What value will come in place of question mark (?) in the questions given below?
`4 3/4 xx 2 1/2 - 2 3/4 = ?`

Options

A. `9 2/16`
B. `7 13/16`
C. `9 9/16`
D. `7 17/19`

Answer

To solve the equation \( 4 \frac{3}{4} \times 2 \frac{1}{2} - 2 \frac{3}{4} = ? \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. **Convert \( 4 \frac{3}{4} \)**:
\[ 4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \]

2. **Convert \( 2 \frac{1}{2} \)**:
\[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]

3. **Convert \( 2 \frac{3}{4} \)**:
\[ 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \]

### Step 2: Substitute the Improper Fractions into the Equation
Now we can rewrite the equation using the improper fractions:
\[ \frac{19}{4} \times \frac{5}{2} - \frac{11}{4} \]

### Step 3: Perform the Multiplication
Next, we multiply the two fractions:
\[ \frac{19}{4} \times \frac{5}{2} = \frac{19 \times 5}{4 \times 2} = \frac{95}{8} \]

### Step 4: Subtract the Fractions
Now we need to subtract \( \frac{11}{4} \) from \( \frac{95}{8} \). To do this, we need a common denominator. The least common multiple (LCM) of 8 and 4 is 8.

1. Convert \( \frac{11}{4} \) to have a denominator of 8:
\[ \frac{11}{4} = \frac{11 \times 2}{4 \times 2} = \frac{22}{8} \]

2. Now perform the subtraction:
\[ \frac{95}{8} - \frac{22}{8} = \frac{95 - 22}{8} = \frac{73}{8} \]

### Step 5: Convert the Result Back to a Mixed Number
To convert \( \frac{73}{8} \) back to a mixed number:
1. Divide 73 by 8:
- 8 goes into 73 a total of 9 times (since \( 8 \times 9 = 72 \)).
- The remainder is \( 73 - 72 = 1 \).

Thus, we can express \( \frac{73}{8} \) as:
\[ 9 \frac{1}{8} \]

### Final Answer
The value that will come in place of the question mark (?) is:
\[ 9 \frac{1}{8} \]

---