Answer:
   
   Both Talmud Bavli and Talmud Yerushalmi mostly ignore the Tosefta. The
   Babylonian and the Jerusalem gemaras to the Mishna usually proceed
   independently of material contained in the Tosefta.
   
   The only explicit quotation of the Tosefta in the Talmuds is in
   Masekhot Yoma, 70A. However, many baraitot (authoritative legal
   material that was not redacted as part of the Mishna) quoted in the
   gemara correspond very closely to teachings in the Tosefta, agreeing
   in substance but differing in wording.
   
   Many rabbis in the gemara discuss a problem that seems already to have
   been solved in the Tosefta. The question is, are they unfamiliar with
   the Tosefta, or was the Tosefta considered non-authoritative, or were
   they simply unable to recall the Tosefta?
   
   The complete Hebrew text of the Tosefta is appended to the backs of
   Hebrew versions of the Talmud. An English translation by Jacob Neusner
   is available. There are also translations of complete Tosefta chapters
   available in different scholarly works.

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