1 1/8 inches + 5 27/32 inches + 7 3/16 inches

1/8 = 4/32
3/16 = 6/32
4 + 6 + 27 = 37
37/32 = 1 5/32
1 + 5 + 7 + 1 = 14
Total: 14 5/32

I wouldn't call it chaos, it's a straightforward algorithm:

1. Identify the largest denominator
2. Multiply each other fraction by [largest denominator divided by current fraction's denominator] (e.g. 32/8 = 4, so 1/8 * 4/4 = 4/32)
3. Determine the sum of every numerator
4. Divide and simplify the number if necessary
5. Determine the sum of the integers, including any integers added in the previous step

This works for every measurement because the denominator is always a power of 2.

With that said I absolutely prefer metric.