## Elementary Technical Mathematics

$-1$
$\displaystyle \left(\frac{-2}{-3} \right)\div\left(\frac{2}{-3} \right)=$ Apply the equivalent fractions rule, $\quad \displaystyle \frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$ $=\displaystyle \left(+\frac{2}{3} \right)\div\left(-\frac{2}{3} \right)$ Dividing two numbers with different signs: Divide their absolute values; the sign of the result is $"-"$. $=-\left(\displaystyle \frac{2}{3} \div \frac{2}{3} \right)$ Dividing with a fraction $\displaystyle \frac{a}{b}$ equals multiplying with the reciprocal, $\displaystyle \frac{b}{a}$. $=-\left(\displaystyle \frac{2}{3} \cdot \frac{3}{2} \right)$ Multiply fractions: Reduce by the common factors, 2 and 3 $=-\left(\displaystyle \frac{1}{1} \cdot \frac{1}{1} \right)$ Now, multiply the numerators and place the product over the product of the denominators. $=-\displaystyle \frac{1}{1}$ $=-1$