As an ex-high school maths teacher I can say that your book is (probably - I only read pars of it) almost entirely useless because the level of the language used is well above than of the intended recipient - assuming you intend for the students to read this book and not just their teacher(who generally already knows what they're teaching). Sentences like "Multiplecation can also be done by modular arithmetic"... WTF?

OTOH assuming your language level is correct and these students are not the intended recipient, then your level of detail and reasoning is off. eg, negative numbers are not just the answer to "what's smaller than zero?" (zero itself is at least a book's worth of problems), but like many of math's number types, originated in previously insoluble equations - in this case equations of the form x-y=? when y>x.