To find the reciprocal of the mixed number \(3 \frac{3}{2}\), we first need to convert it to an improper fraction.
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Convert the mixed number to an improper fraction: \[ 3 \frac{3}{2} = 3 + \frac{3}{2} = \frac{3 \times 2}{2} + \frac{3}{2} = \frac{6}{2} + \frac{3}{2} = \frac{9}{2} \]
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The reciprocal of a fraction is obtained by flipping the numerator and the denominator. So, the reciprocal of \(\frac{9}{2}\) is: \[ \frac{2}{9} \]
Thus, the reciprocal of \(3 \frac{3}{2}\) is \(\frac{2}{9}\).