## Elementary Technical Mathematics

$2$
Convert each mixed number to an improper fraction: $=\frac{3(4)+2}{3} \div \frac{2(3)+1}{2} \times \frac{2(1)+1}{2} \\=\frac{14}{3} \div \frac{7}{2} \times \frac{3}{2}$ The order of operations states that multiplication and division have the same degree of priority and that whichever comes first from the left must be performed ahead of the other.. Perform division first while using the rule $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ to obtain: $=(\frac{14}{3} \times \frac{2}{7})\times \frac{3}{2}$ Cancel common factors then multiply to obtain: $\require{cancel} \\=\frac{\cancel{14}2}{\cancel{3}} \times \frac{\cancel{2}}{\cancel{7}} \times \frac{\cancel{3}}{\cancel{2}} \\=2$