Question

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

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Esmeralda

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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.

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