Short answer
Write it as "three thirty in the afternoon" or "3.30 pm". Avoid "half past three" in formal wording. For a wedding at 3.30 pm, say "at three thirty in the afternoon" on a traditional invitation.
On a formal wedding invitation, the time is usually written out in words. So for 3.30 pm, you would write "three thirty in the afternoon". This matches the elegant style of the rest of the invitation, where the date is often written as "Saturday, the fifteenth of June".
If you prefer a simpler or more modern style, you can write "3.30 pm" or "3:30pm". That is perfectly acceptable, especially for a less formal invitation. Just be consistent across all your stationery.
Avoid writing "half past three" on a formal invitation, as that sounds more like spoken English. It is not wrong, but it does not match the traditional written style.
If the ceremony starts at 3.30 pm, you might also want to say when the reception begins, for example "Reception to follow at five o'clock". That helps guests know what to expect.
Remember that the time on the invitation is the time the ceremony starts, not the time guests should arrive. You can add "Guests are asked to arrive by three fifteen" if you want to be clear, but it is not essential.
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