What value will come in place of question mark(?) in the question
`413/576 xx 32/59 xx ?`= 1`1/4`

Options

A. 3`1/7`
B. 3`3/14`
C. 3`2/7`
D. 3`1/5`

Answer

To solve the equation \( \frac{413}{576} \times \frac{32}{59} \times ? = 1 \frac{1}{4} \), we need to find the value of the question mark (?). Let's break it down step by step.

### Step 1: Convert the mixed number to an improper fraction
First, we convert \( 1 \frac{1}{4} \) to an improper fraction.

\[ 1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} \]

### Step 2: Set up the equation
Now we can rewrite the equation using the improper fraction:

\[ \frac{413}{576} \times \frac{32}{59} \times ? = \frac{5}{4} \]

### Step 3: Isolate the question mark
To find the value of ?, we can isolate it by dividing both sides of the equation by \( \frac{413}{576} \times \frac{32}{59} \):

\[ ? = \frac{5}{4} \div \left( \frac{413}{576} \times \frac{32}{59} \right) \]

### Step 4: Rewrite the division as multiplication
Dividing by a fraction is the same as multiplying by its reciprocal:

\[ ? = \frac{5}{4} \times \frac{576 \times 59}{413 \times 32} \]

### Step 5: Simplify the expression
Now we can simplify the right side. Let's calculate \( \frac{576 \times 59}{413 \times 32} \):

1. Calculate \( 576 \div 32 = 18 \)
2. Now we have \( ? = \frac{5}{4} \times \frac{18 \times 59}{413} \)

### Step 6: Calculate \( 18 \times 59 \)
Now calculate \( 18 \times 59 \):

\[ 18 \times 59 = 1062 \]

### Step 7: Substitute back into the equation
Now substitute back into the equation:

\[ ? = \frac{5}{4} \times \frac{1062}{413} \]

### Step 8: Simplify further
Now we can simplify \( \frac{5 \times 1062}{4 \times 413} \):

1. Calculate \( 5 \times 1062 = 5310 \)
2. Calculate \( 4 \times 413 = 1652 \)

So we have:

\[ ? = \frac{5310}{1652} \]

### Step 9: Reduce the fraction
Now we can reduce \( \frac{5310}{1652} \) to its simplest form.

After calculating the GCD, we find that:

\[ ? = \frac{45}{14} \]

### Step 10: Convert to mixed number
Finally, convert \( \frac{45}{14} \) to a mixed number:

\[ 45 \div 14 = 3 \quad \text{(remainder 3)} \]

So,

\[ ? = 3 \frac{3}{14} \]

### Final Answer
Thus, the value that comes in place of the question mark (?) is \( 3 \frac{3}{14} \).

---