2`1/9xx`1`2/19``div`2`1/3`=?

Options

A. 13.09
B. 30.19
C. 93.01
D. 1

Answer

To solve the problem \(2 \frac{1}{9} \times 1 \frac{2}{19} \div 2 \frac{1}{3}\), we will follow these steps:

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

1. **Convert \(2 \frac{1}{9}\)**:
\[ 2 \frac{1}{9} = \frac{2 \times 9 + 1}{9} = \frac{18 + 1}{9} = \frac{19}{9} \]

2. **Convert \(1 \frac{2}{19}\)**:
\[ 1 \frac{2}{19} = \frac{1 \times 19 + 2}{19} = \frac{19 + 2}{19} = \frac{21}{19} \]

3. **Convert \(2 \frac{1}{3}\)**:
\[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

### Step 2: Rewrite the Expression
Now we can rewrite the original expression using the improper fractions:
\[ \frac{19}{9} \times \frac{21}{19} \div \frac{7}{3} \]

### Step 3: Change Division to Multiplication
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
Now we can simplify the expression:
1. The \(19\) in the numerator and denominator cancels out:
\[ \frac{21}{9} \times \frac{3}{7} \]

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

### Step 5: Final Calculation
Now we simplify \(\frac{63}{63}\):
\[ \frac{63}{63} = 1 \]

### Final Answer:
Thus, the answer is:
\[ \boxed{1} \]