What would you get if you continued this sequence of fraction sums?
1/2 + 2/1 =
2/3 + 3/2 =
3/4 + 4/3 =
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
There are many solutions to this problem. Here is one correct solution received from a student at West Flegg Middle School in Norfolk.
Hence, they share 76 pounds between them.
It also works if you share 80 pounds between them, starting with 42 for Dee and 38 for Dum. Ewan, from King Edward VII School in Sheffield, used algebra to make sure he found all the possible solutions.