1. The problem is to simplify the expression $25 - (16 \times \frac{8}{9})$. 2. According to the order of operations, we first calculate the multiplication inside the parentheses. 3. Multiply $16$ by $\frac{8}{9}$: $$16 \times \frac{8}{9} = \frac{16 \times 8}{9} = \frac{128}{9}$$ 4. Now the expression becomes: $$25 - \frac{128}{9}$$ 5. Convert $25$ to a fraction with denominator $9$ to subtract: $$25 = \frac{25 \times 9}{9} = \frac{225}{9}$$ 6. Subtract the fractions: $$\frac{225}{9} - \frac{128}{9} = \frac{225 - 128}{9} = \frac{97}{9}$$ 7. The simplified result is $\frac{97}{9}$ or approximately $10.78$.