## Elementary Technical Mathematics

$-\dfrac{33}{38}$
Write each mixed number in improper fraction form to obtain: $=\dfrac{4(2)+3}{4}\div \left(-\dfrac{6(3)+1}{6}\right) \\=\dfrac{11}{4}\div \left(-\dfrac{19}{6}\right)$ Use the rule $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$. Note that the product and quotient of two numbers with different signs is negative. $\require{cancel} =\dfrac{11}{4} \times \left(-\dfrac{6}{19}\right) \\=\dfrac{11}{\cancel{4}^2} \times \left(-\dfrac{\cancel{6}^3}{19}\right) \\=\dfrac{11}{2} \times \left(-\dfrac{3}{19}\right) \\=-\dfrac{11(3)}{2(19)} \\=-\dfrac{33}{38}$