Distinct Digit Fraction Sums: Revisited

On the page Distinct Digit Fraction Sums, we presented an activity wherein fractions formed by using various combinations of distinct digits had sums that were always 1. To refresh your memory, here is the introductory example again:

                      1     6
                     --- + ---  =  1
                      4     8

On this page, we intend to expand on that concept in a simple and natural way. Now we are allowing the sum of our fractions to be any number from 2 to 9.

Observe:

  2     5             2     8           4     7
 --- + ---  =  2     --- + --- = 3     --- + --- = 4
  6     3             6     3           8     2

See? It’s not so difficult now, or is it?

We challenge you to find more such examples and submit them to WTM. We’ll post your creations in the charts below.

Please note: that in order for your solution to even be considered for posting, you must write “DDFS” in the subject line of your email; otherwise we will merely ignore it and delete it. Thank you.

trottermath@gmail.com or ttrotter3@yahoo.com


# Solution Name Date
1 2/6 + 5/3 = 2 WTM 9/27/03
2 2/6 + 8/3 = 3 WTM 9/27/03
3 4/8 + 7/2 = 4 WTM 9/27/03
4 4/8 + 3/2 = 2 Nicholas Kruckenberg 10/1/03
5 6/8 + 5/4 = 2 Nicholas Kruckenberg 10/1/03
6 5/2 + 6/4 = 4 Nicholas Kruckenberg 10/1/03
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