## Elementary Technical Mathematics

$-1\displaystyle \frac{1}{8}$
Rewrite the fractions so they have a common denominator. LCD=24. $\displaystyle \left(\frac{-2\cdot 8}{24} \right)$+$\displaystyle \left(\frac{-5\cdot 4}{24} \right)$+$\displaystyle \left(\frac{1\cdot 6}{24} \right)$+$\displaystyle \left(\frac{1\cdot 3}{24} \right)$= Combine the numerators $=\displaystyle \frac{-16+(-20)+6+3}{24}$ Add the terms with like signs $=\displaystyle \frac{-(16+20)+(6+3)}{24}$ $=\displaystyle \frac{-(36)+(+9)}{24}$ Add the terms with different signs $=\displaystyle \frac{-27}{24}$ Apply the equivalent fractions rule, $\quad \displaystyle \frac{a}{-b}=\frac{-a}{b}=-\frac{a}{b}$ Reduce by the common factor, $3$ $= -\displaystyle \frac{9}{8}$ Write as a mixed number =$-1\displaystyle \frac{1}{8}$