## Elementary Technical Mathematics

$-3\displaystyle \frac{1}{3}$
$\displaystyle \left(\frac{-5}{-8} \right) \cdot\left(-5\frac{1}{3} \right)=$ Apply the equivalent fractions rule, $\quad \displaystyle \frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$ ... $\displaystyle \frac{-5}{-8}=-\frac{5}{-8}=-(-\frac{5}{8})=+\frac{5}{8}$ Also, write the mixed number as an improper fraction $=\displaystyle \left(+\frac{5}{8} \right) \cdot\left(-\frac{16}{3} \right)$ Multiplying two numbers with different signs: Multiply their absolute values; the sign of the result is $"-"$. $=-\left(\displaystyle \frac{5}{8} \cdot \frac{16}{3} \right)$ Multiply fractions: Reduce by the common factor, $8$. $=-\left(\displaystyle \frac{5}{1} \cdot \frac{2}{3} \right)$ Now, multiply the numerators and place the product over the product of the denominators. $=-\displaystyle \frac{10}{3}$ Write the improper fraction as a mixed number. $=-3\displaystyle \frac{1}{3}$