Q1.
Is (– 7) – (– 5) the same as (– 7) + (+ 5)?
Answer
Yes — both give – 2.
With tokens: put down 7 red. Take away 5 red → 2 red are left → – 2
With tokens: put down 7 red and add 5 green → 5 zero pairs cancel → 2 red are left → – 2
With tokens: put down 7 red and add 5 green → 5 zero pairs cancel → 2 red are left → – 2
Why the two are the same: removing 5 negative tokens and adding 5 positive tokens have exactly the same effect on the pocket — each of them pushes the value up by 5. This is the token-model proof of the rule a – (– b) = a + b: subtracting a number is the same as adding its inverse.