To find the sum of \(-4 \frac{1}{2}\) and \(3 \frac{1}{4}\), let's break the problem down step by step.

1. Convert the mixed numbers to improper fractions:
   - \(-4 \frac{1}{2} = -\frac{9}{2}\)
   - \(3 \frac{1}{4} = \frac{13}{4}\)

2. Find a common denominator for the fractions. The least common denominator between 2 and 4 is 4.
   - Rewrite \(-\frac{9}{2}\) as \(-\frac{18}{4}\).

3. Add the fractions:
   \[
   -\frac{18}{4} + \frac{13}{4} = \frac{-18 + 13}{4} = \frac{-5}{4}
   \]

4. Convert the improper fraction \(\frac{-5}{4}\) to a mixed number:
   \[
   \frac{-5}{4} = -1 \frac{1}{4}
   \]

So, \(-4 \frac{1}{2} + 3 \frac{1}{4} = -1 \frac{1}{4}\).

Would you like a detailed breakdown of any part of the process?

Here are 5 related questions to expand your knowledge:
1. How do you subtract mixed numbers?
2. What is the process of converting improper fractions back to mixed numbers?
3. How do you add fractions with different denominators?
4. Can negative numbers affect the outcome of mixed number addition?
5. How does the concept of absolute value apply to negative fractions?

**Tip:** Always convert mixed numbers to improper fractions first for easier calculations when adding or subtracting.

Learn how to add mixed numbers like −4 1/2 and 3 1/4 using step-by-step guidance. This problem involves converting mixed numbers to improper fractions, finding a common denominator, and converting back to a mixed number. Ideal for students in Grades 5-7.

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