Multiplicative inverse is a number which when multiplied with another, equals to 1
All you have to do is take the reciprocal of the fraction so for you, the multiplicative inverse would be [tex]\frac{2}{9}[/tex]
We can also solve this using simple algebra.
Here's how:
[tex]\frac{9}{2} * x = 1\\x = \frac{1}{\frac{9}{2}}\\x = 1 * \frac{2}{9}\\x = \frac{2}{9}[/tex]
That's all :D
