How do we write a fraction of numerator as the sum of three unit fractions ?
bogus
Are you talking about "Egyptian Fractions" ?
which says, that every proper fraction can be expressed as a sum of
fractions with a numerator of 1.
e.g. 17/22 = 1/2 + 1/4 +1/44
e.g 4/5 = 1/2 + 1/5 + 1/10
Here is a good treatment of the subject:
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html#section6.1.1
I found a simple applet that will even find them for you
http://www.calcul.com/show/calculator/egyptian-fraction?n=7&d=12
To write a fraction as the sum of three unit fractions, you need to follow the steps below:
1. Start with a fraction with the desired numerator, let's call it "a", and an arbitrary denominator, denoted by "b": a/b.
2. Express "a" as a sum of three distinct positive integers, let's call them "x," "y," and "z": a = x + y + z.
3. Rewrite the fraction as follows: a/b = (x/b) + (y/b) + (z/b).
By following these steps, you can express any fraction with a given numerator as the sum of three unit fractions.