What should come in place of the question mark (?) in the following questions:
`2 3/5 xx 2 4/13 xx 1 1/3 + 1 7/9 = ? `

Options

A. `2 1/4`
B. `4 1/4`
C. `7/8`
D. None of these

Answer

To solve the equation \(2 \frac{3}{5} \times 2 \frac{4}{13} \times 1 \frac{1}{3} + 1 \frac{7}{9} = ?\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
Convert each mixed number to an improper fraction.

- \(2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}\)
- \(2 \frac{4}{13} = \frac{2 \times 13 + 4}{13} = \frac{26 + 4}{13} = \frac{30}{13}\)
- \(1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3}\)
- \(1 \frac{7}{9} = \frac{1 \times 9 + 7}{9} = \frac{9 + 7}{9} = \frac{16}{9}\)

### Step 2: Multiply the Improper Fractions
Now we will multiply the first three improper fractions together.

\[ \frac{13}{5} \times \frac{30}{13} \times \frac{4}{3} \]

### Step 3: Simplify the Multiplication
When multiplying fractions, we can cancel common factors.

- The \(13\) in the numerator and denominator cancels out:
\[ \frac{1}{5} \times \frac{30}{1} \times \frac{4}{3} = \frac{30 \times 4}{5 \times 3} = \frac{120}{15} \]

### Step 4: Simplify the Result
Now simplify \(\frac{120}{15}\):
\[ \frac{120}{15} = 8 \]

### Step 5: Add the Result to the Last Fraction
Now, we will add \(8\) to \(1 \frac{7}{9}\):
\[ 8 + 1 \frac{7}{9} = 8 + \frac{16}{9} \]

### Step 6: Convert \(8\) to a Fraction with the Same Denominator
Convert \(8\) to a fraction with a denominator of \(9\):
\[ 8 = \frac{8 \times 9}{9} = \frac{72}{9} \]

### Step 7: Add the Two Fractions
Now add \(\frac{72}{9}\) and \(\frac{16}{9}\):
\[ \frac{72}{9} + \frac{16}{9} = \frac{72 + 16}{9} = \frac{88}{9} \]

### Step 8: Convert Back to a Mixed Number
Convert \(\frac{88}{9}\) back to a mixed number:
\[ 88 \div 9 = 9 \quad \text{(with a remainder of 7)} \]
So, \(\frac{88}{9} = 9 \frac{7}{9}\).

### Final Answer
Thus, the answer is:
\[ 9 \frac{7}{9} \]