How to have excel add/subtract fractions to satisfy given relationships

I have a table (A14:I21) with data given in measurements of feet (A1=88.5542'). The values in that table are based on simple math relationships that I set. I then converted these values to feet-inches (see table K14:AA21) by separating the whole number and decimal portions (0.5542'*12 = 6.6504"). The decimal portion (6.6504") is formatted to show as a fraction to 1/16" accuracy (except for values in the Q column).

I want excel to instead provide the fractions so that they STILL satisfy the math relationships I set. Since the fractions are rounded, it's not always adding up as I would like. In other words, I want excel to now treat the fractions as they are formatted, not their decimal values. For instance, C+F+G should equal A. If you look at Beam 6, however, this does not hold true.

EDIT: I've attached the file.

Any suggestions? Thanks in advance!