A farmer 8

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

Correct answer:

v =  4/9

Step-by-step explanation:

$$\begin{gathered} c=\frac{1}{3}\doteq 0.3333 \\ r=1-c=1-\frac{1}{3}=\frac{1\cdot 3}{3}-\frac{1}{3}=\frac{3}{3}-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}\doteq 0.6667 \\ m=\frac{1}{3}\cdot r=\frac{1}{3}\cdot \frac{2}{3}=\frac{1\cdot 2}{3\cdot 3}=\frac{2}{9}\doteq 0.2222 \\ s=c+m=\frac{1}{3}+\frac{2}{9}=\frac{3}{9}+\frac{2}{9}=\frac{3+2}{9}=\frac{5}{9}\doteq 0.5556 \\ v=1-s=1-\frac{5}{9}=\frac{1\cdot 9}{9}-\frac{5}{9}=\frac{9}{9}-\frac{5}{9}=\frac{9-5}{9}=\frac{4}{9}=0.4444 \end{gathered}$$

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