What value will come in place of question mark(?) in the question
4`1/8`+3`2/3`+2`3/4` = ?

Options

A. 19`1/24`
B. 19`11/24`
C. 19`11/16`
D. None of these

Answer

To solve the equation \( 4 \frac{1}{8} + 3 \frac{2}{3} + 2 \frac{3}{4} = ? \), we will first convert the mixed numbers into improper fractions, then add them together, and finally convert the result back into a mixed number if necessary.

### Step 1: Convert mixed numbers to improper fractions

1. **Convert \( 4 \frac{1}{8} \)**:
\[ 4 \frac{1}{8} = \frac{(4 \times 8) + 1}{8} = \frac{32 + 1}{8} = \frac{33}{8} \]

2. **Convert \( 3 \frac{2}{3} \)**:
\[ 3 \frac{2}{3} = \frac{(3 \times 3) + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \]

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: Find a common denominator

The denominators are 8, 3, and 4. The least common multiple (LCM) of these numbers is 24.

### Step 3: Convert each fraction to have the common denominator

1. **Convert \( \frac{33}{8} \)**:
\[ \frac{33}{8} = \frac{33 \times 3}{8 \times 3} = \frac{99}{24} \]

2. **Convert \( \frac{11}{3} \)**:
\[ \frac{11}{3} = \frac{11 \times 8}{3 \times 8} = \frac{88}{24} \]

3. **Convert \( \frac{11}{4} \)**:
\[ \frac{11}{4} = \frac{11 \times 6}{4 \times 6} = \frac{66}{24} \]

### Step 4: Add the fractions

Now we can add the fractions:
\[ \frac{99}{24} + \frac{88}{24} + \frac{66}{24} = \frac{99 + 88 + 66}{24} = \frac{253}{24} \]

### Step 5: Convert the improper fraction back to a mixed number

To convert \( \frac{253}{24} \) back to a mixed number:
1. Divide 253 by 24:
- \( 253 \div 24 = 10 \) remainder \( 13 \)

Thus, we can express it as:
\[ 10 \frac{13}{24} \]

### Final Answer
The value that comes in place of the question mark (?) is:
\[ 10 \frac{13}{24} \]

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