What will come in place of question mark (?) in the given questions?
`3'1/8+2'5/24=?`

Options

A. `6'1/3`
B. `5'1/3`
C. `6'1/8`
D. `5'3/4`

Answer

To solve the problem \( 3 \frac{1}{8} + 2 \frac{5}{24} = ? \), we will follow these steps:

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

For \( 3 \frac{1}{8} \):
\[ 3 \frac{1}{8} = \frac{(3 \times 8) + 1}{8} = \frac{24 + 1}{8} = \frac{25}{8} \]

For \( 2 \frac{5}{24} \):
\[ 2 \frac{5}{24} = \frac{(2 \times 24) + 5}{24} = \frac{48 + 5}{24} = \frac{53}{24} \]

### Step 2: Find a Common Denominator
Next, we need to find a common denominator to add the two fractions. The denominators are 8 and 24. The least common multiple (LCM) of 8 and 24 is 24.

### Step 3: Convert the First Fraction
Now we convert \( \frac{25}{8} \) to have a denominator of 24:
\[ \frac{25}{8} = \frac{25 \times 3}{8 \times 3} = \frac{75}{24} \]

### Step 4: Add the Fractions
Now we can add the two fractions:
\[ \frac{75}{24} + \frac{53}{24} = \frac{75 + 53}{24} = \frac{128}{24} \]

### Step 5: Simplify the Result
Now we simplify \( \frac{128}{24} \):
\[ \frac{128 \div 8}{24 \div 8} = \frac{16}{3} \]

### Step 6: Convert to Mixed Number
Finally, we convert \( \frac{16}{3} \) back to a mixed number:
\[ 16 \div 3 = 5 \quad \text{(whole number)} \quad \text{with a remainder of } 1 \]
So, \( \frac{16}{3} = 5 \frac{1}{3} \).

Thus, the answer is:
\[ ? = 5 \frac{1}{3} \]

---