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Let's break down the problem. We are asked to find which of the given expressions are equal to \( 4 \frac{3}{4} \).

First, convert \( 4 \frac{3}{4} \) into an improper fraction:
\[
4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4}
\]

Now let's evaluate each option and check if they match \( \frac{19}{4} \).

---

### **Option A:**
\[
7 \frac{1}{2} - 2 \frac{1}{4}
\]
Convert the mixed numbers into improper fractions:
\[
7 \frac{1}{2} = \frac{14 + 1}{2} = \frac{15}{2}, \quad 2 \frac{1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\]
Now, subtract:
\[
\frac{15}{2} - \frac{9}{4} = \frac{30}{4} - \frac{9}{4} = \frac{30 - 9}{4} = \frac{21}{4}
\]
This does **not** equal \( \frac{19}{4} \).

---

### **Option B:**
\[
1 \frac{7}{16} + 3 \frac{5}{16}
\]
Convert the mixed numbers into improper fractions:
\[
1 \frac{7}{16} = \frac{16 + 7}{16} = \frac{23}{16}, \quad 3 \frac{5}{16} = \frac{48 + 5}{16} = \frac{53}{16}
\]
Now, add:
\[
\frac{23}{16} + \frac{53}{16} = \frac{23 + 53}{16} = \frac{76}{16} = \frac{19}{4}
\]
This **equals** \( \frac{19}{4} \).

---

### **Option C:**
\[
5 \frac{11}{12} - 1 \frac{1}{6}
\]
Convert the mixed numbers into improper fractions:
\[
5 \frac{11}{12} = \frac{60 + 11}{12} = \frac{71}{12}, \quad 1 \frac{1}{6} = \frac{6 + 1}{6} = \frac{7}{6}
\]
Now, subtract:
\[
\frac{71}{12} - \frac{7}{6} = \frac{71}{12} - \frac{14}{12} = \frac{71 - 14}{12} = \frac{57}{12} = \frac{19}{4}
\]
This **equals** \( \frac{19}{4} \).

---

### **Option D:**
\[
2 \frac{1}{4} + 2 \frac{5}{8}
\]
Convert the mixed numbers into improper fractions:
\[
2 \frac{1}{4} = \frac{8 + 1}{4} = \frac{9}{4}, \quad 2 \frac{5}{8} = \frac{16 + 5}{8} = \frac{21}{8}
\]
Now, add:
\[
\frac{9}{4} + \frac{21}{8} = \frac{18}{8} + \frac{21}{8} = \frac{18 + 21}{8} = \frac{39}{8}
\]
This does **not** equal \( \frac{19}{4} \).

---

### Final Answer:
The correct options are **B** and **C**.

Would you like any further explanation or details?

Here are five related questions:
1. How do you convert mixed numbers to improper fractions?
2. How do you subtract fractions with different denominators?
3. What are the steps to convert improper fractions back to mixed numbers?
4. How do you compare fractions with different denominators?
5. What is the process for adding fractions with like denominators?

**Tip:** When working with mixed numbers, always convert them to improper fractions first for easier calculation.

Which of the following expressions are equal to 4 3/4? Select all that apply.

Find out which expressions are equal to 4 3/4 by converting mixed numbers into improper fractions. This test prep question covers converting mixed numbers, adding and subtracting fractions with different denominators, and comparing fractions. Suitable for students in Grades 6-8.

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