You can take mod 7 anywhere you like as you go. It's a tool to make the arithmetic easier.
No, you don't need to do it relentlessly as you go, but it can be used in an ad hoc manner to keep the numbers small.
Having said that, if you have 24, you can reduce it (mod 7) to 10, which you might find it easier to work with rather than reducing it to 3. Similarly if you start with 27 you can reduce it to -1 (mod 7). You don't always need to reduce things to the range [0..7).
(Note, by convention the square bracket implies "included" and the round bracket implies "excluded", so [0..7) is the collection {0,1,2,3,4,5,6}.)
