Find \( 1 \frac{1}{5}\left(-4 \frac{5}{8}\right) \). Write in the simplest form

To solve \( 1 \frac{1}{5}\left(-4 \frac{5}{8}\right) \), we first convert the mixed numbers to improper fractions. For \( 1 \frac{1}{5} \): \[ 1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \] For \( -4 \frac{5}{8} \): \[ -4 \frac{5}{8} = -\left(4 + \frac{5}{8}\right) = -\left(\frac{32}{8} + \frac{5}{8}\right) = -\frac{37}{8} \] Now, multiply the two improper fractions: \[ \frac{6}{5} \cdot \left(-\frac{37}{8}\right) = -\frac{6 \cdot 37}{5 \cdot 8} = -\frac{222}{40} \] Next, simplify \( -\frac{222}{40} \): Finding the greatest common divisor (GCD) of 222 and 40, we see that it is 2. So we divide both the numerator and denominator by 2: \[ -\frac{222 \div 2}{40 \div 2} = -\frac{111}{20} \] Thus, the final answer in simplest form is: \[ -\frac{111}{20} \] This value can also be written as a mixed number: \[ -5 \frac{11}{20} \] So the answer to \( 1 \frac{1}{5}\left(-4 \frac{5}{8}\right) \) in the simplest form is: \[ -\frac{111}{20} \quad \text{or} \quad -5 \frac{11}{20} \]