Fractions, singular or plural?

A question for native speakers of English:
Which one is correct?
1. the 2/3 of the tube has contracted
2. the 2/3 of the tube have contracted

i would say 2/3 of the tube have contracted because it's two 1/3. If it was 1/3 : 1/3 of the tube has contracted.

I would say it can go either way: Understood as singular in regards to a measure; and plural when discussing the items as individual portions/pieces of the whole (eg. the two thirds [i.e. "third parts"] of the tube have contracted). I personally prefer viewing it as singular: the 2/3 [portion] of the tube has contracted...

With words that indicate portions—percent, fraction, part, majority, some, all, none, remainder, and so forth —look at the noun in your of phrase (object of the preposition) to determine whether to use a singular or plural verb. If the object of the preposition is singular, use a singular verb. If the object of the preposition is plural, use a plural verb.

Examples:

One-third of the city is unemployed.

One-third of the people are unemployed.

<<Examples:

One-third of the city is unemployed.

One-third of the people are unemployed. >>

This then would qualify as exception to the rule, yes?
--to the rule of not referring to the noun/nouns in the prepositional phrase, but I like it. It kinda makes sense...

That looks like the rule to me.

Let's see...

Three-fifths of the world is poor. (singular)
Two-thirds of the garden was uprooted.(singular)
A quarter of the boxes were disposed of. (plural)
Half of the buildings were destroyed (plural)
Half of the building was destroyed. (singular)

Both sound odd to me using "the".