Final answer:
Paul consumed 1/8 cup of butter when he ate 1/6 of the batch of brownies, which originally contained 3/4 cup of butter.
Step-by-step explanation:
The question asks to determine what fraction of a cup of butter Paul consumed when he ate 1/6 of the batch of brownies, where he initially used 3/4 cup of butter for the entire batch. To find the solution, we multiply the fraction of the brownies eaten by the total amount of butter used:
Amount of butter consumed = Fraction of batch eaten × Total butter used
Amount of butter consumed = 1/6 × 3/4
Amount of butter consumed = 1/6 × 3/4 = 3/24 = 1/8 cup of butter
Therefore, Paul consumed 1/8 cup of butter when he ate 1/6 of the batch of brownies.