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Addition and Subtraction with Time

Combining measures of time

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Addition and Subtraction with Time
Credit: Ron Kroetz
Source: https://www.flickr.com/photos/ronkroetz/8279076048/
License: CC BY-NC 3.0

Maria needs to run a couple errands before meeting with her friend. She thinks she will spend 15 minutes at the post office, 1 hour and 25 minutes at the mall, and 20 minutes to drive to her friend’s house. If Maria leaves her house at 1:00 pm, around what time will she reach her friend’s house?

In this concept, you will learn how to add and subtract measures of time.

Adding and Subtracting with Time

Time is most commonly measured using the units second, minute, and hour. Of the three, the second is the smallest unit and the hour is the largest unit. Use this information to convert units of time.

60 seconds = 1 minute

60 minutes = 1 hour

Multiply when converting a larger unit to a smaller unit. Divide when converting a smaller unit to a larger unit.

Let's look at some examples.

Convert 120 seconds to minutes. 

120 seconds = _____ minutes

This involves converting a smaller unit to a larger unit. 60 seconds equals 1 minute. Divide the number of seconds by 60.

120 ÷ 60 = 2

120 seconds = 2 minutes

Now, convert 4 hours to minutes.

4 hours = _____ minutes

This involves converting a larger unit to a smaller unit. 1 hour equals 60 minutes. Multiply the number of hours by 60.

4 × 60 = 240

4 hours = 240 minutes

To add measures of time, add the like units first. Start with the smallest unit. Add seconds to seconds, minutes to minutes, and hours to hours. Then, simplify the answer when necessary by converting the units.

Find the sum of 1 hour 55 minutes and 45 minutes.

\begin{align*}1 \ \text{hr} & 55 \ \text{min} \\ + \quad \quad & 45\ \text{min}\\ \hline 1 \ \text{hr} & 100\ \text{min} \end{align*}

You know that 60 minutes equal 1 hour. Simplify 100 minutes by converting it in terms of hours and minutes.

100 minutes = ____ hours ___ minutes

Divide the number of minutes by 60.

100 ÷ 60 = 1 R40

100 minutes = 1 hour 40 minutes

Rewrite 100 minutes as 1 hour 40 minutes. This will add 1 hour to the total number of hours.

\begin{align*} & 1 \ \text{hr} \ 100 \ \text{min}\\ =& 1\ \text{hr} + 1 \ \text{hr} \ 40 \ \text{min}\\ = &2\ \text{hr} \ 40 \ \text{min}\end{align*}

The sum of 1 hour 55 minutes and 45 minutes is 2 hours 40 minutes.

To subtract measure of time, start by subtracting the smallest unit first. You may need to borrow from the larger unit. Then, simplify the answer when necessary by converting the units.

Find the difference between 2 minutes 30 seconds and 1 minute 40 seconds.

\begin{align*}2 \ \text{min} & 30\ \text{sec} \\ - \ 1 \ \text{min} & 40\ \text{sec}\\ \hline \end{align*} You cannot subtract 40 from 30. Borrow from the minute unit. 1 minute equals 60 seconds. Add 60 seconds to 30 seconds.

\begin{align*}\cancel{2}^1 \ \text{min} & \cancel{30}^{90}\ \text{sec} \\ - \quad 1 \ \text{min} & 40\ \text{sec}\\ \hline 0 \ \text{min} & 50 \ \text{sec}\end{align*}

The difference between 2 minutes 30 seconds and 1 minute 40 seconds is 50 seconds.

Time can also be described as fractional units of time, for example: "a quarter of an hour" or "half an hour."  You know that 1 hour equals 60 minutes. To find a fraction of an hour, multiply the fraction by 60 minutes.

\begin{align*}\frac{1}{4} (60) = \frac{60}{4} = 15\end{align*}

A quarter hour is 15 minutes. 

Examples

Example 1

Earlier, you were given a problem about Maria on her way to a friend’s house.

Maria leaves her house at 1:00 pm and thinks she will spend 15 minutes at the post office, 1 hour and 25 minutes at the mall, and 20 minutes driving to her friend’s house. Find the total time of her errands and the drive time to determine what time Maria will arrive at her friend’s house.

