"The back of his pants is/are..."

In English, when there are fractional expressions such as a half of, a part of, a percentage of, a majority of, a third of, etc., the verb agreement depends on the plurality of the nouns that follow them. For example:

50% (A half, A third, A part, etc.) of the university was destroyed by fire. (Not were because university is singular.)

50% (A half, A third, A part, etc.) of the parents were at the meeting. (Not was because parents are plural.)

[Examples are from Subject-Verb Agreement at elc.polyu.edu.hk]

If you change the word back to "back part (of his pants)" or "back half (of his pants)", the two phrases contain the words part and half and the rule applies. Therefore, the verb should agree to pants, not to back.

However, the word side seems trickier than back in "the back of his pants". A pair of glasses has only two sides and if it is the one side of the two sides which is bent, it should use a singular verb as in

The side of my glasses is bent.

No, you’re not by any means mistaken. The book’s author and the Googled answer are mistaken. Meanwhile, there’s some over-engineering going on above.

user140086 was making a case until ‘side’ became trickier but precisely as a pair of glasses has ‘only’ two sides, a pair of pants has ‘only’ two faces: back and front. (Did anyone think three, five or 17 sides could have made a grammatical difference?)

Clearly, the subjects are indeed ‘the back’ or ‘the side’, not ‘his pants’ or ‘his glasses.’ A part is one thing, a portion quite another.

Finish thinking about how if you change the word back to "back part (of his pants)" or "back half (of his pants)", the two phrases contain the words part and half and the rule applies… It does, but which rule?

‘The back half of his pants are…’ sounds no worse than ambiguous but we’ve just seen ‘half’ equated with ‘part’, haven’t we?

Is it - could it ever be - right to use ‘the back part (of his pants) are…’?

Of course the verb should agree with the subject but the subject is clearly ‘the back part (of…)’ and not by any stretch of the imagination ‘his pants’.

The relationships between parts or sides of pants or glasses and percentages or fractions of universities or groups of parents are not comparable; the limited extent to which might they have been arithmetically similar is completely over-ridden by their obvious linguistic differences.

A side or a part, in the sense of pants, is clearly both countable and capable of independent existence.

A percentage or fraction of a university or group of parents is clearly countable only as a portion of the whole, and cable of independent existence only as a ruin or sub-group. What place does transubstantiation have in grammar?

Clearly ‘the back of one's pants’ includes the entire backside and more clearly, that can’t come close to ‘encompassing the whole pair’. To exactly the extent that ‘the back…’ includes the entire backside of the pants (thus encompassing the whole pair) so ‘the front…’ includes the entire frontside of the pants (thus encompassing the whole pair). Equally clearly, they cancel each other out, removing the pants and all their parts from further perusal.

‘The back pocket of my pants is torn’ is correct and should be obviously so. ’The back of my pants are wet’ apparently sounds reasonable to some; it sounds risible to me. A pocket can’t be relevant. A pocket is no more a part of a pair of pants than a button or a bow. Both equate to the add-on extras we might find on a car; neither to the car itself.

If one is speaking of parts of two things, "pants, a pair of pants" in this case, shouldn't it then be "backs"? Shouldn't it be "the backs of his pants are..."? Sounds weird but isn't it the way it should be? Or does grammar go beyond logics?