1. **State the problem:** Simplify the expression $-\left(-\frac{7}{9}\right) - \sqrt{\frac{49}{100}}$. 2. **Recall the rules:** - The negative of a negative number is positive: $-(-a) = a$. - The square root of a fraction is the fraction of the square roots: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$. 3. **Simplify each part:** - For $-\left(-\frac{7}{9}\right)$, this becomes $\frac{7}{9}$. - For $\sqrt{\frac{49}{100}}$, calculate $\frac{\sqrt{49}}{\sqrt{100}} = \frac{7}{10}$. 4. **Combine the results:** $$\frac{7}{9} - \frac{7}{10}$$ 5. **Find a common denominator:** The least common denominator of 9 and 10 is 90. $$\frac{7}{9} = \frac{7 \times 10}{90} = \frac{70}{90}$$ $$\frac{7}{10} = \frac{7 \times 9}{90} = \frac{63}{90}$$ 6. **Subtract the fractions:** $$\frac{70}{90} - \frac{63}{90} = \frac{70 - 63}{90} = \frac{7}{90}$$ 7. **Final answer:** $$\boxed{\frac{7}{90}}$$