A farmer uses 1/3 of his land to plant cassava, 1/3 of the remaining to plant maize and the rest vegetables. What fraction did the farmer use to plant vegetables

To solve this problem, we'll first find out what fraction of the land the farmer used to plant cassava and maize, and then subtract that fraction from 1 to find the fraction used for planting vegetables. 1. The farmer uses \( \frac{1}{3} \) of his land to plant cassava. 2. After planting cassava, \( \frac{2}{3} \) of the land remains. 3. Then, the farmer uses \( \frac{1}{3} \) of this remaining land to plant maize. 4. This means \( \frac{2}{3} \times \frac{1}{3} = \frac{2}{9} \) of the land is used for planting maize. 5. After planting cassava and maize, the fraction of land remaining for planting vegetables is \( 1 - \left(\frac{1}{3} + \frac{2}{9}\right) \). Now, let's calculate: \[1 - \left(\frac{1}{3} + \frac{2}{9}\right) = 1 - \left(\frac{3}{9} + \frac{2}{9}\right) = 1 - \frac{5}{9} = \frac{9}{9} - \frac{5}{9} = \frac{4}{9}\] So, the farmer used \( \frac{4}{9} \) of his land to plant vegetables.