What is the value of expression $8\frac{5}{6}-3\frac{3}{8}+1\frac{7}{12}?$

The given expression is $8\frac{5}{6}-3\frac{3}{8}+1\frac{7}{12}$.
 

On simplifying, we get:

$8\frac{5}{6}-3\frac{3}{8}+1\frac{7}{12}$

$=\frac{\left(6\times 8\right)+5}{6}-\frac{\left(8\times 3\right)+3}{8}+\frac{\left(12\times 1\right)+7}{12}$

$=\frac{53}{6}-\frac{27}{8}+\frac{19}{12}$

$=\frac{\left(53\times 4\right)-\left(27\times 3\right)+\left(19\times 2\right)}{24}$  [L.C.M. (6,8,12) = 24]

$=\frac{212-81+38}{24}$

$=\frac{169}{24}$

$=\mathbf{7}\frac{\mathbf{1}}{\mathbf{24}}$

Therefore, the value of expression $8\frac{5}{6}-3\frac{3}{8}+1\frac{7}{12}$is $\mathbf{7}\frac{\mathbf{1}}{\mathbf{24}}$.