Terumot and ma'aserot on heter mechirah fruit
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I saw that when ma'aser was taken from fruit such as avocado and citruses, it was taken without a blessing. Why is this so? Is it because according to both Ashkenazim and Sephardim the fruit began to form during the shemitah year, exempting them from ma'aser?
From your question, I understand that the fruit you saw was fruit of heter mechirah. For such fruit, since Jews are the ones who harvest them, there are opinions obligating them in terumot and ma'aserot (Rambam, Terumot Vema'aserot 1:11). However, if non-Jews performed the harvest, there is no need to separate terumot or ma'aserot. For public systems (groceries and the like), since it is not certain who performed the harvest, terumot and ma'aserot should be separated without a blessing.