First, add the time for each activity.

 \begin{align*}1 \ \text{hr} & 25 \ \text{min} \\ & 20 \ \text{min} \\ + \quad & 15\ \text{min}\\ \hline 1 \ \text{hr} & 60\ \text{min} \end{align*}

Then, simplify 60 minutes. 60 minutes equals 1 hour. This will add 1 hour to the total number of hours.

 \begin{align*} & 1 \ \text{hr} \ 60\ \text{min}\\ =& 1\ \text{hr} + 1 \ \text{hr} \\ = &2\ \text{hr}\end{align*}

2 hours after 1:00 pm is 3:00 pm. Maria should arrive at her friend’s house at 3:00 pm.

Example 2

What is \begin{align*}\frac{1}{8}\end{align*} of an hour in minutes?

To figure this out, multiply \begin{align*}\frac{1}{8}\end{align*} times 60 minutes.

\begin{align*}\frac{1}{8}(60) = \frac{60}{8} = 7\frac{1}{2}\end{align*}

 \begin{align*}\frac{1}{8}\end{align*}  of an hour is \begin{align*}7 \frac{1}{2}\end{align*} minutes.

Example 3

Convert the following units: 180 minutes = ______ hours.

Convert minutes to hours. There are 60 minutes in 1 hour. Divide the number of minutes by 60.

180 ÷ 60 = 3

180 minutes = 3 hours

180 minutes is equal to 3 hours. 

Example 4

Convert the following units: 1 hour 5 minutes + 45 minutes = _____.

First, add the like units.

 \begin{align*}1 \ \text{hr} & 5 \ \text{min} \\ + \ \quad & 45\ \text{min}\\ \hline 1 \ \text{hr} & 50\ \text{min} \end{align*}

The sum is 1 hour 50 minutes.

Example 5

Convert the following units: 5 hours 10 minutes – 30 minutes = _____.

First, subtract the like units starting from the smallest unit. 

 \begin{align*}5 \ \text{hr} & 10 \ \text{min} \\ - \ \quad & 30\ \text{min}\\ \hline \end{align*}

You cannot subtract 30 from 10 so you must borrow from the hour unit. 1 hour equals 60 minutes. Add 60 minutes to the 10 minutes and subtract.

 \begin{align*}\cancel{5}^4 \ \text{hr} & \cancel{10}^{70} \ \text{min} \\ - \quad \quad & 30\ \text{min}\\ \hline 4 \ \text{hr} & 40\ \text{min} \end{align*}

The difference is 4 hours 40 minutes.

Review

Add the following units of time.

  1. 15 minutes + 60 minutes = ______
  2. 10 minutes + 20 minutes = ______
  3. 15 seconds + 45 seconds = ______
  4. 1 hour 50 minutes + 20 minutes = ______ 
  5. 75 minutes + 15 minutes 10 seconds = ______ 

Subtract the following units of time.

  1. 35 minutes - 10 minutes = ______ 
  2. 60 minutes - 10 minutes = ______ 
  3. 1 hour 75 minutes - 20 minutes = ______ 
  4. 2 hour 10 minutes - 20 minutes = ______ 
  5. 1 hour 5 seconds - 5 minutes = ______ 

Convert the following units and fractional units of time.

  1. 3000 seconds = ______ minutes
  2. 6000 seconds = ______ hours ______ minutes
  3. 360 minutes = ______ hours
  4. 300 minutes = ______ hours
  5. 12,000 seconds = ______ minutes
  6. \begin{align*}\frac{1}{4}\end{align*} hour = ______ minutes
  7. \begin{align*}\frac{1}{8}\end{align*} hour = ______ minutes
  8. \begin{align*}\frac{1}{2}\end{align*} hour = ______ minutes

Review (Answers)

To see the Review answers, open this PDF file and look for section 6.14. 

Resources

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Vocabulary

Elapsed Time

The time from the start of an event to the end of the event.

Units of Time

Units of time are how we measure time using seconds, minutes and hours.

Image Attributions

  1. [1]^ Credit: Ron Kroetz; Source: https://www.flickr.com/photos/ronkroetz/8279076048/; License: CC BY-NC 3.0

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