Let's solve the given problem:

We are tasked to calculate $\frac{7}{2} + \frac{3}{4}$ and express the answer as a fraction in its simplest form.

Steps:

1. Find the least common denominator (LCD): The denominators are 2 and 4. The least common denominator is 4.

2. Convert fractions to have the same denominator:

   • For $\frac{7}{2}$, multiply numerator and denominator by 2: $\frac{7}{2} = \frac{14}{4}$
   • $\frac{3}{4}$ already has the denominator 4.

3. Add the fractions: $\frac{14}{4} + \frac{3}{4} = \frac{14 + 3}{4} = \frac{17}{4}$

4. Express as a mixed number (if needed): $\frac{17}{4} = 4 \, \text{remainder} \, 1 = 4 \frac{1}{4}$

Final Answer:

The answer is: $\boxed{\frac{17}{4}}$ or as a mixed number: $\boxed{4 \frac{1}{4}}$

Would you like to explore more about fractions or mixed numbers?

Relative Questions:

1. How can we find the least common denominator for more complex fractions?
2. What are some strategies to convert improper fractions to mixed numbers?
3. How do you simplify fractions with large numerators and denominators?
4. How do fractions apply in real-life scenarios such as cooking or measurement?
5. What is the difference between proper, improper, and mixed fractions?

Tip:

Always simplify fractions at the end of your calculation to ensure the answer is in its simplest form!