Say, for example, I'd like to express that I have four complete six-slice pizzas and one with five out of six slices. Would I say "I have 29/6 pizzas"? "4 and 5/6 of a pizza" for mixed fractions?
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Generally one uses only a fraction when expressing a ratio: 1/6 of a pizza, 1/3 of a pizza; it seems reasonable to extend this to improper fractions because you are comparing the amount of pizza you have to a "standard" size. However, using an improper fraction is discouraged in general and therefore would be somewhat jarring to use "naked", so I'd be inclined to write it out in some fashion: "I have twenty-nine sixths of a pizza" (longest, but best) or "I have 29 6ths of a pizza" (shortest and rather poor-looking, and can still easily cause a pause for interpretation) over "I have 29/6 of a pizza" (forces the reader to stop and figure out what you mean, which is just bad).
If you eliminate the improper fraction, it's no longer a ratio and therefore is best expressed as a plural: "I have 4 and 5/6 pizzas."