Final answer:
After converting the fractions to have a common denominator, it becomes clear that wheat (3/8) occupies the most land, while corn (1/12) occupies the least land on the farmer's property.
Step-by-step explanation:
The farmer plants a variety of crops on his land: 1/12 with corn, 1/4 with soybeans, 3/8 with wheat, and 3/16 with potatoes. To determine which crop takes up the most land and the least, we need to compare the fractions. Converting all fractions to have a common denominator, which is the least common multiple (LCM) of all the denominators, we get:
- Corn: 1/12 = 2/24
- Soybeans: 1/4 = 6/24
- Wheat: 3/8 = 9/24
- Potatoes: 3/16 = 4.5/24
From these conversions, it is clear that wheat, with a fraction of 9/24, takes up the most land, and corn, with a fraction of 2/24, takes up the least land.