Use a number line to help represent the situation from the exercise. Recall how to describe changes on a number line using absolute values. How does this compare to Adam's solution?
See solution.
Practice makes perfect
We want to find an error that Adam might had made when finding the location of a submarine. We can use a number line to help us visualize the given situation. From the exercise, we know that the submarine travels 200 meters below the surface. Then it increases its depth by 45 meters. Let's list the steps we can follow to create a number line for this situation.
First, we start at 0.
Then, we move 200 units to the left. This represents the depth of the traveling submarine.
Finally, we move 45 units to the left to represent the submarine increasing its depth.
Now, we can mark these steps on a number line.
As we can see from the graph, the sum of - 200 and - 45 is located 45 units to the left of - 200. We can add the two integers to find the submarine's depth. Let's take a look at the expression that represents this situation.
-200+(-45)
Notice that we are adding two integers with the samesigns, both negative. Because of this, we will add the absolute values of the integers. Let's do it!
Keep in mind that we moved to the left of 0 on the number line two times. Because of this, the result is negative and we can say that the submarine is 245 meters below the surface of the ocean. Adam said the new location of the submarine is -155 meters. Instead of adding the two absolute values, it looks like he subtracted |-45| from |-200|.
