"Freshman sums" are the results of an arithmetical process (also called "mediant averaging" ) popularized by Ervin Wilson, who also coined the term.
The freshman sum of two fractions is the sum of their numerators divided by the sum of their denominators.
For example, the freshman sum of 5/4 and 4/3 is 9/7. The operation is briefly described also in Lloyd and Boyle (1978).
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