Calc to reduce fractions?

[mitchDig]

I was wondering if anyone would know of a calculation that could reduce fractions to whole numbers and fractions after a fraction has been multiplied. As an example... 1/3 x 5 = 1 2/3

Thank you for your help.

Mitch

[BobWeaver]

You can use this formula to convert a decimal number (from field 'Num') to the simplest whole number and fraction:

Let ( [precision=100;

p0=Abs(Num);n0=Mod(p0;1);

p1=1/Case(n0 ;n0;1);n1=Mod(p1;1);

p2=1/Case(n1 and (p1/n1<precision);n1;1);n2=Mod(p2;1);

p3=1/Case(n2 and (p1*p2/n2<precision);n2;1);n3=Mod(p3;1);

p4=1/Case(n3 and (p1*p2*p3/n3<precision);n3;1);n4=Mod(p4;1);

p5=1/Case(n4 and (p1*p2*p3*p4/n4<precision);n4;1);n5=Mod(p5;1);

p6=1/Case(n5 and (p1*p2*p3*p4*p5/n5<precision);n5;1);n6=Mod(p6;1);

p7=1/Case(n6 and (p1*p2*p3*p4*p5*p6/n6<precision);n6;1);

d=Round(p1*p2*p3*p4*p5*p6*P7;0); n=Round(p0*d;0);nf=Round(n0*d;0);

sgn=Choose(Sign(Num)+1;"-";"";"");

whole=Div(n;d);

fraction=Case(d=1;"";nf;nf&"/"&d;"")];

Trim(sgn&Case(not p0;0;whole;whole&" ";"")&fraction))

With 'precision' set to 100 it will find the simplest fraction that is accurate to within 1/100. Changing that value will change the required precision of the result accordingly.

< edited: corrected a problem when the input value was zero. >

[mitchDig]

Thank you so much for this great calculation, but I'm not sure how to use it. Currently I'm trying to use it with three fields called "Fraction", "FractionMultiplier" and "FractionResult". Would I need more than these three fields? How would this be written?

Thank you so much for your help!

Mitch

[comment]

You're not saying much about the rules of such multiplication. Based on your single example, I'm guessing you want something like this:

FractionResult (result is text) =

Let ( [

pos = Position ( Fraction ; "/" ; 1 ; 1 ) ;

num = Left ( Fraction ; pos - 1 ) ;

denom = Right ( Fraction ; length ( Fraction ) - pos ) ;

integer = Div ( num * FractionMultiplier ; denom ) ;

num1 = Mod ( num * FractionMultiplier ; denom )

] ;

Case ( integer ; integer & " " ) &

Case ( num1 ; num1 & "/" & denom )

)

[mitchDig]

Here's my scenario...

The user would type a fraction in the first field called "Fraction"(The user is instructed to enter fractions only, but it would be nice if the calculation could handle whole numbers and fraction just in case it was entered incorrectly), then the user would enter the multiplier in the "FractionMultiplier" field and the "FractionResult" field would disply the multiplied fraction. The multiplied fraction would be reduced to lowest terms in whole numbers and fractions. Does a script/button need to be created to trigger the calculation?

Thank you,

Mitch

[BobWeaver]

See attached file

FracCalc.fp7.zip

[comment]

It really depends on what KIND of fractions you expect as input.

Basically, there are two ways to approach this: either you multiply the numerator only, or you convert the fraction to a decimal representation first.

In the first case, the problem is to reduce the result: e.g. 1/4 * 2 = 2/4, and this needs be reduced to 1/2. This requires finding the greatest common divisor, and IIRC this is a recursive calc, so you need either a script or a custom function.

In the second case, 1/3 * 2 becomes 0.3333333 * 2 = .66666666, and it is difficult to get a computer to realize that this is close enough to 2/3.

There is a nice shortcut for fractions with multiples of 2 in the denominator (such as used for measurements in inches)- see http://www.onegasoft.com/tools/commonfractions/index.shtml

[comment]

For fractions of relatively small integers.

[BobWeaver]

You can increase the precision as necessary, but as you stated earlier, if you have a decimal result of .666666 should the result be the inaccurate fraction 2/3 or the exact fraction 666666/1000000?

I assume the user would want 2/3 so I made the calculation find the most accurate representation with a denominator of 128 or smaller. But, it's a simple change to the precision value to get larger denominators.

[BobWeaver]

Here's another version where you can play around with the accuracy of the result.

FracCalc.fp7.zip

[mitchDig]

Thank you Bob!

This is an excellent solution! I encourage anyone who's interested in seeing how this works to download it.

Thanks again,

Mitch

[comment]

if you have a decimal result of .666666 should the result be the inaccurate fraction 2/3 or the exact fraction 666666/1000000?

I don't know. That's why I pointed out the difficulties. If it's acceptable to have some limits placed upon a solution, that's fine. But I believe the limits should be stated.

[BobWeaver]

In my first post where I gave the continued fraction formula, I did explain about setting the value of the precision variable to the desired maximum allowed denominator.

I should also explain that it is possible for a decimal number to expand into more than the 7 terms given in the formula, in which case the result would not be exact. However that situation would result in a very large denominator, and the user would have to decide if the resulting approximation to a smaller denominator fraction is acceptable.

[comment]

I believe we are of the same mind on this. I didn't connect your earlier warning with the later attachment - as will happen with "Jump to first unread post".

[BobWeaver]

Ah well, I've certainly been guilty of that more times than I care to remember.

I have discovered that while the continued fraction algorithm, that this calc is based on, will find the simplest fraction in theory, in the real world (i.e., limited precision of computer arithmetic), the roundoff errors accumulate surprisingly fast in this particular formula. So, accumulated roundoff error in the formula is at least as significant as the accuracy of the original input number. But, I think this formula should be okay for fractions with up to 4 digit denominators.

[comment]

Well, the poster is happy, so we can leave that until next time. Perhaps you should try using the SetPrecision() function.

[BobWeaver]

Wow, I never noticed that function before. Yes, that makes a considerable difference.

[McNite]

:

Hi, I took the time to join after finding these posts through a search. I joined just so I could thank you for these posts. I have been trying to get FM to work for recipes since version 2.1. I am not advanced enough to have figured this cacl out for myself anyway but I have tried to play with every version from 2.1 to 5.5 and could not get

1 1/3 mulitplied by double (2) to look like 2 2/3.

You guys are the GREATEST. thanks. However, because of you I now have no excuse not to enter 3,000 recipes that are building bigger every day.