Why do we say 24 x 7 x 365 rather than 24 x 365?

Solution 1:

There are several variants of this, "24/7", "24-7", "24/365", "24X365" and so on.

Those with a multiplication are clearly depending on the fact that e.g. 24×7 will indeed, if calculated, give the number of hours in a week.

The main point of that expression is not to convey 168 nor for "24×365" to convey 8760 (which forgets leap years anyway). It's to convey that information which is also available in the forms which don't use the multiplication symbol, viz that the service, shop, etc. is available at every hour and at every day of the week and/or year.

"24-7-365" conveys availability at every hour and at every day of the week and at every day of the year. The "7" is redundant when we have the "365" but it relates to a different concern: It might be more important to me that a service is available on Saturdays than that it is available on Christmas, so I might care about the "7" more than I do about the "365" even though the latter logically entails the former.

The mathematically incorrect "24×7×365" is just a merging of that with the forms where the arithmetic actually does work, because similar common expressions will always end up being merged, especially when written quickly.

Solution 2:

The expression is written several ways: 24-7-365, 24/7/365, or 24x7x365. The last one is not a mathematical formula indicating multiplication, but merely a variation in punctuation. The 365 is an intensifier of the far more common 24/7, since "24 hours a day, 7 days a week" covers everything, though perhaps it assures the reader that the service is also available on legal holidays. Without the 24/7, 24x365, however, does look like a multiplication problem, thus won't likely replace 24-7-365 any time soon.

Solution 3:

This has nothing to do with multiplication, this is an English language abbreviation for measurements.

Think of a piece of wood that is 10 inches high and 4 inches wide and 2 inches thick. You could describe its size as 10x4x2.

This same approach is also used with measurements of time.

24 x 7 is an abbreviation for 24 hours a day, 7 days a week

24 x 7 x 365 is an abbreviation for 24 hours a day, 7 days a week, 365 days a year

These are abbreviations not formulae.