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Yes, two thirds is more than a half but not by a lot.
Since 500 mL is half of a litre, 800 mL is more than half.
If I ask you if you want a half a pie or a third of a pie, I hope you will grab the half.
This is possible when you can have values of less than zero. If I have $100 of wealth, a 150% decrease in my wealth would mean I am now $50 in debt.
One half is bigger then two fifths.