To simplify a fraction, the two numbers must be divided by their GCD. The following script calculates the GCD using the Euclidean Algorithm.
Script to Simplify Fractions
define simplify fraction (numerator) (denominator) GCD (numerator) (denominator) // calculates GCD of numbers set [numerator v] to ((numerator) / (GCD)) // divides numerator by GCD set [denominator v] to ((denominator) / (GCD)) // divides denominator by GCD define GCD (a) (b) // euclidean algorithm for GCD if <(b) = (0)> then // if b = 0 set [GCD v] to (a) // stop and return value else GCD (b) ((a) mod (b)) // return equal GCD with smaller numbers end
Example Use Cases
when gf clicked simplify fraction (36) (48) :: custom say (join (numerator) (join [/] (denominator))) // 3/4
when gf clicked simplify fraction (2) (10) :: custom say (join (numerator) (join [/] (denominator))) // 1/5
Simplify Fraction algorithm
The simplify fraction () () :: custom block simplifies a fraction by calculating the GCDs with GCD () () :: custom and divides the numerator and denominator with the resulting GCD.
GCD algorithm
The GCD uses the Euclidean algorithm. The key insight is that (b :: custom) and ((a::custom) mod (b::custom)) has the same GCD as (a :: custom) and (b :: custom). The numbers produced by (b :: custom) and ((a::custom) mod (b::custom)) get smaller and smaller each time the operation is applied. Eventually (b::custom) will be equal to 0 and the process will stop.
