Unit 5: Making Change, Time & Perimeter
Topic D: Adding Units of Time
Sometimes we need to add units of time to find out how much in total it will take to do some job or to travel to some other place.
To add units of time, do this:
Place the numbers to be added in columns – minutes with minutes, hours with hours, seconds with seconds
Add each column. Be sure to write the unit of time.
Example A
[latex]\begin{array}[t]{rr}&12\text{ h, }45\text{ min} \\+ &10 \text{ h, }05\text{ min} \\ \hline \\ \end{array}[/latex]
Step 1: Add the minutes to the minutes
[latex]\begin{array}[t]{rr}&45\text{ min} \\+& 05\text{ min}\\ \hline &50 \text{ min}\end{array}[/latex]
Step 2: Add the hours to the hours
12 h + 10 h = 22 h
The sum of [latex]\begin{array}[t]{rr}&12\text{ h, }45\text{ min}\\+& 10\text{ h, }05\text{ min}\\ \hline &22\text{ h, }50\text{ min}\end{array}[/latex]
Example B
[latex]\begin{array}[t]{rr}&4\text{ h, }50\text{ min, }15\text{ s}\\ +& 21\text{ h, }05\text{ min, }40\text{ s}\\ \hline \\ \end{array}[/latex]
Step 1: Add the seconds to the seconds.
15 s + 40 s = 55 s
Step 2: Add the minutes to the minutes.
[latex]\begin{array}[t]{rr}&50\text{ min}\\+& 05\text{ min}\\ \hline& 55\text{ min}\end{array}[/latex]
Step 3: Add the hours to the hours.
4 h + 21 h = 25 h
The sum of [latex]\begin{array}[t]{rr}& 4\text{ h, }50 \text{ min, }15\text{ s}\\ + &21\text{ h, }05\text{ min, }40\text{ s}\\ \hline &24\text{ h, }55\text{ min, }55\text{ s}\end{array}[/latex]
Exercise One
Add the times. Check your work using the answer key at the end of the exercise.
- [latex]\begin{array}[t]{rr}&3\text{ h, }20\text{ min}\\+& 5\text{ h, }15\text{ min} \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&11\text{ h, }05 \text{ min}\\+& 4\text{ h, }40\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&9\text{ h, }50\text{ min}\\+& 14\text{ h, }05\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&2\text{ h, }10\text{ min}\\+& 6\text{ h, }25\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&7\text{ h, }35\text{ min}\\+& 1\text{ h, }10\text{ min} \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&10\text{ h, }30\text{ min}\\+& 8\text{ h, } 20\text{ min} \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&1\text{ h, }55\text{ min, }15\text{ s}\\+&28\text{ h, }0\text{ min, }40\text{ s}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&4\text{ h, }45\text{ min, }05\text{ s}\\+& 15\text{ h, }10\text{ min, }50\text{ s} \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&7\text{ h, }35\text{ min, }20\text{ s}\\+&6\text{ h, }15\text{ min, }30\text{ s}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&3\text{ h, }25\text{ min, }45\text{ s}\\+& 8\text{ h, }30\text{ min, }10\text{ s}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&3\text{ h, }45\text{ min, }15\text{ s}\\+& 12\text{ h, }05\text{ min, }35\text{ s} \\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&4\text{ h, }50\text{ min, }30\text{ s}\\+& 5\text{ h, }0\text{ min, }25\text{ s} \\ \hline \\ \end{array}[/latex]
Answers to Exercise One
- 8 h, 35 min
- 15 h, 45 min
- 23 h, 55 min
- 8 h, 35 min
- 19 h, 45 min
- 18 h, 50 min
- 29 h, 55 min, 55 s
- 19 h, 55 min, 55 s
- 13 h, 50 min, 50 s
- 11 h, 55 min, 55 s
- 15 h, 50 min, 50 s
- 9 h, 50 min, 55 s
Exercise Two
Rewrite each question in columns. Be careful to write seconds under seconds, minutes under minutes and hours under hours. Check your work using the answer key at the end of the exercise.
