Parquet floor’s finish getting damaged on shifting piano a fraction (7)

I believe the answer is:

quarter

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'fraction' is the definition.
(quartering is a kind of fractioning)

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for quarter that I've seen before include "A fourth - city district" , "Clemency" , "Area of town; mercy" , "Town district" , "Mercy; fraction" .)

I've seen this clue in The Times.

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