What is the missing figure in the expression given ?
`16/7xx16/7- (ox)/7xx9/7+9/7xx9/7=1`

Options

A. 1
B. 7
C. 4.57
D. 32

Answer

To solve the expression \( \frac{16}{7} \times \frac{16}{7} - \frac{(o \times x)}{7} \times \frac{9}{7} + \frac{9}{7} \times \frac{9}{7} = 1 \), we will follow these steps:

### Step 1: Rewrite the expression
We can rewrite the expression for clarity:
\[ \frac{16}{7} \times \frac{16}{7} - \frac{(o \times x)}{7} \times \frac{9}{7} + \frac{9}{7} \times \frac{9}{7} = 1 \]

### Step 2: Calculate the first multiplication
Calculate \( \frac{16}{7} \times \frac{16}{7} \):
\[ \frac{16 \times 16}{7 \times 7} = \frac{256}{49} \]

### Step 3: Calculate the last multiplication
Calculate \( \frac{9}{7} \times \frac{9}{7} \):
\[ \frac{9 \times 9}{7 \times 7} = \frac{81}{49} \]

### Step 4: Substitute back into the expression
Substituting back, we have:
\[ \frac{256}{49} - \frac{(o \times x)}{7} \times \frac{9}{7} + \frac{81}{49} = 1 \]

### Step 5: Combine the fractions
Combine \( \frac{256}{49} \) and \( \frac{81}{49} \):
\[ \frac{256 + 81}{49} - \frac{(o \times x) \times 9}{49} = 1 \]
This simplifies to:
\[ \frac{337}{49} - \frac{(o \times x) \times 9}{49} = 1 \]

### Step 6: Clear the fraction by multiplying through by 49
Multiply every term by 49 to eliminate the denominator:
\[ 337 - 9(o \times x) = 49 \]

### Step 7: Rearrange the equation
Rearranging gives:
\[ 337 - 49 = 9(o \times x) \]
\[ 288 = 9(o \times x) \]

### Step 8: Solve for \( o \times x \)
Divide both sides by 9:
\[ o \times x = \frac{288}{9} = 32 \]

### Conclusion
Thus, the missing figure \( o \times x \) is equal to 32.