It is not always necessary to repeat articles with paired items: We bought a computer and printer. However, if one of the items requires a and the other requires an, both articles must be included.
Articles are sometimes omitted in recipes and other instructions that are meant to be followed while they are being read. In nearly all other forms of writing, whether formal or informal, such omissions are inappropriate.
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Choosing and using articles can be challenging for multilingual writers. See 29.