How many integers are thee between -15 and 15?

Answer 1

If by between, you mean not counting the endpoints, then consider this:

Look at 14 and 15 which are consecutive integers. There are no integers between them. Now lets look at the difference: 15 - 14 = 1. So the difference is 1, but 0 integers between. We could guess that the number of integers between is |x - y| -1. So |15 - 14| - 1 = 0.

How about others. Take 10 and 15: the integers between are 11, 12, 13, 14 {4 total}. So |15 - 10| - 1 = 4. So it seems to work [in fact that is it]

Since we are counting integers, we want the absolute value.

So |15 - -15| - 1 = 29. Now lets see if this makes sense. We have 1 to 14 then -1 down to -14 so that's 28, and then you have zero, which makes 29.

What if you meant inclusive. So if you looked at 14 and 15 you wanted to include the endpoints and get the answer 2.

Go through the procedure again and you find the formula for that is |x-y|+1, so your answer is |15 - -15|+1 = 31. Go through the other way and you have 15 twice makes 30 then add 1 for zero to get 31.