The following is an excerpt from the PRD section on Variant Channeling (found here on Paizo's site (emphasis is mine):
When using positive energy to heal, affected creatures gain only half the normal amount of healing but also receive a specific beneficial effect.
Some variant channeling abilities are enhanced when used on particular creature types. Such channeling increases the normal healing or damage from channeled energy by 50% for that creature type, rather than the default half healing or damage for the alternative channeling. For example, a 7th-level cleric normally heals 4d6 points of damage with channeled positive energy; with the Nature alternative channeling, that cleric instead heals only half that amount (2d6) when channeling, but heals animals and fey an additional +50% over the unhalved value (4d6 + 50%).
I can not find any other reference in the core rules that talks about dividing dice-based abilities this way. Is this an error in the example (should it be 4d6, rolled and divided by 2?), or is there another reference on how this division is done?
If this is a standard way of dividing, how would you divide an odd number of dice?
I'm siding towards "error" because there is a lot of inconsistent wording in this whole section that leaves certain things open to GM interpretation. i.e. does the base damage inherit the properties of, i.e., fire? It even explicitly says as part of _or_ instead of in the text which means there's no official answer.