To determine how many whole pieces of \( \frac{1}{5} \) yard can be cut from a \( \frac{7}{9} \) yard piece of yarn, we need to divide \( \frac{7}{9} \) by \( \frac{1}{5} \).
The division of fractions can be performed by multiplying by the reciprocal:
\[ \frac{7}{9} \div \frac{1}{5} = \frac{7}{9} \times \frac{5}{1} = \frac{7 \times 5}{9 \times 1} = \frac{35}{9} \]
Now, \( \frac{35}{9} \) is an improper fraction. To find out how many whole pieces can be cut out, we can divide 35 by 9:
\[ 35 \div 9 = 3 \quad \text{(whole number)} \quad \text{with a remainder of } 8 \]
We can also express \( \frac{35}{9} \) as a mixed number:
\[ 35 \div 9 = 3 \quad \text{with a remainder of } 8, \text{ which can be written as } 3 \frac{8}{9} \]
Thus, Roberto can cut 3 whole pieces of \( \frac{1}{5} \) yard from his \( \frac{7}{9} \) yard piece of yarn.
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