13/6:3/2-1/9

To solve the expression \( \frac{13}{6} : \frac{3}{2} - \frac{1}{9} \), we can follow these steps:

1. Division of Fractions: Dividing by a fraction is the same as multiplying by its reciprocal. So, \[ \frac{13}{6} : \frac{3}{2} = \frac{13}{6} \times \frac{2}{3}. \]

2. Multiply the fractions: \[ \frac{13 \times 2}{6 \times 3} = \frac{26}{18}. \]

3. Simplify \(\frac{26}{18}\): Both 26 and 18 have a common factor of 2. \[ \frac{26 \div 2}{18 \div 2} = \frac{13}{9}. \]

4. Now subtract \(\frac{1}{9}\): \[ \frac{13}{9} - \frac{1}{9} = \frac{13 - 1}{9} = \frac{12}{9}. \]

5. Simplify \(\frac{12}{9}\): Both 12 and 9 have a common factor of 3. \[ \frac{12 \div 3}{9 \div 3} = \frac{4}{3}. \]

Thus, the final result is: \[ \frac{4}{3}. \]