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To give you some examples:

1) I've difficulty understanding why, for instance, 5 - (-2) = 5 + 2. The only explanation I have is: 5 - (-2) = 5 + -1*(-1*2) = 5 + (-1*-1)*2 = 5+2.

2) I can't really intuitively understand implicit differentiation.

3) I've difficulty grasping the basic counting principle, etc...

I need a book which starts from the very bottom (covering many topics) and explains why some rules are the way they are. I'm thinking to buy

*Finite Math and Applied Calculus*by Stefan Waner and Steven Costenoble. What's your opinion about the book?

Can you recommend me other books?

Thanks for reading.