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I'm trying to learn arithmetic from scratch again. Even though I can use it, I'm not sure if I can teach it to someone and I believe if you can't teach something properly, there might be loopholes in your understanding. Hence, I'm looking for a book that discusses various topics of arithmetic, like numbers (counting, fractions, integers, rational, real), numerals, place value number systems, addition, multiplication, division, etc very explicitly.

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You might check out the OpenStax Prealgebra text. It seems to have much of what you’re looking for.

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https://www.amazon.com/Math-Ages-SAT-High-School/dp/B08P2XRCLR/ref=sr_1_3?crid=1TWKUIXC302BL&keywords=high+school+maths&qid=1673731187&s=books&sprefix=high+school+math%2Cstripbooks-intl-ship%2C184&sr=1-3

I have used this book to help me understand mathematics and prepare for my exams. It is helpful for all levels and the explanations are clear and friendly.

:)

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I would unironcially recommend Tao's Analysis-1. The issue of pinning down numbers as a logically consistent concept is much more complicated than one may think it to be.

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