Sorting Fractions in VB.Net

Rationalise (Canonise) the Fractions before Sorting

Before fractions are sorted, they are rationalised; i.e., they are put in a form where their denominators become the same. This same denominator is the LCM of the denominators of all the separate fractions.
After this is done, the new numerators can easily be sorted in a preferred order.

Steps for Sorting of Fractions VB.Net code

The following steps will guide us in writing our code.
Let's illustrate with ⁵/₉, ³/₇, ¹/₂

Step 1:

Find the LCM of the denominators.
⇒ LCM of 9, 7 & 2 = 126

Step 2:

In a turn by turn fashion, divide the found LCM from Step 1 by each denominator, multiplying the quotient by the corresponding numerator.
⇒ ^{((5 x 14), (3 x 18), (1 x 63))}/₁₂₆
= ^{(70, 54, 63)}/₁₂₆

Step 3:

Go ahead and sort the numerators in our order of choice.
         ⇒ In ascending order:
         ⁵⁴/₁₂₆, ⁶³/₁₂₆, ⁷⁰/₁₂₆
         = ³/₇, ¹/₂, ⁵/₉

Create a new class file; Project, Add Class.
Call it SortFraction.vb.
Optionally, create a new module file; Project, Add Module.
Call it SortFractionModule.vb.
Type out the adjoining Visual Basic (VB.Net) codes for sorting fractions in ascending and descending orders.

Note: You can instead comment out the VB.Net code in the main module from the previous lesson or simply continue from where it stopped.

So!

Feel free to try out your own set of numerators and denominators for fractional sorting.

VB.Net code for SortFraction Class File

Public Class SortFraction
    Inherits AddFraction

    Dim final_numerators() As Integer
    Dim final_denominators() As Integer
    Dim copy_numerators() As Integer
    Dim send_back As New Dictionary(Of String, Integer())

    Private Sub takeOff()
        ReDim final_numerators(numerators.Count - 1)
        ReDim final_denominators(denominators.Count - 1)
        ReDim copy_numerators(numerators.Count - 1)

        ' STEPS 1, 2:
        canonizeFraction()

        For index = 0 To new_numerators.Count - 1
            copy_numerators(index) = new_numerators(index)
        Next
    End Sub

    Private Sub Land()
        ' map sorted (transformed) fractions To the original ones
        Dim position As Integer
        For index = 0 To copy_numerators.Count - 1
            ' get index using list value
            position = Array.IndexOf(new_numerators, copy_numerators(index))
            final_numerators(index) = numerators(position)
            final_denominators(index) = denominators(position)
        Next index

        send_back.Add("numerators", final_numerators)
        send_back.Add("denominators", final_denominators)
    End Sub

    ' Returns a dictionary Of the New fraction
    Public Function sortAscending() As Dictionary(Of String, Integer())
        takeOff()

        ' STEP 3:
        ' sort ascending
        Array.Sort(copy_numerators)

        Land()
        Return send_back
    End Function

    ' Returns a dictionary Of the New fraction
    Public Function sortDescending() As Dictionary(Of String, Integer())
        takeOff()

        ' STEP 3:
        ' sort descending
        Array.Sort(copy_numerators)
        Array.Reverse(copy_numerators)

        Land()
        Return send_back
    End Function

End Class

Main Module

Module Algebra_SortFraction

    Sub Main()
        ''
        ' Sorting fractions
        ''
        Dim numerators = {9, 3, 5, 7}
        Dim denominators = {2, 4, 12, 18}
        Dim fractions As New Dictionary(Of String, Integer())
        fractions.Add("numerators", numerators)
        fractions.Add("denominators", denominators)

        Console.WriteLine("    Sorting in ascending order the fractions:" & vbCrLf)
        ' Print as fraction
        For Each numerator In fractions.Item("numerators")
            Console.Write(String.Format("{0,13}", numerator))
        Next
        Console.Write(Environment.NewLine & String.Format("{0,12}", " "))
        For wasted = 0 To numerators.Count - 2
            Console.Write(String.Format("{0}", "-   ,        "))
        Next
        Console.WriteLine(String.Format("{0,1}", "-"))
        For Each denominator In fractions.Item("denominators")
            Console.Write(String.Format("{0,13}", denominator))
        Next
        Console.WriteLine("")

        ' use the SortFraction Class
        Dim sort_fract As New SortFraction
        sort_fract._init_(fractions)
        fractions = sort_fract.sortAscending()

        Console.WriteLine(Environment.NewLine)

        ' Print as fraction
        For Each numerator In fractions.Item("numerators")
            Console.Write(String.Format("{0,13}", numerator))
        Next
        Console.Write(Environment.NewLine & String.Format("{0,12}", "Answer  =   "))
        For wasted = 0 To numerators.Count - 2
            Console.Write(String.Format("{0}", "-   ,        "))
        Next
        Console.WriteLine(String.Format("{0,1}", "-"))
        For Each denominator In fractions.Item("denominators")
            Console.Write(String.Format("{0,13}", denominator))
        Next

    End Sub

End Module

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