This is an old revision of the document!
Arithmetic structure of rational numbers
Definition
$\langle \mathbb Q,+_\mathbb{Q},\cdot_\mathbb{Q} \rangle$ |
$[\langle a,b\rangle]+_\mathbb{Q}[\langle m,n\rangle]=[\langle a\ n+b\ m,b\ n\rangle]$ |
$[\langle a,b\rangle]\cdot_\mathbb{Q}[\langle m,n\rangle]=[\langle a\ m,b\ n\rangle]$ |
The operations $+$ and $\cdot$ on the right hand sides are these of arithmetic structure of integers.
Discussion
We'll generally use the notation introduced in integer as well as
$\frac{a}{b}\equiv\langle a,b\rangle$
We'll also often omit the multiplication sign.
Reference
Wikipedia: Rational number