You have applied the rules of integers to solve word problems. Now, you will review ways to add and subtract decimals, and then use what you learn to solve problems relating to addition and subtraction of positive and negative decimals.

Click on the image below to open a base-ten model interactive in a new web browser tab or window. The interactive represents the two addends in an addition problem, or the minuend and subtrahend in a subtraction problem. Use the manipulative to work through at least 3 problems.

Directions

• Click on a block and drag it on top of its opposite block to remove zero pairs.
• Click on a block and drag it to the next column to regroup.
• Click “Next Problem” to move to the next problem when you are ready.

Interactive popup. Assistance may be required.

Need additional help for addition?

Interactive popup. Assistance may be required.

Need additional help for subtraction?

Use what you noticed in the interactive to answer the following questions.

• In the original problem, 4.3 – 1.5, when you dragged a ones rod into the tenths column, it split into 10 tenths. How does that relate to the regrouping that was recorded symbolically in the image shown below?
  
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  Check Your Answer

  The 10 tenths were added to the 3 tenths that were already present in the minuend, or first number in the subtraction problem, so the 3 in the tenths place was rewritten as 13. Since 1 one was removed for regrouping, the 4 in the ones place was rewritten as 3.
• In an addition problem, such as 6.4 + 4.8, when you regroup 10 tenths into 1 one and drag the ones rod into the ones place, how did that action appear in the regrouping that was recorded symbolically such as the regrouping shown in the image below?
  
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  Check Your Answer

  The 10 tenths were combined to make 1 one, and that 1 was carried over and rewritten with the other digits in the ones place.

Pause and Reflect

Why is it important to line up the decimal point when adding or subtracting decimal numbers?

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Check Your Answer

Lining up the decimal point helps to preserve place value so that you know you are adding like digits to like digits, or subtracting like digits from like digits.

When regrouping 1 one and 3 tenths into 13 tenths, why do you cross out the original 3 in the tenths place and replace it with 13?

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Check Your Answer

When the 1 one is broken into 10 tenths and combined with the original 3 tenths, there is now a total of 13 tenths from which the tenths in the subtrahend, or second number in the subtraction problem, can be removed.

Practice

The table below shows the average length, in minutes, of songs from different genres that are on Mitzi’s MP3 player. Use this information to answer questions 1 - 3.

1. How much longer is a country song than a rock song?

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   Need a hint?

   What operation does the phrase "how much longer" suggest that you need to perform?
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   Check Your Answer

   
   
   A country song is 0.68 seconds longer than a rock song.
2. If Mitzi listens to one hip hop song and one classical song without a break in between, how many minutes of music will that be?

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   Mitzi is combining two songs. What operation does that suggest?
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   Check Your Answer

   
   
   The two songs together will be 10.95 minutes of music.
3. How much more time will Mitzi spend listening to one rock song and one country song, back to back, than she would if she listened to one classical song?

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   Need a hint?

   Mitzi is combining two songs. What operation does that suggest? What operation does the phrase, “how much more time” suggest that you will need to use?
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   Check Your Answer

   First, determine the combined length of one rock song and one country song.
      3.55
   + 4.23
      7.78
   
   Next, determine the difference between this combined length and the length of one classical song.
   
      7.78
   − 6.76
      1.02
   
   Mitzi will spend 1.02 more minutes listening to one rock and one country song than she would if she listened to one classical song.
4. At 7:00 a.m., the temperature in Seguin, Texas, was 68.5°F. By 10:00 a.m., the temperature change was +12.3°F, and then a cold front came through. By 3:00 p.m., the temperature change was −23.7°F. What was the temperature at 3:00 p.m.?

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   Need a hint?

   Use addition to the starting temperature to determine the final temperature. Be mindful of the signs of the temperature changes!
   Interactive popup. Assistance may be required.

   Check Your Answer

   68.5°F + 12.3°F – 23.7°F = 57.1°F
   
   At 3:00 p.m., the temperature was 57.1°F.