Question

Why do you change the sign when subtracting a negative number?

Answer 1

This is because minus times minus is equals plus so the sign must change

Answer 2

Suppose  I am in debt to someone to the value of  $5.  Then we can say that my net worth is -5. Now my friend wants to help me out with my debt by 'taking away' the -5. He can do this by giving me $5 and now my debt is zero.

so  we can say that  these 2 are equivalent   -5-(-5) = -5 + 5 = 0.

Hope this helps.