Compute. \( \frac{7}{3} \cdot\left(\frac{2}{3}-\frac{2}{9}\right) \) Answer:

To compute the expression: \[ \frac{7}{3} \cdot \left( \frac{2}{3} - \frac{2}{9} \right) \] Let's follow the steps below: 1. **Subtract the Fractions Inside the Parentheses:** \[ \frac{2}{3} - \frac{2}{9} \] To subtract these fractions, find a common denominator. The least common denominator (LCD) of 3 and 9 is 9. - Convert \(\frac{2}{3}\) to a denominator of 9: \[ \frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9} \] - Now subtract: \[ \frac{6}{9} - \frac{2}{9} = \frac{4}{9} \] 2. **Multiply by \(\frac{7}{3}\):** \[ \frac{7}{3} \cdot \frac{4}{9} \] Multiply the numerators and the denominators: \[ \frac{7 \times 4}{3 \times 9} = \frac{28}{27} \] 3. **Simplify the Result (if necessary):** The fraction \(\frac{28}{27}\) is an improper fraction and can be expressed as a mixed number: \[ \frac{28}{27} = 1 \frac{1}{27} \] However, it's often acceptable to leave the answer as an improper fraction. **Final Answer:** \[ \frac{28}{27} \]