- Fabio worked 8 h, 48 min on his homework. The following week, he worked 9 h, 10 min on his homework. How much time in total did he work on his homework?
- Day one of the holiday trip took 11 h, 32 min. Day two took 10 h, 26 min. How much time did we travel in two days?
Answers to Exercise Two
- 17h, 58mins
- 21h, 58mins
Subtracting Units of Time
We need to subtract units of time to find out how much time it took to do some job or to travel to some other place.
To subtract units of time, do this:
Place the numbers to be subtracted in columns – minutes with minutes, hours with hours, seconds with seconds
Subtract each column. Be sure to write the unit of time.
Example C
[latex]\begin{array}[t]{rr}&2\text{ h, }45\text{ min}\\ − &1\text{ h, }05\text{ min}\\ \hline \\ \end{array}[/latex]
Step 1: Subtract the minutes from the minutes.
45 min − 05 min = 40 min
Step 2: Subtract the hours from the hours.
2 h − 1 h = 1 h
The difference of [latex]\begin{array}[t]{rr}&2\text{ h, }45\text{ min}\\ −& 1\text{ h, }05\text{ min}\\ \hline &1\text{ h, }40\text{ min}\end{array}[/latex]
Example D
[latex]\begin{array}[t]{rr}&5\text{ h, }45\text{ min, }10\text{ s}\\ −& 2\text{ h, }35\text{ min, 0}5\text{ s} \\ \hline \\\end{array}[/latex]
Step 1: Subtract the seconds from the seconds.
10 s − 05 s = 05 s
Step 2: Subtract the minutes from the minutes
45 min − 35 min = 10 min
Step 3: Subtract the hours from the hours
5 h − 2 h = 3 h
The sum of [latex]\begin{array}[t]{rr}&5\text{ h, }45\text{ min, }10\text{ s}\\−& 2\text{ h, }35\text{ min, }05\text{ s}\\ \hline &3\text{ h, }10\text{ min, }05\text{ s} \end{array}[/latex]
Exercise Three
- [latex]\begin{array}[t]{rr}&12\text{ h, }55\text{ min}\\-& 3\text{ h, }5 \text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&9\text{ h, }45\text{ min}\\-& 6\text{ h, }10 \text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&24\text{ h, }50\text{ min}\\-& 8\text{ h, }35 \text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&11\text{ h, }40\text{ min}\\-& 4\text{ h, }15 \text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&7\text{ h, }30\text{ min}\\-& 5\text{ h, }05\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&12\text{ h, }20\text{ min}\\-& 10\text{ h, }05\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&16\text{ h, }45\text{ min, }55\text{ s}\\-& 9\text{ h, }25\text{ min, }15\text{ s}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&17\text{ h, }50\text{ min, }35\text{ s}\\-& 8\text{ h, }15\text{ min, }20\text{ s}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&13\text{ h, }55\text{ min, }40\text{ s}\\-& 5\text{ h, }30\text{ min, }10\text{ s}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&15\text{ h, }40\text{ min, }50\text{ s}\\-& 6\text{ h, }20\text{ min, }25\text{ s}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&14\text{ h, }50\text{ min, }40\text{ s}\\-& 7\text{ h, }35\text{ min, }05\text{ s}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}&28\text{ h, }50\text{ min, }30\text{ s}\\-& 9\text{ h, }35\text{ min, }0\text{ s}\\ \hline \\ \end{array}[/latex]
Answers to Exercise Three
- 9 h, 50 min
- 3 h, 35 min
- 16 h, 15 min
- 7 h, 25 min
- 2 h, 25 min
- 2 h, 15 min
- 7 h, 20 min, 40 s
- 9 h, 35 min, 15 s
- 8 h, 25 min, 30 s
- 9 h, 20 min, 25 s
- 7 h, 15 min, 35 s
- 19 h, 15 min, 30 s
Exercise Four
Rewrite each question in columns. Be careful to write seconds under seconds, minutes under minutes and hours under hours. Check your work using the answer key at the end of the exercise.
- Milan works 45 h, 30 min each week. He has worked 32 h, 15 min this week. How much more time can he work?
