Calculate Fractions in VB.NET

Scope

In this brief article we'll see a simple method to convert the decimal part of a number into its fractional representation, developing a reusable class to do it. To that end, we'll use Visual Basic .NET.

Calculate and simplify a fraction

To calculate a fraction, we must separate a number's integral part from the decimal one, to work on the latter to express it in terms of numerator and denominator. Let's take for example the number 12.65. We will first express it as 12 + 0.65, proceeding then in writing our decimal part as the most large non-simplified fraction. Since we have two decimals after the dot, the larger denominator we need is 100. So, we can express our 0.65 as 65/100. Then, using the common rules based on finding the Greatest Common Divisor (GDC), we can simplify our fraction, down to 13/20.

Finding the Greatest Common Divisor

The following is an easy snippet of code to help determine the GDC between two numbers:

Private Function gcd(ByVal n1 As Integer, ByVal n2 As Integer) As Long
      Dim minimum As Long
      If n1 < n2 Then
          minimum = n1
      Else
          minimum = n2
      End If
      For i As Long = minimum To 1 Step -1
          If n1 Mod i = 0 And n2 Mod i = 0 Then
              Return i
          End If
      Next
End Function

Calculate a fraction

Here follows the routine that will calculate our fraction. It needs a decimal-type input parameter (as the 12.65 used previously).

Public Function Calculate(value As Decimal) As String
        Dim intPart As Long = Math.Truncate(value)
        Dim numerator As Long = CType((value - intPart).ToString.Substring(2), Long)
        Dim denominator As Long = CType("1" & StrDup(numerator.ToString.Length, "0"), Long)

        Dim _gcd As Long = gcd(numerator, denominator)
        Dim nDiv As Long = _gcd

        While nDiv > 1

            If numerator Mod nDiv = 0 And denominator Mod nDiv = 0 Then
                numerator /= nDiv
                denominator /= nDiv
                nDiv = _gcd
            Else
                nDiv -= 1
            End If

        End While

        Dim retVal As String = ""
        If intPart > 0 Then retVal = intPart.ToString & " + ("
        retVal &= numerator.ToString + " / " + denominator.ToString
        If intPart > 0 Then retVal &= ")"
        Return retVal
End Function

The function will save the integral part of the number for later use, then proceed to calculate the maximum denominator, by adding a number of zeros to equal the number of decimal places. A call to our previously written GCD routine will compute the gretest Common Divisor between our numerator and denominator, entering a loop for dividing the numerator and denominator to determine their common divisors, until no common divisor is available.

Finally, having determined the simplyfied numerator and denominator, the routine will produce their string representation, joining the integral part. So, for our previous example of value = 12.65, the output will be: 12 + (13/20).

As the reader can note, in case no integral part is present, the fraction will be expressed without parenthesis.

Fraction class

The complete source for a reusable class can be the following:

Public Class Fraction

    Dim _value As Decimal
    Dim _fraction As String

    Public ReadOnly Property Value As String
        Get
            Return _fraction
        End Get
    End Property

    Public Property Number As Decimal
        Get
            Return _value
        End Get
        Set(value As Decimal)
            _value = value
            _fraction = Calculate(_value)
        End Set
    End Property

    Public Sub New(value As Decimal)
        _value = value
        _fraction = Calculate(_value)
    End Sub

    Public Sub New()
        _value = 0
        _fraction = 0
    End Sub

    Private Function gcd(ByVal n1 As Integer, ByVal n2 As Integer) As Long
        Dim minimum As Long
        If n1 < n2 Then
            minimum = n1
        Else
            minimum = n2
        End If

        For i As Long = minimum To 1 Step -1
            If n1 Mod i = 0 And n2 Mod i = 0 Then
                Return i
            End If
        Next
    End Function

    Public Function Calculate(value As Decimal) As String
        Dim intPart As Long = Math.Truncate(value)
        Dim numerator As Long = CType((value - intPart).ToString.Substring(2), Long)
        Dim denominator As Long = CType("1" & StrDup(numerator.ToString.Length, "0"), Long)

        Dim _gcd As Long = gcd(numerator, denominator)
        Dim nDiv As Long = _gcd

        While nDiv > 1

            If numerator Mod nDiv = 0 And denominator Mod nDiv = 0 Then
                numerator /= nDiv
                denominator /= nDiv
                nDiv = _gcd
            Else
                nDiv -= 1
            End If

        End While

        Dim retVal As String = ""
        If intPart > 0 Then retVal = intPart.ToString & " + ("
        retVal &= numerator.ToString + " / " + denominator.ToString
        If intPart > 0 Then retVal &= ")"
        Return retVal
    End Function

End Class

In the source code that comes with that article, I've implemented a simple Windows Forms form, with a TextBox and some Labels, to show how the previous code works.



The code behind will be as simple as this:

Public Class Form1

    Dim f As New Fraction

    Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
        f.Number = CType(TextBox1.Text, Decimal)
        Label3.Text = f.Value
    End Sub
End Class

When the Button is clicked, the Number property of our Fraction class will be initialized with a cast towards Decimal type of what is contained in TextBox1.

Next, the property Value (that will contain our fraction string) will be shown in Label3.

Source Code

The sample code for this article can be downloaded from this link.