Question

Simplify: $5\frac{1}{6}-3\frac{1}{4}+3\frac{1}{3}+4$.

Answer 1

$$\begin{gathered} 5\frac{1}{6}-3\frac{1}{4}+3\frac{1}{3}+4=\frac{31}{6}-\frac{13}{4}+\frac{10}{3}+4 \\ =\frac{31\times 2}{6\times 2}-\frac{13\times 3}{4\times 3}+\frac{10\times 4}{3\times 4}+\frac{4\times 12}{1\times 12} \\ =\frac{62}{12}-\frac{39}{12}+\frac{40}{12}+\frac{48}{12} \\ =\frac{62+40+48-39}{12} \\ =\frac{111}{12} \\ =\frac{37}{4} \\ =9\frac{1}{4} \end{gathered}$$