- The trip from Vancouver to Calgary takes 17 h, 40 min on the bus. The trip from Vancouver to Kamloops takes 5 h, 05 min. How much longer must you travel to get to Calgary?
- The flight from Vancouver to Toronto leaves at 12 h, 30 min. The flight arrives in Toronto at 15 h, 53 min. How long is the flight from Vancouver to Toronto?
- Over two months, Lola has used her cell phone for 43 h, 37 min, 58 s. In June, she used her cell phone for 21 h, 22 min, 25 s. How much time has she used her cell phone this month?
Answers to Exercise Four
- 13h, 15min
- 12h, 35min
- 3h, 23min
- 22h, 15min, 33s
Topic D: Self-Test
Mark /24 Aim 19/24
- Find the sums. (4 marks)
- [latex]\begin{array}[t]{rr}& 12\text{ h, }15\text{ min}\\+& 4\text{ h, }35\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 7\text{ h, }50\text{ min}\\+&10\text{ h, }05\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 11\text{ h, }40\text{ min}\\+& 2\text{ h, }10\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 1\text{ h, 25}\text{ min}\\+& 15\text{ h, }20\text{ min}\\ \hline \\ \end{array}[/latex]
- Find the sums. (4 marks)
- [latex]\begin{array}[t]{rr}& 9\text{ h, }42\text{ min}\\+& 3\text{ h, }16\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 5\text{ h, }53\text{ min}\\+& 8\text{ h, }02\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 6\text{ h, }38\text{ min}\\+& 3\text{ h, }21\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 22\text{ h, }33\text{ min}\\+& 14\text{ h, }16\text{ min}\\ \hline \\ \end{array}[/latex]
- Rewrite each question in columns and find the sums. (4 marks)
- Ingrid walked the dogs for 3 h, 15 min on Monday. On Tuesday, she walked the dogs for 2 h, 40 min. Find the total time that Ingrid walked the dogs.
- Bianca rode the bus to college for 2 h, 36 min on Wednesday. On Thursdays, the same trip took 3 h, 21 min. How long was she on the bus altogether?
- Find the differences. (4 marks)
- [latex]\begin{array}[t]{rr}& 12\text{ h, }55\text{ min}\\-& 4\text{ h, }35\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 9\text{ h, }45\text{ min}\\-& 3\text{ h, }30\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 11\text{ h, }50\text{ min}\\-& 7\text{ h, }15\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 40\text{ h, }40\text{ min}\\-& 15\text{ h, }05\text{ min}\\ \hline \\ \end{array}[/latex]
- Find the differences. 4 marks
- [latex]\begin{array}[t]{rr}& 8\text{ h, }58\text{ min}\\-& 6\text{ h, }34\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 14\text{ h, }47\text{ min}\\-& 5\text{ h, }29\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 11\text{ h, }36\text{ min}\\-& 2\text{ h, }18\text{ min}\\ \hline \\ \end{array}[/latex]
- [latex]\begin{array}[t]{rr}& 18\text{ h, }41\text{ min}\\-& 9\text{ h, }26\text{ min}\\ \hline \\ \end{array}[/latex]
- Rewrite each question in columns and find the sums. (4 marks)
- During rush hour, it took Marco 2 h, 51 min to drive home. During non-rush hour, it took Marco 1 h, 48 min to drive home. Find the difference.
- Kade and Amia left from the Kelowna at the same time. Kade took 5 h, 37 min to drive home. Amia took 4 h, 29 min to drive home. Find the difference.
Answers to Topic D Self-Test
-
- 16 h, 50 min
- 17 h, 55 min
- 13 h, 50 min
- 16 h, 45 min
-
- 12 h, 58 min
- 13 h, 55 min
- 9 h, 59 min
- 36 h, 49 min
-
- 5 h, 55 min
- 5 h, 57 min
-
- 8 h, 20 min
- 6 h, 15 min
- 4 h, 35 min
- 25 h, 35 min
-
- 2 h, 24 min
- 9 h, 18 min
- 9 h, 18 min
- 9 h, 15 min
-
- 1 h, 03 min
- 1 h, 08 min