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This is taken from an exercise book, but I don't quite get it why the answer is ''have'' on this.
An increasing number of patients seem to be dissatisfied with conventional medicine and has/have turned to alternative therapies.
Which one is the subject here, the ''an increasing number'' or the ''patients''?
For starters, "have " matches with "seem". If you use the plural conjugation with one verb, you have to use it with both.
More significantly, the subject of the verbs is not "number" but rather "number of patients". Numbers can't be dissatisfied with their medical care, only people can. It's a plural collective. Consider this similar example:
Many children are playing outdoors today.
In the same way "an increasing number" is simply a quantifier that tells us how many patients feel this way. However, we could rewrite the sentence as:
The number of patients (who are) dissatisfied with conventional medicine is increasing.
