Yes, you are correct that "fractional share" is not a purchase method. First, if you report this as a sale listed on a 1099-B, this question doesn't appear. You must have selected "Other" for your form type.
You can select the purchase method for the stock that caused you to get the fractional share.
For example, you purchased stock A and then it was acquired by company B. You received shares in company B and a fractional share was sold. In that case you would say "I purchased it" because you purchased stock A.
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