# Arithmetic of rational numbers (Math 0)

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.

Children:

- Addition of rational numbers (Math 0)
The simplest operation on rational numbers is addition.

- Subtraction of rational numbers (Math 0)
In which we meet anti-apples.

- Division of rational numbers (Math 0)
“Division” is the idea of “dividing something up among some people so that we can give equal amounts to each person”.

- Rational arithmetic all works together
The various operations of arithmetic all play nicely together in a certain specific way.

- Order of rational operations (Math 0)
Our shorthand for all the operations on rationals is very useful, but full of brackets; this is how to get rid of some of the brackets.

Parents:

- Rational number
The rational numbers are “fractions”.

- Field structure of rational numbers
In which we describe the field structure on the rationals.