Bereishis 22:6 indicates that Avraham placed the wood for the sacrifice on Yitzchak, took something to start the fire, and the מַּאֲכֶלֶת which Rashi translates as knife.
However, in the next pasuk Yitzchak makes note of the wood and kindling when he inquires הִנֵּה הָאֵשׁ וְהָעֵצִים, וְאַיֵּה הַשֶּׂה, לְעֹלָה - "Here are the fire and the wood, but where is the lamb for the burnt offering?", but makes no mention of the knife! Why not?
The sefer שער בת רבים brings from the Alshich and the Abarbanel that the reason that Yitzchok only asked about the wood and the fire was because he was asking a very clever question which would force Avraham to tell him the truth:
He asked: Behold, you brought fire and wood from home even though these are things which you can get anywhere, even in the wilderness - wood from one of the bushes, and fire by hitting two stones together - but where is the lamb for a burnt offering? You can't find this in the wilderness, so why did you not bring it from home?
But he did not ask about the knife because that is something which is not found in the wilderness and therefore it was understandable why he brought it with him from home.
Therefore, Avraham had to answer: "Hashem will provide for Himself the lamb", miraculously, and if not "for a burnt offering, my son" - you will be an unblemished offering to Hashem. And from this answer Yitzchok knew that Hashem had chosen him to be a burnt offering, yet nevertheless, "and they both went together" happily and with a complete heart - this one to slaughter and this one to be slaughtered.
I would offer my own answer that from when the things were invented until very recently, it was completely normal to carry a knife as an all purpose tool and/or for eating (as implied by מאכלת). It might be appropriate to ask why the Torah even mentions that Avraham took a knife with him.
