First of all I must make a claim. Rules are shortcuts. Shortcuts that people use to not bother in understanding the complete picture of something. And this includes the rules of calculation between negative and positive numbers. Furthermore, I believe that these rules are counterintuitive or perhaps not counterintuitive, but it fails to explain what it means. Rule 1: When adding numbers with unlike signs, add the absolute value of the two numbers and copy the sign of the larger number. Okay, but I just can't explain to myself how 5-20 is the same as 5+ -20= -15. Moreover, why is 5-(-4) equivalent to 5+4= 9 Furthermore, -5 x -4 =20 This kind of thinking its fine at first. But if you apply it to real world problems, it just won't make sense. How can I make sense of this. And also I can't find a book that tries to explain this.