To solve $-\frac{33}{4} + \frac{45}{8}$, follow these steps:

1. Find a common denominator. The least common denominator (LCD) between 4 and 8 is 8.
2. Rewrite the fractions with the common denominator: $-\frac{33}{4} = -\frac{66}{8}$
3. Now, you can add the fractions: $-\frac{66}{8} + \frac{45}{8} = \frac{-66 + 45}{8} = \frac{-21}{8}$
4. So, the final answer is: $-\frac{21}{8}$ This can also be written as $-2\frac{5}{8}$ in mixed number form.

Would you like any further details on this process?

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Here are 5 related questions for practice:

1. $-\frac{15}{3} + \frac{20}{5}$
2. $\frac{9}{2} - \frac{7}{4}$
3. $\frac{18}{9} + \frac{5}{6}$
4. $-\frac{25}{8} + \frac{17}{4}$
5. $\frac{33}{10} - \frac{23}{5}$

Tip: When adding or subtracting fractions, always ensure both fractions have the same denominator before performing the operation.