Just a few images that some may find helpful when describing calculations with negatives
Multiplying involves the concept of an "enlargement" operation.
Then the distinction between the multiplying effect of 1 (stays the same) and -1 (flips it over)
Which also works on negatives
...and so we can multiply by any sized positive or negative number.
Now I know I haven't included "taking away" negatives but my explanation takes more than one image to explain - but consider 5 - (-2). Since we know that 5 = 7-2, then 5 - (-2) can be written as (7-2) - (-2). Using this argument alongside appropriate diagrams with learners has proven to be succesful.