What major topics are there in arithmetic and what order to learn them?

[mark2142]

TL;DR Summary: What topics to cover to safely say I know arithmetic ?

I am learning arithmetic from Indian NCERT textbook. Currently I have finished addition ,substraction of 2 digit numbers and divisions, multiplication of 1 digit numbers. I am moving pretty slowly. Can someone tell me what topics to cover first to build a framework and then go on in detail. I want to learn fast. It has taken me a year now learning arithmetic. I want to speed up. Thanks for the help in advance. (I also have a book called arithmetic for the practical man by Thompson.)

 

[fresh_42]

I could be wrong since your description lacks details, so I have to make guesses. This sounds to me as if you were currently studying something like taught in this book:
https://openstax.org/details/books/prealgebra-2e

You could go on from there to the other (free pdf) books on that webpage.

 

[jedishrfu]

Here’s a youtube video called the Map of Mathematics

 

[mark2142]

I could be wrong since your description lacks details, so I have to make guesses. This sounds to me as if you were currently studying something like taught in this book:
https://openstax.org/details/books/prealgebra-2e

You could go on from there to the other (free pdf) books on that webpage.

1. How did indians come up with such positional system ? Even though its simple but Looks mysterious.

2. Why 400 + 20 +3 is written as 423 ? Why have we omitted zeros ?

3. Why four hundred is written as 400 and not as 4 hundred or 4. Similarly why twenty is written as 20 and not as 2 ten or 2 ?

4. What is place value notation ? Is it different from place value ?