4/45 x 9-2/3 :5

To solve the expression \( \frac{4}{45} \times 9 \frac{2}{3} \div 5 \), we will first convert the mixed number \( 9 \frac{2}{3} \) into an improper fraction and then perform the operations step by step.

1. Convert the mixed number \( 9 \frac{2}{3} \): \[ 9 \frac{2}{3} = 9 + \frac{2}{3} = \frac{27}{3} + \frac{2}{3} = \frac{29}{3} \]

2. Now we rewrite the expression: \[ \frac{4}{45} \times \frac{29}{3} \div 5 \]

3. Convert division by 5 into multiplication by the reciprocal of 5: \[ \div 5 = \times \frac{1}{5} \] So, we rewrite the expression: \[ \frac{4}{45} \times \frac{29}{3} \times \frac{1}{5} \]

4. Multiply the fractions: \[ = \frac{4 \times 29 \times 1}{45 \times 3 \times 5} \] \[ = \frac{116}{675} \]

5. Simplify the fraction if possible: The GCD of 116 and 675 is 1, so \( \frac{116}{675} \) is in simplest form.

Thus, the final answer is: \[ \frac{116}{675} \]