How do you say 7/7?
Solution 1:
For a shop, the sign on the outside would normally say either "Open 7 days a week" or "Open every day".
I can't think of a commonly used shorthand way to say it (based on my own experience in the UK).
Solution 2:
I have started to hear 7/7 (pronounced as seven seven) used in UK english and have readily taken it to mean seven out of seven days. When written as 7/7 I would not expect misunderstanding. The only exception to this that I can see is that if a sign outside a shop displayed this e.g. 7/11, it might be taken to mean hours of opening. In these circumstances, 'Open 7 Days' would be preferable.
Solution 3:
I've never encountered that expression here (US, Ohio) but in general a fraction X/Y (that isn't subdividing a unit) is read "X of Y." In this case, I'd find "7 of 7" support a fairly easy concept to comprehend, especially if there are other service plans like 5/7 or 3/7 (five days a week, or three days a week). I wouldn't treat it as a known idiom, however, you'd need to introduce it before using it.
One additional consideration --if you're using both "24/7" and "7/7" as stock phrases, you're switching the units of the first number (from hours to days), which is confusing.
Solution 4:
Common phrases regarding shop or service availability:
Written: Available 24/7
Verbal: Available twenty four seven
Written: Available 24hrs
Verbal: Available twenty four hours
Written: Open 7 Days
Verbal: Open seven days
Written: Open 7 Days a week
Verbal: Open seven days a week
Written: Open 365 days
Verbal: Open three hundred and sixty five days / Open three sixty five days
Written: Open 365 days a year
Verbal: Open three hundred and sixty five days a year
I haven't seen the term 7/7 used, but given that its form is similar to 24/7 I'd suggest that 'seven seven' should be used.
I would suggest that 7 days would be a better term to use over 7/7 though - it's more explicit that it's referring to days a week and it's one less syllable. I don't see what 7/7 confers over 7 days or 24/7, except for being a cutesy variant of 24/7.