We need to find the missing fraction in the equation $21\frac{2}{9} - \frac{\square}{\square} = 10\frac{8}{9}$ and express the answer in the form of a mixed number.

1. Problem Description

We need to find the missing fraction in the equation $21\frac{2}{9} - \frac{\square}{\square} = 10\frac{8}{9}$ and express the answer in the form of a mixed number.

2. Solution Steps

First, let the missing fraction be $x$.

So, the equation becomes $21\frac{2}{9} - x = 10\frac{8}{9}$.

We can rewrite the equation to solve for $x$:

$x = 21\frac{2}{9} - 10\frac{8}{9}$.

To subtract mixed numbers, we can subtract the whole numbers and the fractions separately.

So, $x = (21-10) + (\frac{2}{9} - \frac{8}{9})$.

$x = 11 + (\frac{2-8}{9})$.

$x = 11 + (\frac{-6}{9})$.

Since the fraction part is negative, we need to borrow 1 from the whole number part.

$x = 10 + 1 + (\frac{-6}{9})$.

$x = 10 + \frac{9}{9} + \frac{-6}{9}$.

$x = 10 + \frac{9-6}{9}$.

$x = 10 + \frac{3}{9}$.

$x = 10\frac{3}{9}$.

Simplify the fraction: $\frac{3}{9} = \frac{1}{3}$.

$x = 10\frac{1}{3}$.

3. Final Answer

$10\frac{1}{3}$