Stemfractions This article describes how a fraction is written as the sum of stem fractions. A stem fraction is a fraction that has 1 as numerator. A (Windows) program is added that accomplishes the task. Click on the download (lightning) icon at the top of this page. There is no installation procedure, simply copy the program to a folder of choice. In ancient Egypt people did not know fractions like we do. Instead, stemfractions were used. However there were some exceptions: 2 3 and 3 4 , using special symbols. So 2 3 was called “the two parts”. The addition to 1 is “the third part”. Each fraction may be written as the sum of different stemfractions. 8 11  =  1 2  +  1 5  +  1 37  +  1 4070 But this result is not unique: 2 19  =  1 10  +  1 190 , but also 2 19  =  1 11  +  1 70  +  1 14630 However, if we subtract the biggest possible stemfraction, the split up is unique. This is the procedure for stemfraction splitting. Take 5 11 . Because 2 <  11 5  < 3 we have 1 3  <  5 11  <  1 2 So 1 3 is the biggest stemfraction that is smaller than 5 11 . Decrease 5 11 by 1 3 This yields 5 11  −  1 3  =  4 33 . Because 8 <  33 4  < 9 we get 1 9  <  4 33  <  1 8 . So 1 9 the biggest stemfraction smaller than 4 33 . Decrease 4 33 by 1 9 . This yields 4 33  −  1 9  =  1 99 . And we found 5 11  =  1 3  +  1 9  +  1 99 . The same procedure is used over and over. In this proces, the denominator may grow very large. In the program, the denominator size may be 19 digits long, otherwise a "denominator overflow" is reported. Fractions that produce an overflow are: 44/53 , 5/61 , 60/67.... The biggest -non overflow- result is the splitup of 182/193 Interested in the program? [HERE ] is the complete Delphi-7 project.