To solve the problem $-3 \frac{7}{10} + 3 \frac{4}{5}$:

Step 1: Convert the mixed numbers to improper fractions.

• For $-3 \frac{7}{10}$: $-3 \frac{7}{10} = -\left(\frac{3 \times 10 + 7}{10}\right) = -\frac{30 + 7}{10} = -\frac{37}{10}$

• For $3 \frac{4}{5}$: $3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5}$

Step 2: Find a common denominator.

The denominators are 10 and 5. The least common denominator (LCD) is 10.

• Convert $\frac{19}{5}$ to have a denominator of 10: $\frac{19}{5} = \frac{19 \times 2}{5 \times 2} = \frac{38}{10}$

Step 3: Add the fractions.

Now add $-\frac{37}{10}$ and $\frac{38}{10}$: $-\frac{37}{10} + \frac{38}{10} = \frac{-37 + 38}{10} = \frac{1}{10}$

So, the final answer is: $\boxed{\frac{1}{10}}$

Would you like any details or have any questions about this solution?

Here are 5 related questions for further practice:

1. Subtract $-3 \frac{7}{10} - 3 \frac{4}{5}$.
2. Add $5 \frac{1}{2} + 2 \frac{3}{4}$.
3. Convert $-2 \frac{2}{3}$ to an improper fraction.
4. Find the sum of $\frac{3}{4} + \frac{2}{5}$ with different denominators.
5. Simplify the fraction $\frac{25}{100}$.

Tip: When dealing with mixed numbers, always convert them to improper fractions for easier addition or subtraction!