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Adding Rational Numbers Using Properties of Operations
This activity will help you meet these educational goals:
Mathematical Practices—You will make sense of problems and solve them and use mathematics to model real-world situations.

Directions
Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work.

Activity
Raul is performing an experiment. He pours water into a glass and measures the temperature of the water at 72.3°F. Then he adds a few ice cubes to the glass of water. He measures the temperature of the water again and finds that it has changed by -39.1°F.

Complete the steps below to learn more about the temperature change of the water.

Part A
Write an expression that represents the temperature (in degrees Fahrenheit) of the water after Raul added the ice cubes. Write the expression as the sum of two numbers.

Part B
Rewrite the expression in part A by breaking up each of the place values. In this case, the place values are tens, ones, and tenths.

Part C
Next, rearrange the expression in part B using the Commutative Property so the terms with the same place value are next to each other.

Part D
Now group the terms in the expression in part C using the Associative Property.

Part E
Simplify the expression in part D to find the temperature of the water after Raul added the ice cubes. Show your work.

Part F
Several minutes later, Raul decides to measure the water temperature again. He finds that the temperature changed by -0.6°F. What is the temperature of the water now? Show your work.

Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a brief evaluation of your work below. Note what you learned and what challenged you.

Answer :

elizabethjennifer895
72.3+ 39.1= 111.4°F difference. 72.3= 723/10 and -39.1= -391/10. i can’t do the rest i have to go but hope this helped

Part A

The temperature of the water (in degrees Fahrenheit) after Raul added the ice cubes is 72.3 + (-39.1).

Part B

Rewrite the expression in part A by breaking up each of the place values. In this case, the place values are tens, ones, and tenths.

72.3 + (-39.1) = 70 + 2 + 0.3 + (-30) + (-9) + (-0.1)

Part C

Next, rearrange the expression in part B using the Commutative Property so the terms with the same place value are next to each other.

70 + 2 + 0.3 + (-30) + (-9) + (-0.1) = 70 + (-30) + 2 + (-9) + 0.3 + (-0.1)

Part D

Now group the terms in the expression in part C using the Associative Property.

70 + (-30) + 2 + (-9) + 0.3 + (-0.1) = [70 + (-30)] + [2 + (-9)] + [0.3 + (-0.1)]

Part E

Simplify the expression in part D to find the temperature of the water after Raul added the ice cubes. Show your work.

Part F

Several minutes later, Raul decides to measure the water temperature again. He finds that the temperature changed by -0.6°F. What is the temperature of the water now?  

The initial temperature of the water was 33.2°F. After several minutes, the temperature of the water changed by -0.6°F. So, the new temperature of the water is 33.2 + (-0.6) =

(30 + 3) + [0.2 + (-0.6)] = 33 + (-0.4) = 33 – 0.4  = 32.6°F.

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