What should come in place of question mark
`(2)1/9xx(1)2/19div(2)1/3=?-(1)1/2`

Options

A. (3)1/2
B. (1)1/4
C. (2)1/2
D. (2)1/4

Answer

To solve the equation \( (2)1/9 \times (1)2/19 \div (2)1/3 = ? - (1)1/2 \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( (2)1/9 \) to an improper fraction:
\[ (2)1/9 = \frac{2 \times 9 + 1}{9} = \frac{18 + 1}{9} = \frac{19}{9} \]

2. Convert \( (1)2/19 \) to an improper fraction:
\[ (1)2/19 = \frac{1 \times 19 + 2}{19} = \frac{19 + 2}{19} = \frac{21}{19} \]

3. Convert \( (2)1/3 \) to an improper fraction:
\[ (2)1/3 = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

4. Convert \( (1)1/2 \) to an improper fraction:
\[ (1)1/2 = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \]

### Step 2: Substitute the Improper Fractions into the Equation
Now we substitute the improper fractions back into the equation:
\[ \frac{19}{9} \times \frac{21}{19} \div \frac{7}{3} = ? - \frac{3}{2} \]

### Step 3: Perform the Division
To divide by a fraction, we multiply by its reciprocal:
\[ \frac{19}{9} \times \frac{21}{19} \times \frac{3}{7} \]

### Step 4: Simplify the Expression
1. Cancel \( 19 \) in the numerator and denominator:
\[ \frac{21}{9} \times \frac{3}{7} \]

2. Now, multiply the fractions:
\[ \frac{21 \times 3}{9 \times 7} = \frac{63}{63} = 1 \]

### Step 5: Set Up the Equation
Now we have:
\[ 1 = ? - \frac{3}{2} \]

### Step 6: Solve for the Question Mark
To find \( ? \), we add \( \frac{3}{2} \) to both sides:
\[ ? = 1 + \frac{3}{2} \]

### Step 7: Convert 1 to a Fraction
Convert \( 1 \) to a fraction with a common denominator:
\[ 1 = \frac{2}{2} \]
Thus,
\[ ? = \frac{2}{2} + \frac{3}{2} = \frac{5}{2} \]

### Step 8: Convert Back to Mixed Number
Convert \( \frac{5}{2} \) back to a mixed number:
\[ \frac{5}{2} = 2 \frac{1}{2} \]

### Final Answer
The value that should come in place of the question mark is:
\[ 2 \frac{1}{2} \]