I think I was a little unclear above. Let me try this again: The article tries to make a statement about the superiority of base-12 by pointing out that you can divide 12 by 2, 3 and 4 and get integers as result. Then it tries to show how bad base-10 is by dividing ONE (not ten) by 2, 3 and 4. And while that would be a decent argument had the author used ten (only 10 / 2 = 5, the others are still rationals), I think it's WTF worthy to use one instead here.
I'm unconvinced that a base-12 numbering system is particularly better than base-10, but I can explain what the author was trying to say about fractions and decimals. In base-12, one half would be represented as 0.6, one third as 0.4, and one quarter as 0.3. In base-10, the number immediately following the decimal mark is the tenths place, so one half is 0.5, or five tenths; in base-12, that first digit after the decimal mark would be the twelfths place, so one half would be 0.6, for six twelfths.