  • Final answer: 1610.

Exercise
This timeline shows major scientific discoveries in the 20th century:
When was penicillin discovered?
In the year

  • Look at the timeline: “Discovery of penicillin” points to 1928.
  • This is the year it happened.
  • Final answer: 1928.

Exercise
This timeline shows key computing advancements in the 20th century:
When was the transistor invented?
In the year

  • Look at the timeline: “Invention of the transistor” points to 1947.
  • This is the year it was invented.
  • Final answer: 1947.

Mcq
This timeline shows key dates in Roman history:
When was Julius Caesar born?Choose one answer:





  • Look at the timeline: “Julius Caesar born” points to 100 BC.
  • This is his birth year.
  • Final answer: 100 BC.

Mcq
This timeline shows key events in ancient Greek history:
When was Alexander the Great born?
Choose one answer:





  • Look at the timeline: “Alexander the Great born” points to 356 BC.
  • This is his birth year.
  • Final answer: 356 BC.