Use a number line to help represent the situation from the exercise. Recall how to describe changes on a number line using absolute values.
See solution.
Practice makes perfect
Change in Temperature in City A
We want to write an expression that represent the change in temperature for City A. We can use a number line to do this. From the exercise, we know that the temperature rises 9^(∘) from 8AM to 9AM, and then the temperature drops 8^(∘) in the following hour. Let's list the steps we will follow to create a number line for this situation.
First, we start at 0.
Then, we move 9 units to the right. This represents the temperature rise.
Finally, we move 8 units to the left to represent the temperature drop during the next hour.
Now we can mark these steps on the number line.
As we can see from the graph, the sum of 9 and - 8 describes the situation from the exercise. That means that the expression 9+(-8) represents the change in temperature for City A. We can solve the expression we just created to find the integer that represents the temperature change. Let's take another look at this expression.
9+(-8)
We can add the two integers, 9 and -8, to solve the expression. Notice that we are adding two integers with differentsigns, one positive and one negative. This means that we will subtract the absolute values of the integers. Let's do it!
Keep in mind that |9| is greater than |-8|. This means that the change in temperature is positive, so the integer that represents it is 1.
Change in Temperature in City B
We want to write an expression that represents the change in temperature for City B. We can use another number line to help us do this. We know from the exercise that the temperature drops 5^(∘) from 8AM to 9AM, then it drops another 4^(∘) in the next hour. Let's list the steps we will follow to create a number line for this situation.
First, we start at 0.
Then, we move 5 units to the left. This represents the first temperature drop.
Finally, we move 4 units to the left to represent the temperature drop during the next hour.
Now we will mark these steps on the number line.
As we can see from the graph, the sum of -5 and - 4 describes the situation from the exercise. That means that the expression -5+(-4) represents the change in temperature for City B. Just as before, we will solve the expression we created.
-5+(-4)
We can add the two integers, -5 and -4 to solve the expression. Notice that we are adding two integers with the same signs, both negative. Because of this, we will add the absolute values of the integers. Let's do it!
We moved two times to the left, so the result is also negative. This means that we can say that the integer that represents the change of temperature in City B is -9.
Comparison
We want to determine which city has the greater temperature change from 8AM to 10AM. We will compare the absolute values of the two integers we found. Let's take a look at the integers.
Change in temperature for City A: 1^(∘) Change in temperature for City B: -9^(∘)
Now we will find the absolute values of the two numbers above.
|1|&=1
|-9|&=9
As we can see, |-9| is greater than |1|. Because of this, we can say that the change in temperature is greater for City B.
