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6.14: Addition and Subtraction with Time

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Have you ever lost something that you needed to do a job?

While working, Travis accidentally loses his measuring tape. He searches everywhere, but can’t seem to find it. “Uncle Larry, I can’t find my measuring tape,” Travis says. “I’m going to ride my bike to the hardware store and get a new one.”

“Alright Travis, but we are having a meeting at 11 and I would like you to be back for it,” Uncle Larry says.

Travis looks down at his watch. It is 10:15. He knows that he can make it, but he will need to hurry. Travis dashes out the door and jumps onto his bike. He rides to the store, gets his measuring tape and returns back. It takes Travis \frac{1}{2} hour to ride to the store and back. He gets a little distracted in the store, but after 10 minutes, he finds and buys the measuring tape. Did Travis make it back in time for the meeting? You will need to learn some information about calculating time to be sure.

Pay close attention and you will be able to figure this problem out at the end of the Concept.

Guidance

We add and subtract units of time every day. Sometimes, we are trying to figure out whether we will be on time or late. In other situations, we are trying to figure out a movie time or the time to meet a friend, or how long the soccer game actually lasted.

To calculate units of time, we are going to need to know how to convert minutes to seconds to hours.

One of the first things that you need to know how to do when working with time is to convert different units.

How do we convert units?

The easiest way is to simply multiply or divide. Sometimes, you will be able to accomplish this using mental math. In fact, you should try to figure things out in your head whenever possible. In this Concept, you can see the work the long way too, but mental math is almost always quicker.

120 minutes = _______ hours

First, try to figure this one out in your head using mental math. Now let’s look at the solution.

To convert a smaller unit to a larger unit, we divide.

There are 60 minutes in one hour, so we divide 120 minutes by 60 and we get 2.

120 minutes = 2 hours

We can also do this the other way around.

How many minutes are there in 4 hours? To solve this problem, we are going from a larger unit to a smaller unit, so we multiply.

4 \times 60 = 240

There are 240 minutes in 4 hours.

What about when you have fractional units of time?

Sometimes, we measure time using fractional units. We might use the phrase  \frac{3}{4} of an hour or \frac{1}{2} an hour.” We can also figure out how many minutes these fractional units of time are.

Here are some given fractional units of time. We can figure out whether or not these measures are accurate.

Let’s test it out and prove that \frac{1}{4} hour is equal to 15 minutes. If we know that there are 60 minutes in one hour then we can multiply \frac{1}{4}(60) and that will give us the number of minutes.

\frac{1}{4} (60) = \frac{60}{4} = 15

Our work is accurate. We can also figure out any fraction of an hour using this method.

Try a few of these on your own.

Example A

180 minutes = ______ hours

Solution: 3 hours

Example B

5 hours = ______ minutes

Solution: 300 minutes

Example C

180 seconds = ______ minutes

Solution: 30 minutes

Now back to Travis and his time dilemma. Here is the original problem again.

While working, Travis accidentally loses his measuring tape. He searches everywhere, but can’t seem to find it. “Uncle Larry, I can’t find my measuring tape,” Travis says. “I’m going to ride my bike to the hardware store and get a new one.”

“Alright Travis, but we are having a meeting at 11 and I would like you to be back for it,” Uncle Larry says.

Travis looks down at his watch. It is 10:15. He knows that he can make it, but he will need to hurry. Travis dashes out the door and jumps onto his bike. He rides to the store, gets his measuring tape and returns back.

It takes Travis \frac{1}{2} hour to ride to the store and back. He gets a little distracted in the store, but after 10 minutes, he finds and buys the measuring tape.

Did Travis make it back in time for the meeting? You will need to learn some information about calculating time to be sure.

Now we need to add up the time that it took Travis to go to the store, buy the measuring tape and get back.

Riding time = 30 minutes of riding time total-15 minutes there and 15 minutes back.

10 minutes in the store.

30 + 10 = 40 total minutes

How much time was there from 10:15 when Travis left until the meeting at 11:00?

11 - 10:15 = 45 minutes

45 - 40 = 5 minutes

Travis arrived back at the work site with five minutes to spare.

Vocabulary

Here are the vocabulary words in this Concept.

Elapsed Time
the time from the start of an event to the end of the event.
Units of Time
how we measure time using seconds, minutes and hours.

Guided Practice

Here is one for you to try on your own.

What is \frac{1}{8} of an hour in minutes?

Answer

To figure this out, we multiply \frac{1}{8} times 60 since we want our answer in minutes.

\frac{1}{8}(60) = \frac{60}{8} = 7.5

Our answer is 7.5 minutes or 7 \frac{1}{2} minutes.

Video Review

Here are videos for review.

Khan Academy Time Differences

James Sousa Operations with Time

Practice

Directions: Add the following units of time.

1. 15 minutes plus 60 minutes = ______

2. 10 minutes and twenty minutes = ______

3. 15 seconds and 45 seconds = ______

4. 50 minutes and 20 minutes = ______ hours ______ minutes

5. 75 minutes and 15 minutes = ______ hours

6. 35 minutes and 10 minutes = ______ minutes

7. 60 minutes and 10 minutes = ______ hours ______ minutes

8. 75 minutes and 20 minutes = ______ hours ______ minutes

9. 120 minutes and ten minutes = ______ hours ______ minutes

10. 300 seconds and 5 minutes = ______ minutes

Directions: Convert the following units and fractional units of time.

11. 3000 seconds = ______ minutes

12. 4 hours = ______ minutes

13. 6000 seconds = ______ hours ______ minutes

14. 120 minutes = ______ hours

15. 360 minutes = ______ hours

16. 300 minutes = ______ hours

17. 12,000 seconds = ______ minutes

18. \frac{1}{4} hour = ______ minutes

19. \frac{1}{8} hour = ______ minutes

20. \frac{1}{2} hour = ______ minutes

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Date Created:

Oct 29, 2012

Last Modified:

Aug 18, 2014
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