We have a diver standing 7 feet above the water, who then descends 12 feet. How deep in the water is the diver?
Let's think about it this way: first our diver drops 7 feet from whatever perch s/he is on to land on the water. So we've gone down 7 out of our 12 or we can say:
#12-7#, which is to say we have 12 feet to go down and have already gone down 7. How many more feet do we have to go down until we stop?
#12-7=5# feet more. And so the diver is 5 feet under the water.
We can also think of the surface of the water as #0# and any distance above the water as positive and any distance under the water as negative. So we start at #+7# or in other words seven feet above the water, and end up at #-5# or in other words five feet under the water. And we can express this in math terms like this:
#7-12=-5# or we start at 7 feet above the water, move 12 feet towards the water (also known as "down") and end up 5 feet below the water.
