You misunderstand 分 here.

分 does not mean "division" here. Here 分 means the "points" (test score), in an exam or a contest where the perfect score is 10.

分 can also means "perdec" (*per ten*, a tenth).

> 三分  3 points (out of 10), 3 perdec (3/10)
>
> 五分  5 points (out of 10), 5 perdec (5/10)
>
> 十分 ①[original meaning] 10 points (out of 10), perfect score, full marks ②[extended meaning] "perfectly", very, extremely
>
> 幾分  how many points (out of 10), how many perdec

Assuming that there is an exam called "love", how many points can I get from the exam?

>我愛你有幾分？
>
> How many points do I love you?
>
> How many perdec do I love you?
>
> = How much do I love you?


Extra examples:

> 三分天注定，七分靠打拼。 [famous lyrics]
>
> Three points depend on fate, while seven points depend on hardworking.
>
> 3/10 depends on fate, 7/10 depends on hardworking.
>
> [Chinese version of "nature versus nurture"]

> 逢人只說三分話，未可全拋一片心。[idiom]
>
> Every time you meet a person, you should only say 3 perdec (3/10) of your mind. You should not "throw the entire heart to them" (tell all you mind).

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As for proportion, Western culture prefers to use "percent" (*per hundred*, a hundredth), while Chinese culture traditionally uses "perdec" (*per ten*, a tenth), known as 分, 成, 折.

Examples:
> 三分  three perdec (three tenths, 3/10)
>
> 七分 seven perdec (seven tenths, 7/10)
>
> 三成  three perdec (three tenths, 3/10)
>
> 七成 seven perdec (seven tenths, 7/10)

折 is only used for discounts.

> 九折 nine perdec remaining (i.e. 10% discount)
>
> 八折 eight perdec remaining (i.e. 20% discount)