https://file.aiquickdraw.com/mathbot/file/1727352545679ktimt2sp.jpg

The expression from the image is:

\[
-5 \frac{1}{3} - \left( -7 \frac{1}{4} \right)
\]

### Step-by-step solution:

1. **Convert the mixed numbers to improper fractions**:
   - \( -5 \frac{1}{3} = -\left( \frac{5 \times 3 + 1}{3} \right) = -\frac{16}{3} \)
   - \( -7 \frac{1}{4} = -\left( \frac{7 \times 4 + 1}{4} \right) = -\frac{29}{4} \)

2. **Simplify the expression**:
   \[
   -\frac{16}{3} - (-\frac{29}{4}) = -\frac{16}{3} + \frac{29}{4}
   \]

3. **Find a common denominator**:
   - The least common denominator (LCD) between 3 and 4 is 12.

   Rewrite both fractions with denominator 12:
   \[
   -\frac{16}{3} = -\frac{64}{12}, \quad \frac{29}{4} = \frac{87}{12}
   \]

4. **Add the fractions**:
   \[
   -\frac{64}{12} + \frac{87}{12} = \frac{-64 + 87}{12} = \frac{23}{12}
   \]

Thus, the result is:

\[
\frac{23}{12}
\]

This can also be expressed as a mixed number:

\[
1 \frac{11}{12}
\]

Let me know if you'd like further clarification or additional steps.

Here are 5 related questions you might find interesting:
1. How do you convert a mixed number into an improper fraction?
2. What are the steps to add fractions with different denominators?
3. What is the importance of finding the least common denominator in fraction addition?
4. How do you convert improper fractions back to mixed numbers?
5. How can you simplify complex expressions involving negative mixed numbers?

**Tip:** Always be careful with the signs when adding and subtracting negative numbers to avoid errors.

Learn how to solve the mixed number expression -5 1/3 - (-7 1/4) with a step-by-step solution. This guide covers converting mixed numbers to improper fractions, finding the least common denominator, and adding or subtracting fractions. Suitable for students in Grades 6-8.

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