Problem 1382

1. We start with the given relationship between Fahrenheit temperature $F$ and Celsius temperature $C$:
$$F = \frac{9}{5} \cdot C + 32$$

2. We need to find the temperature in Fahrenheit degrees that is one-fifth as large if measured in Celsius degrees. This means we need to find $F$ such that:
$$F = \frac{1}{5} C$$

3. Substitute $F = \frac{1}{5} C$ into the original equation:
$$\frac{1}{5} C = \frac{9}{5} \cdot C + 32$$

4. To eliminate the fractions, multiply every term by 5:
$$C = 9C + 160$$

5. Rearrange the equation to isolate $C$:
$$C - 9C = 160$$
$$-8C = 160$$

6. Solve for $C$:
$$C = \frac{160}{-8}$$
$$C = -20$$

7. Now, substitute $C = -20$ back into the equation $F = \frac{1}{5} C$ to find $F$:
$$F = \frac{1}{5} \cdot (-20)$$
$$F = -4$$

The final answer is $\boxed{ F = -4 }$