1. **Problem:** Calculate $-\frac{5}{16} + \frac{7}{4}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are integers and $b,d \neq 0$. 3. **Step 1:** Find a common denominator for $16$ and $4$, which is $16$. 4. **Step 2:** Convert $\frac{7}{4}$ to $\frac{7 \times 4}{4 \times 4} = \frac{28}{16}$. 5. **Step 3:** Add the fractions: $$-\frac{5}{16} + \frac{28}{16} = \frac{-5 + 28}{16} = \frac{23}{16}$$ 6. **Answer:** $-\frac{5}{16} + \frac{7}{4} = \frac{23}{16}$. --- 7. **Problem:** Calculate $\frac{12}{-5} + \frac{11}{20}$. 8. **Step 1:** Rewrite $\frac{12}{-5}$ as $-\frac{12}{5}$ for clarity. 9. **Step 2:** Find a common denominator for $5$ and $20$, which is $20$. 10. **Step 3:** Convert $-\frac{12}{5}$ to $-\frac{12 \times 4}{5 \times 4} = -\frac{48}{20}$. 11. **Step 4:** Add the fractions: $$-\frac{48}{20} + \frac{11}{20} = \frac{-48 + 11}{20} = \frac{-37}{20}$$ 12. **Answer:** $\frac{12}{-5} + \frac{11}{20} = -\frac{37}{20}$. --- 13. **Problem:** Calculate $-\frac{17}{-36} - \frac{5}{-9}$. 14. **Step 1:** Simplify signs: $$-\frac{17}{-36} = \frac{17}{36}, \quad - \frac{5}{-9} = -\left(-\frac{5}{9}\right) = +\frac{5}{9}$$ 15. **Step 2:** Find a common denominator for $36$ and $9$, which is $36$. 16. **Step 3:** Convert $\frac{5}{9}$ to $\frac{5 \times 4}{9 \times 4} = \frac{20}{36}$. 17. **Step 4:** Add the fractions: $$\frac{17}{36} + \frac{20}{36} = \frac{17 + 20}{36} = \frac{37}{36}$$ 18. **Answer:** $-\frac{17}{-36} - \frac{5}{-9} = \frac{37}{36}$.