Final answer:
The farmers picked 1/2 a barrel of tomatoes on Thursday, which is calculated by taking 3/4 of the 2/3 barrel they picked on Wednesday.
Step-by-step explanation:
To find out how many barrels of tomatoes the farmers picked on Thursday, we need to calculate 3/4 of the amount they picked on Wednesday. They picked 2/3 of a barrel on Wednesday, so on Thursday they picked:
2/3 of a barrel × 3/4 = (2 × 3) / (3 × 4)
= 6/12 (since 2 × 3 = 6 and 3 × 4 = 12)
= 1/2 (since 6/12 simplifies to 1/2)
So, the farmers picked 1/2 a barrel of tomatoes on Thursday.