Elementary Technical Mathematics

$\displaystyle \frac{1}{4}$
Apply the equivalent fractions rule, $\quad \displaystyle \frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$ $... = \displaystyle \left(-\frac{2}{5} \right)\left(-\frac{3}{4} \right)\left(+\frac{15}{18} \right)$ Multiplication is associative, $= \displaystyle \left[\left(-\frac{2}{5} \right)\left(-\frac{3}{4} \right)\right]\cdot\left(+\frac{15}{18} \right)$ The brackets hold a product of two numbers with the same sign; the result is positive and we multiply the absolute values. $= \displaystyle \left[\frac{2}{5} \cdot\frac{3}{4} \right]\cdot\left(+\frac{15}{18} \right)$ Multiply fractions: first, reduce by the common factor, $2$ $= \displaystyle \left[\frac{1}{5} \cdot\frac{3}{2} \right]\cdot\left(+\frac{15}{18} \right)$ Now, multiply the numerators and place the product over the product of the denominators. $=\displaystyle \frac{3}{10}\cdot\frac{15}{18}$ Reduce by the common factors, 3 and 5. $=\displaystyle \frac{1}{2}\cdot\frac{3}{6}$ Reduce by the common factor, 3 $=\displaystyle \frac{1}{2}\cdot\frac{1}{2}$ = $\displaystyle \frac{1}{4}$