Hyphenation of Fractions

Different sources that I have consulted seem to give conflicting advice on the hyphenation of fractional numbers.

The first source states:

Fractions are written out in words. They are hyphenated only when they come right in front of a noun, called a “direct” adjective.

The second source states:

Do Not Use Hyphens with Numbers Used as Quantifiers. When the number is a quantifier to a noun, do not use a hyphen.

I see that when it comes before a noun it is both quantifier and adjective

Examples:

The journey takes one and three-quarter hours.

The journey takes twenty-three and a quarter hours. (the fraction does not come before the noun to say it is adjective)

On the other hand, consider the following example from the same source:

1. It is a two-hour journey.
2. It is a two-and-a-half-hour journey.
3. It is a twenty-three-and-a-quarter-hour journey.
4. It is a 23.25-hour journey.
5. It is a one-and-three-quarter-hour journey.

I agree with the last five examples because all fractions come before the noun (journey) describing the particular journey in question, distinguishing it from other journeys.

Suppose I have the following question:

Rewrite the following sentences, adding hyphens where needed.

The report shows that two thirds of the population are under fifty five years of age.

Is (two thirds) in the above example a noun? Is it adjective? The source advises that when the fraction is a noun don’t hyphenate, but they appear to adopt the opposite and hyphenate. So, which rule should one follow?

Once fraction comes before a noun = no doubt = adjective modifying the noun

But, what is the rule when it comes after the noun or comes in front but is followed by (of + noun)? examples: two-thirds of people / of the population etc.

• The second rule is about numbers in general, not fractions. It is rare to use fractions in formal English other than a half etc. And grammar books especially for students don't cover every obscure case. (But science has its own rules) Commented Jul 29, 2022 at 19:02