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 ten.
分 can also means "perdec" (per ten, a tenth), as a synonym of 成.
三分 three points (out of ten), three perdec (3/10)
五分 five points (out of ten), five perdec (5/10)
十分 ①[original meaning] ten points (out of ten), perfect score, full marks ②[extended meaning] "perfectly", very, extremely
幾分 how many points (out of ten), how many perdec
Assuming that there is an exam called "love", how many points can I get from the exam?
How many points (out of ten) do I love you?
How many perdec do I love you?
= How much do I love you?
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"]
Every time you meet a person, you should only tell them three perdec (3/10) of your mind. You should not "throw the entire heart to them" (tell them all your mind).
Some knowledge about the Chinese culture of proportions
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.
三分 = three perdec (three tenths, 3/10)
七分 = seven perdec (seven tenths, 7/10)
八成 = eight perdec (eight tenths, 8/10)
九成 = nine perdec (nine tenths, 9/10)
折 is only used for discounts.
九折 = nine perdec remaining (i.e. 10% discount)
八折 = eight perdec remaining (i.e. 20% discount)
八五折 (8.5折) = 8.5 perdec remaining (i.e. 15% discount)
As 分 is also a traditional Chinese unit of length, which is currently defined as ⅓ centimetre (in mainland China) or 10/33 centimetre (in Taiwan), some people believe that it is better to parse it as the depth of love measured in this length unit, instead of points or perdecs.
[literally] into the wood for three fen of depth
[figuratively] written in a forceful hand, penetrating, profound
Wait, this dispute might really be the different usage of 分 between mainland China and Taiwan, because the dictionaries really shows different definitions:
Xiandai Hanyu Cidian dictionary from mainland China:
⑧ 十分之一（用于某些计量单位或抽象事物）：分米 | 分升 | 九分成绩，一分缺点
⑧ a tenth (for some units or something abstract): 分米 (decimetre) | 分升 (decilitre) | 九分成绩，一分缺点 (nine tenths of achievement, and one tenth of shortcoming)
Ministry of Education Mandarin Chinese Dictionary from Taiwan:
(6) A unit to measure depth, e.g. 一分努力，一分收穫 (one fen of hardworking produces one fen of rewards) and 逢人只說三分話 (every time you meet a person, you should only say three fen of words)