Elementary Technical Mathematics

$-3\dfrac{1}{4}$
Convert each mixed number to improper fraction: $\\=-\dfrac{3}{4}+\left(-\dfrac{6(1)+1}{6}\right)+\left(-\dfrac{3(1)+1}{3}\right) \\=-\dfrac{3}{4}+\left(-\dfrac{7}{6}\right)+\left(-\dfrac{4}{3}\right)$ Make the fractions similar using their LCD, which is $12$: $\\=-\dfrac{3(3)}{4(3)}+\left(-\dfrac{7(2)}{6(2)}\right)+\left(-\dfrac{4(4)}{3(4)}\right) \\=-\dfrac{9}{12}+\left(-\dfrac{14}{12}\right)+\left(-\dfrac{16}{12}\right) \\=-\dfrac{-9-14-16}{12} \\=-\dfrac{39}{12} \\=-\dfrac{13}{4} \\=-3\dfrac{1}{4}$