BrainDen.com - Brain Teasers
• 0

# An interesting property of division.

## Question

Suppose we have the fraction 19/95. To reduce this fraction simple cancel out the nines. 19/95 = 1/5 The cool thing is it doesn't matter how many nines we have on top we can always just cross them out and properly reduce the fraction (assuming that the 1 is preceeding the numerator and a 5 is following the denominator)

for example:

199/995 = 1/5

19999/99995 =1/5

and so on...

Same accounts for
16/64=1/4=1666...6/666...64

also 26/65 = 2/5, 266...6/666...65 = 2/5,

and 49/98 = 4/8, and 499...9/999...8 = 4/8.

and 16/64, 19/95, 26/65, 49/98 are all cases that satisfy a such property.

And It is easy to prove! Have at it.

## 5 answers to this question

• 0

What about 29/97, 46/68, 29/95 and others? This property does not apply to them, I think. (You made an interesting discovery, though)

Edited by Kikacat123

##### Share on other sites
• 0

I never meant to suggest the property applies to every combination. Just the ones I listed.

##### Share on other sites
• 0

Dim x As Single
Dim z As Single
Dim y As Single
For x = 1 To 1000
For z = 1 To 1000
If 10 * x / z <> 1 Then
y = 9 * x / (10 * x / z - 1)
If y = CLng(y) And y > 0 And (y <> x Or y <> z) Then
If CSng(x & y) / CSng(y & z) = x / z Then
Debug.Print x & ", " & z & ", " & y & ": " & x & y & "/" & y & z & "=" & x & "/" & z
End If
End If
End If
Next z
Next x
End Sub

##### Share on other sites
• 0

I can only read HTML. What code are you using? Or do you mean code as in a cipher?

##### Share on other sites
• 0

I can only read HTML. What code are you using? Or do you mean code as in a cipher?

visual basic

## Create an account

Register a new account