Elementary Technical Mathematics

$3\frac{1}{4}$
Convert each mixed number to an improper fraction: $=\frac{3(1)+2}{3}+\frac{6(3)+5}{6}-\frac{4(2)+1}{4} \\=\frac{5}{3} + \frac{23}{6} - \frac{9}{4}$ Make the fractions similar using their LCD of $12$ to obtain: $=\frac{5(4)}{3(4)}+\frac{23(2)}{6(2)}-\frac{9(3)}{4(3)} \\=\frac{20}{12}+\frac{46}{12}-\frac{27}{12} \\=\frac{20+46-27}{12} \\=\frac{39}{12} \\=3\frac{3}{12} \\=3\frac{1}{4}$