The slashes aren't maths operators, they're language/grammar/shorthand. The lexeme as a whole is merely a mnemonic for the linger phrase: "24 hours per day, 7 days per week, 365 days per year."
It's not that the individual segments relate to each other. Rather they answer three sets of questions:
What are your daily hours? All of them. 24 hours / day.
What weekdays are you open? Again, all of them. 7 days/week.
What holidays do you observe per year? None, we're open 365 days/year.
Since there's rarely a monthly cycle to business closings and there aren't a standard number of days per month, that's elided.
It also helps to realize that human timekeeping is really based on three independent phenomena which are utterly unrelated. There are day-based units: seconds, minutes, and hours are all subdivisions of the period of rotation of Earth about its axis.
The month is based on the Moons orbit about Earth. That it is roughly 30 days is a notional convenience, similarly its rough divisibility by 4 into 7 day periods. The week is entirely synthetic (though profoundly persistent).
And the year on Earth's orbit about the Sun. Again, relationship to days and months are entirely arbitrary.
That's why it often seems time units are arbitrary. They are.
There's a brief book which Kay's this ought and traces the calendar through time, The Seven Day Cycle.