Do 1/3 and 2/6 name the same part of one whole?

Yes, if you were to divide 1/3 you would get 1/6. 
Now since you divided 1/3 into two parts to get 1/6, now if you would like to get 1/3 out then you must double 1/6 into 2/6 which would be equal to 1/3

I hope this made sense, I know you wanted a more simple yes or no but i believe if you explain to someone how they got the answer than you wouldn't need help next time. xx

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