3 8/9 : 5

To divide the mixed number \(3 \frac{8}{9}\) by \(5\), we can follow these steps:

1. Convert the mixed number to an improper fraction: \[ 3 \frac{8}{9} = \frac{3 \times 9 + 8}{9} = \frac{27 + 8}{9} = \frac{35}{9} \]

2. Now we need to divide \(\frac{35}{9}\) by \(5\). Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of \(5\) is \(\frac{1}{5}\). \[ \frac{35}{9} \div 5 = \frac{35}{9} \times \frac{1}{5} = \frac{35 \times 1}{9 \times 5} = \frac{35}{45} \]

3. We can simplify \(\frac{35}{45}\) by finding the greatest common divisor (GCD) of \(35\) and \(45\), which is \(5\). \[ \frac{35 \div 5}{45 \div 5} = \frac{7}{9} \]

So, \(3 \frac{8}{9} : 5 = \frac{7}{9}\).