What household measure might be used to give 1/2 ounce of cough syrup?

In a common household 1/2 ounces of cough syrup would be given with a table spoon, or even a regular spoon.

Explanation:

Most cough syrup's don't come with withe the little cups to help measure the amount of cough syrup to be taken. Therefore people use spoons, which might be a table spoon. The probability of someone using a table spoon is 50/50 because, there are various types of spoons out there.

That being said your answer would be: Spoon/Table spoon.

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