To simplify the expression \(3:9 \cdot 29465\), first convert the ratio into a fraction. The ratio \(3:9\) can be written as \(\frac{3}{9}\).
Now simplify \(\frac{3}{9}\):
\[ \frac{3}{9} = \frac{1}{3} \]
Now multiply this fraction by \(29465\):
\[ \frac{1}{3} \cdot 29465 = \frac{29465}{3} \]
Now, perform the division:
\[ 29465 \div 3 = 9821.6667 \text{ (approximately)} \]
Thus,
\[ 3:9 \cdot 29465 \approx 9821.67 \]
If you need a more exact answer, the value is \(9821\) with a remainder.
Alternatively, \(29465\) divided by \(3\) gives \(9821\) with a remainder of \(2\), which means you can express the result as:
\[ 9821 \frac{2}{3} \text{ or } 9821.67 \]