Properties of Fractions
For all fractions `a//b` and `c//d`, where `b!=0` and `d!=0`:
Equality	`a/b=c/d` if and only if `ad=bc`
Equivalent fractions	`a/b=(ac)/(bc)`, `c!=0`
Addition	`a/b+c/b=(a+c)/b`
Subtraction	`a/b-c/b=(a-c)/b`
Multiplication	`a/b*c/d=(ac)/(bd)`
Division	`a/b-:c/d=a/b*d/c=(ad)/(bc)`, `c!=0`
Sign	`-a/b=(-a)/b=a/(-b)`

The equality property of fractions contains the terminology "if and only if," which implies each of the following:

If `a/b=c/d`, then `ad=bc`

If `ad=bc`, then `a/b=c/d`

Division Property of Zero

For `a!=0`, `0/a=0`. (Zero divided by any nonzero number is zero.)

`a=0` is undefined. (Division by zero is undefined.)