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.

Question

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

Answer 1

Let's go through each part step by step.

Part A

Raul's initial temperature of the water is 72.3°F. After adding ice cubes, the temperature changes by -39.1°F. We can represent the new temperature as:

\[ 72.3 + (-39.1) \]

Part B

Now we want to break each number into its place values:

• 72.3 = 70 + 2 + 0.3
• -39.1 = -30 + -9 + -0.1

So, the expression can be rewritten as:

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

Part C

Next, we rearrange the expression so that the terms with the same place value are next to each other:

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

Part D

Using the Associative Property, we can group the terms:

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

We will keep the grouping as is since it is already grouped by place value. So we will keep:

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

Part E

Now we can simplify each group:

1. \(70 + (-30) = 40\)
2. \(2 + (-9) = -7\)
3. \(0.3 + (-0.1) = 0.2\)

Putting it all together, we have:

\[ 40 + (-7) + 0.2 \]

Now let's combine them:

1. \(40 + (-7) = 33\)
2. Finally, \(33 + 0.2 = 33.2\)

Thus, the temperature of the water after Raul added the ice cubes is:

\[ \text{Temperature} = 33.2°F \]

Part F

Several minutes later, Raul finds that the temperature changed by -0.6°F. We can calculate the new temperature by adding this change to the previous temperature:

\[ 33.2 + (-0.6) \]

Now simplifying this:

\[ 33.2 - 0.6 = 32.6 \]

So, the temperature of the water now is:

\[ \text{New Temperature} = 32.6°F \]