## Elementary Technical Mathematics

$\displaystyle \frac{11}{16}$
First, write mixed numbers as improper fractions, Apply the equivalent fractions rule, $\quad \displaystyle \frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$ $\displaystyle \left(-\frac{11}{4} \right)\div\left(+\frac{8}{5} \right)\left(-\frac{2}{5} \right)$ Dividing with a fraction $\displaystyle \frac{a}{b}$ equals multiplying with the reciprocal, $\displaystyle \frac{b}{a}$ = $\displaystyle \left(-\frac{11}{4} \right)\cdot\left(+\frac{5}{8} \right)\left(-\frac{2}{5} \right)$ There are 2 minus signs in the product: the result is positive. = $+\displaystyle \left(\frac{11}{4} \cdot\frac{5}{8}\cdot\frac{2}{5} \right)$ Reduce by the common factors, 5 and 2 = $\displaystyle \frac{11}{2} \cdot\frac{1}{8}\cdot\frac{1}{1}$ Now, multiply the numerators and place the product over the product of the denominators. = $\displaystyle \frac{11}{16}$