Let’s simplify the original expression step by step. The given expression is:

$-7 \frac{3}{5} + 3 \frac{3}{4}$

Step 1: Rewrite the mixed fractions as improper fractions.

$-7 \frac{3}{5} = -\left(\frac{7 \times 5 + 3}{5}\right) = -\frac{38}{5}$ $3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{15}{4}$

So, the expression becomes:

$-\frac{38}{5} + \frac{15}{4}$

Step 2: Find the least common denominator (LCD).

The denominators are 5 and 4. The LCD of 5 and 4 is:

$\text{LCD} = 20$

Step 3: Convert the fractions to have a denominator of 20.

$-\frac{38}{5} = -\frac{38 \times 4}{5 \times 4} = -\frac{152}{20}$ $\frac{15}{4} = \frac{15 \times 5}{4 \times 5} = \frac{75}{20}$

Step 4: Add the fractions.

$-\frac{152}{20} + \frac{75}{20} = \frac{-152 + 75}{20} = \frac{-77}{20}$

Step 5: Match this with the multiple-choice options.

The value of the expression is $-\frac{77}{20}$. Now, let’s analyze the choices:

1. $-7 \frac{3}{5} - 3 \frac{3}{4}$
   This would yield a different value, since both terms are negative. Incorrect.

2. $-3 \frac{3}{4} + \left( -7 \frac{3}{5} \right)$
   This is equivalent to subtracting both terms. Incorrect.

3. $-7 \frac{3}{5} + \left( -3 \frac{3}{4} \right)$
   This implies both terms are negative, which again is incorrect.

4. $3 \frac{3}{4} - 7 \frac{3}{5}$
   This is rearranged but has the same value as the original expression!

Thus, the correct answer is:

$3 \frac{3}{4} - 7 \frac{3}{5}$

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Do you have any further questions, or need more clarification?

Here are five related questions you might be interested in:

1. How do you convert between mixed fractions and improper fractions?
2. What are some strategies for finding the least common denominator?
3. How do you add and subtract fractions with different denominators?
4. How do you handle negative signs when working with mixed numbers?
5. What are some real-world applications of adding and subtracting fractions?

Tip: Always convert mixed fractions to improper fractions before performing operations to avoid confusion.