When is 分 read ぶ instead of ぶん

Question

I had always thought that when you were talking about percentage, fractions, portions, etc., it was always pronounced ぶん. However, I saw its pronunciation listed as ぶ on Imabi, a renowned website for self-learners. The likelihood of its being an error was rather low, since the author seemed to really know his stuff, solid.

On Imabi, a couple of examples were given:

五分五分{ごぶごぶ}の確率
九分九厘{くぶくりん}勝てる。
*八九分{はっくぶ}

*Strangely, MS-IME does not show 八九分 for はっくぶ, I have to type each kanji separately. Could it be due to its not being an idiom?

The first two seem to be 四字熟語, so I would simply assume the pronunciations are not up for discussion. However, what about other combinations, such as 九割九分? According to this native speaker (ID: ywja):

It's either きゅうわりきゅうぶ or くわりくぶ. Personally, I find that きゅうわりきゅうぶ is more common. Also, it sounds more colloquial and casual to my ears, probably because きゅう sounds more casual than く as the reading of 九.

Question #1.
Her/his explanation appears not to be about personal preference, or regional/dialectic difference. If there is indeed room for variation, as this person suggests, what are some common examples (other than 九) where multiple readings apply for the sake of nuances? For instance, for 四分, what are the possible readings? よぶ, よんぶ, and/or しぶ? In addition, how does one read 何分, 一分, 三分, 八分, 十分, 百分, and so on?

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Unfortunately, that is not all.

First of all, as far as I know, 分 should be read as ぶん for fractions, such as 三分{さんぶん}の一{いち}. The same goes for portions, such as 千人分の生ビール, or 三十年分のビール.

Next, I looked up 分 again in a dictionary, and for this specific pronunciation, ぶ, 研究社 listed only one English translation, "percent." The following are all the sample sentences provided:

1. 銀行は 4 *分の利子で金を貸してくれた。 The bank lent me the money at 4 percent interest.

2. 日本チームに*分がある勝ちそうだ。 The Japanese team is likely to win.

3. 今回は我々のほうが*分がいい。 We have an advantage this time.

4. その仕事は 9 *分どおり済んだ。 The work is 90 percent done.

For 2. & 3., I think ぶ is the only possible reading, since only under ぶ is this meaning listed. In goo辞書, 1st entry under 分（ぶ）:

どちらに傾くかの度合い。自分のほうに有利になる度合い。

Question #2.
For 1. & 4., can you read it as ぶん as well? Moreover, shouldn't it be 9 percent in 4., or 九割?

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Again, under 割（り）（わり）, goo辞書 has this definition：

2. 歩合の単位。1割は10分の1。

And for 分（ぶ）:

5. 全体を10等分したもの。10分の1相当の量。

6. 単位の名。㋐割合・利率で、1割の10分の1。全体の100分の1。

I guess one does not simply consult a dictionary, and go "Eureka!"

Question 3.
How does one decide, then, when （一）分 means one-tenth, but not one-hundredth? Moreover, how does one read it? ぶ, or ぶん?

長文ですみません… いつも迷惑をかけてばかりんですが…どうぞよろしくお願いいたします！

Answer 1

A1: When 分 means 10%, 一分 ～ 九分 is usually read like いちぶ, にぶ, さんぶ, よんぶ, ごぶ, ろくぶ, ななぶ/しちぶ, はちぶ, きゅうぶ/くぶ. But 九分九厘 is an idiom that is always pronounced くぶくりん. 九割九分 is usually きゅうわりきゅうぶ, but くわりくぶ may not be wrong. 何分 is なんぶ.

A2: These are read as 4分【ぶ】の利子, 分【ぶ】がある, 分【ぶ】がいい, 9分【ぶ】どおり. No exceptions. その仕事は9分どおり済んだ and その仕事は9割済んだ effectively mean the same thing, 90%. See below.

A3: 分 read as ぶ essentially means 10%, not 1%. However, 分 appears to mean 1% if it follows 割, which is another term meaning 10%.

割 means "10% of the entire fraction". 分 on its own works like 割, but 分 also works somewhat like the SI prefix deci-; it's used in combination with another unit and refers to one tenth of it. For example, 一寸五分 (いっすんごぶ) means 1.5 sun (≒4.5 cm), and 37度5分 (さんじゅうななどごぶ) means 37.5 ℃. Likewise, when 割 and 分 are used together, 2割5分 means "2.5割", which is 25%. This explains why both 九割九分 and 九分九厘 mean 99%.

That being said, for historical reasons, 分 means 1% even without 割 in financial contexts and baseball contexts. 4分 (よんぶ) automatically means 4% when you are talking about interest rates and batting averages. Outside of these types of situations, you can assume that 分 read as ぶ means 10% (cf 四分咲き → 40%, 七分袖 → 70%, 五分五分 → fifty-fifty).

You seem to correctly understand how to read 3分【ぶん】の1, 30年【ねん】分【ぶん】のビール, 2時30分【ぷん】, and so on, so I won't go into detail about them.