Expressing A Repeating Decimal Number As A Fraction

Hi there!
Recently, someone asked me to come up with a small app that could simply add 2 fractions (with sums being inferior to 1) and display the result as a fraction as well (not in decimal form).
I thought this was going to be easy at first but I got stumped early on with this. Actually adding the 2 fractions is nothing but getting the result as a fraction is another matter.
For the most part I got it working using the function below which works well on decimal numbers without long repeating patterns, but on a fractions such as 1/7 with a decimal equivalent of 0.142857142857142857142857142857143 the function gracefully fails.
I guess what I need is a formula (preferably in VB) that would reduce those long repeating patterns within the numerator and getting the denominator value right before calling the function.

Again, as this sample all I'm trying to achieve is to come up with and display the 17/21 in my MessageBox:
1 2 17
-+-=-
7 3 21
Math was never my forte in school and I wish now that I would have paid a little more attention during my math class ;)
Anyway thanks in advance!

Here's what I got so far:

VB Code:

Private Sub Command1_Click()
Dim lngNumerator As Long, lngDenominator As Long, lngCommonFactor As Long
 
lngNumerator = 5 
lngDenominator = 10
 
If GetCommonFactor(lngNumerator, lngDenominator, lngCommonFactor) Then
     MsgBox lngNumerator & " / " & lngDenominator
End If
 
End Sub
 
Public Function GetCommonFactor(Numerator As Long, Denominator As Long, CommonFactor As Long) As Boolean
    Dim lngIdx As Long
    
    CommonFactor = 1
    
    For lngIdx = Numerator To 2 Step -1
        If Numerator Mod lngIdx = 0 Then
            If Denominator Mod lngIdx = 0 Then
                CommonFactor = lngIdx
                Numerator = Numerator / CommonFactor
                Denominator = Denominator / CommonFactor
                GetCommonFactor = True
                Exit For
            End If
        End If
    Next
 
End Function

a/b + c/d = e/f
e=a*d + c*b
f= b*d
but you would rather do away with common factors so h/i where
h=e/g
i=f/g
where g=gcd(e,f)

some pseudo for gcd(a,b):
d=b
r=a mod b
while (r>0){
n=d
d=r
r=n mod d
}
return d

Quote:

---

Originally posted by kedaman
a/b + c/d = e/f
e=a*d + c*b
f= b*d
but you would rather do away with common factors so h/i where
h=e/g
i=f/g
where g=gcd(e,f)

some pseudo for gcd(a,b):
d=b
r=a mod b
while (r>0){
n=d
d=r
r=n mod d
}
return d

---

Thanks kedaman going with what you gave me I used it with a function I also found on this forum.
I'm using it in the way as in the sample and seems to work great so far.
Thanks for the help. :)

VB Code:

Private Sub Command1_Click()
Dim lngNumerator As Integer, lngDenominator As Integer 
Dim a As Long, b As Long, c As Long, d As Long
a = 1
b = 6
c = 2
d = 7
 
lngNumerator = a * d + c * b
lngDenominator = b * d
 
MsgBox Fraction(lngNumerator, lngDenominator)
 
End Sub
 
Function Fraction(Numerator As Integer, Denominator As Integer) As String
Dim i As Integer
 
For i = CInt(IIf(Denominator >= Numerator, Denominator, Numerator) / 2) To 1 Step -1
    If Numerator Mod i = 0 And Denominator Mod i = 0 Then
        Fraction = (Numerator / i) & "/" & (Denominator / i)
        Exit For
    End If
Next:
 
End Function

In case it may be useful to you, please notice the following example.
If you have a number with a repeating pattern, say, x = 4.820182018201... you can derive a fraction representing it in this fashion.

If the repeating pattern has n figures, then multiply x by 10ⁿ. Here:

10⁴x = 10000x = 48201.82018201...
Substract:
10000x - x = 48197
9999x = 48201

So that x = 48197 / 9999