# Arithmetic of rational numbers (Math 0)

https://arbital.com/p/arithmetic_of_rational_numbers_math_0

by Patrick Stevens Jul 3 2016 updated Aug 1 2016

How do we combine rational numbers together?

[summary: We can take two rational numbers and [addition add] them together, just as we can take two natural numbers and add them together; and all the other operations of the integers can be viewed in the rationals too.]

Now that we've seen what the rational numbers are, we'll move on to working out how to combine them.

There are four main ways to combine rational numbers, and collectively they are called "arithmetic":

Additionally, we can compare rational numbers with each other; and we can show that all of these operations play nicely together in a certain sense.

This page is the start of an arc which will go through all of these ideas. In the process, we'll get you familiar with the notation that we use for rational numbers; it's a very convenient shorthand once you've learnt the conventions.