Reducing Fractions, the easy way. Or, 26/65 = 2/5
by Jonathan Wellons
Need a concrete example? Suppose I have 26/65. The 6's go away and we have 2/5. Check me on a calculator, 2/5 = 26/65 = 0.4.
Not convinced? Take 4784/7475. The 7's and 4's cancel and we get 48/75.
Another example picked at random: 6188/1820, here we can eliminate the 1 and an 8, to get it down to 68/20, which is a lot simpler. Or I'll take another one, say 4277/2730. Let's see, there's a 2 and 7, so we get 47/30. You might think this is some sort of trick, but Math really is this easy. Let's make up some more numbers to prove it: 138/1840, cancel the 1 and 8 and we get 3/40.
31 Comments
j 20060916 14:31:46 
I tried this with 32/35, and it doesn't work. I want my money back.

Jonathan Wellons 20060916 14:34:50 
Oh, good call. Fixed. With anything this easy, I get careless sometimes. 
Fred 20060916 15:02:51 
What about 23/38? 
Jon B 20060916 15:17:59 
In the case of numbers like 181/818 which 8 and 1 would be removed? is there a rule for removing always from the right or left or something? 
dave 20060916 15:27:00 
When I do 12/24, and remove the 2's, I get 1/4 (which is wrong). Is there some way to know it *isn't* going to work? 
Daniel 20060916 17:40:18 
This has to be a joke. 26/65 isn't xy/yz, it's x/y. xy/yz would be 2*6/6*5 which is reducible by eliminating the y in the numerator and denominator. According to your logic 22/23 reduces to 2/3, which it most certainly doesn't. 
Jonathan Wellons 20060916 17:43:28 
Thank you Daniel. You're right on.

Daniel 20060916 17:47:37 
Ah, so it was a test. Can I get a cookie? :) 
Jon B 20060917 07:34:08 
just maybe somebody has a little too much free time.

Larry 20060918 10:46:03 
Ah, yes. Deceptively simple. How easy it is to forget that in the example 26/65 the 6 in the numerator is in the "ones" position while the 6 in the denominator is in the "tens" position. I love these types of things... :) 
Jonathan Wellons 20060918 12:19:19 
Jon B,

Abed 20060918 18:14:48 
Oh boy, like we don't have enough crap on the net as it is! I just hope my boy doesn't google this while trying to do his homework! 
Jonathan Wellons 20060918 22:53:29 
I wouldn't worry Abed, I don't think anyone will use this without testing it first. 
Niels 20060919 05:11:09 
Cool! But don't tell my 16year old daughter. She has enough trouble the old way ;) 
Josh Peters 20060919 09:16:11 
This post would have made for a refreshing change of pace come April 1. 
Kurt Cagle 20060920 10:32:07 
This was the same method that the Indiana State Legislature used in 1880, legislating that pi was equivalent to 3 for all intents and purposes, and that as such 3 should be used. 
shixilun 20060920 12:53:50 
The four proper fractions with twodigit numerators and denominators are as follows:

Jonathan Wellons 20060920 13:05:41 
shixilun,

Hunter 20060927 10:45:43 
Very neat. 
Emily 20070104 14:50:02 
what is 26 out of 3 and 12 5 16 5 and 4out of 3 
20070215 14:35:01 
I've taken an 8th and 9th grade math test twice and failed. I know me and fractions and decimals have a fight every time. 
Denise 20070216 07:18:33 
How do you know what numbers to council out? 
Jonathan Wellons 20070216 11:05:08 
Dear Denise,

20070415 12:57:53 
U SUCK!!! i was looking for an easy answer and do u know wat u did? u just confused me more but thanx for trying (NOT) 
Jonathan Wellons 20070415 13:12:10 
Dear Anonymous,

j 20080130 17:53:34 
how dose 21/25 work? 
Jonathan Wellons 20080131 07:44:34 
Dear j,

hannah 20080311 11:53:40 
I hate fractions because I reducing them can be VERY HARD!

Jonathan Wellons 20080311 12:01:35 
Dear hannah,

Kit 20080720 07:04:03 
I can under stand how simple and easy it works out, like when I tried it with 14/45, I got 1/5. But what I don't understand is how you get33/49 to be 1/7, and 27/22 to be 9/1. It doesn't work out that simple. Is the trick you're talking about only dealing with numbers that have a common number in it? 
Jonathan Wellons 20080721 15:24:27 
Dear Kit,
