Mr. Fishman uses $$ \frac{1}{3} $$ of his yard for growing flowers. This section of the yard is split into 4 equal sections to plant different types of flowers. What fraction of the garden is used for each type of flower? He picked a cucumber from his vegetable garden that weighed $$ \frac{1}{4} $$ of a pound. He cut it into 2 equal pieces. How much does each piece of the cucumber weigh?

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1. Mr. Fishman uses $$ \frac{1}{3} $$ of his yard for growing flowers, and this section is split into 4 equal sections. Each section is therefore:

$$
   \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}
   $$

So, each type of flower occupies $$ \frac{1}{12} $$ of the yard.

2. The cucumber weighs $$ \frac{1}{4} $$ of a pound and is cut into 2 equal pieces. The weight of each piece is:

$$
   \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
   $$

Thus, each piece of the cucumber weighs $$ \frac{1}{8} $$ of a pound.
Each type of flower uses $$ \frac{1}{12} $$ of the yard. Each piece of the cucumber weighs $$ \frac{1}{8} $$ of a pound.

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