How to Reduce Fractions to Lowest Term
Reducing fractions to their lowest terms is all about removing every common factor between the numerator and the denominator.
Reducing Fractions to Lowest Term Code in VB.Net
Let's see this using 12/16.
A common factor to 12 and 16 is 2;
so removing 2 from 12/16 yields
6/8.
Again, 2 is common to both 6 and 8;
removing it yields 3/4.
We stop when nothing else is common (1 does not count).
Create a new class file; Project, Add Class.
Call it LowestTerm.vb.
Optionally, create a new module file; Project, Add Module.
Call it LowestTermModule.vb.
Type out the adjoining Visual Basic (VB.Net) codes for reducing fractions to their lowest terms.
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 numerator and denominator.
VB.Net code for LowestTerm Class File
Public Class LowestTerm
Dim numerator As Integer
Dim denominator As Integer
Dim trial_factor As Integer
' A constructor
Public Sub _init_(fraction As Dictionary(Of String, Integer))
numerator = fraction.Item("numerator")
denominator = fraction.Item("denominator")
' Set trial_factor To the smaller value between numerator And denominator
If numerator < denominator Then
trial_factor = numerator
Else
trial_factor = denominator
End If
End Sub
' Returns a dictionary Of the New numerator And denominator
Public Function reduceFraction() As Dictionary(Of String, Integer)
' We are counting down To test For mutual factors
Do While trial_factor > 1
' Do we have a factor
If numerator Mod trial_factor = 0 Then
' Is this factor mutual?
If denominator Mod trial_factor = 0 Then
' where we have a mutual factor
numerator = CInt(numerator / trial_factor)
denominator = CInt(denominator / trial_factor)
Continue Do
End If
End If
trial_factor -= 1
Loop
Dim send_back As New Dictionary(Of String, Integer)
send_back.Add("numerator", numerator)
send_back.Add("denominator", denominator)
Return send_back
End Function
End Class
Dim numerator As Integer
Dim denominator As Integer
Dim trial_factor As Integer
' A constructor
Public Sub _init_(fraction As Dictionary(Of String, Integer))
numerator = fraction.Item("numerator")
denominator = fraction.Item("denominator")
' Set trial_factor To the smaller value between numerator And denominator
If numerator < denominator Then
trial_factor = numerator
Else
trial_factor = denominator
End If
End Sub
' Returns a dictionary Of the New numerator And denominator
Public Function reduceFraction() As Dictionary(Of String, Integer)
' We are counting down To test For mutual factors
Do While trial_factor > 1
' Do we have a factor
If numerator Mod trial_factor = 0 Then
' Is this factor mutual?
If denominator Mod trial_factor = 0 Then
' where we have a mutual factor
numerator = CInt(numerator / trial_factor)
denominator = CInt(denominator / trial_factor)
Continue Do
End If
End If
trial_factor -= 1
Loop
Dim send_back As New Dictionary(Of String, Integer)
send_back.Add("numerator", numerator)
send_back.Add("denominator", denominator)
Return send_back
End Function
End Class
Main Module
Module Algebra_LowestTerm
Sub Main()
''
' Reduce fractions To Lowest Term
''
Dim fraction As New Dictionary(Of String, Integer)
fraction.Add("numerator", 16)
fraction.Add("denominator", 640)
Console.WriteLine(" To reduce to lowest term, simplifying:")
' Print as fraction
Console.WriteLine(String.Format("{0,45}", fraction.Item("numerator")))
Console.WriteLine(String.Format("{0,45}", "-"))
Console.WriteLine(String.Format("{0,45}", fraction.Item("denominator")))
' use the LowestTerm Class
Dim low_term As New LowestTerm
low_term._init_(fraction)
fraction = low_term.reduceFraction()
Console.WriteLine(Environment.NewLine)
Console.WriteLine(String.Format("{0,46}", fraction.Item("numerator")))
Console.WriteLine(String.Format("{0,46}", "Answer = -"))
Console.WriteLine(String.Format("{0,46}", fraction.Item("denominator")))
End Sub
End Module
Sub Main()
''
' Reduce fractions To Lowest Term
''
Dim fraction As New Dictionary(Of String, Integer)
fraction.Add("numerator", 16)
fraction.Add("denominator", 640)
Console.WriteLine(" To reduce to lowest term, simplifying:")
' Print as fraction
Console.WriteLine(String.Format("{0,45}", fraction.Item("numerator")))
Console.WriteLine(String.Format("{0,45}", "-"))
Console.WriteLine(String.Format("{0,45}", fraction.Item("denominator")))
' use the LowestTerm Class
Dim low_term As New LowestTerm
low_term._init_(fraction)
fraction = low_term.reduceFraction()
Console.WriteLine(Environment.NewLine)
Console.WriteLine(String.Format("{0,46}", fraction.Item("numerator")))
Console.WriteLine(String.Format("{0,46}", "Answer = -"))
Console.WriteLine(String.Format("{0,46}", fraction.Item("denominator")))
End Sub
End Module