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If you would like to write 4/4.5 in the simplest form, you can do this using the following steps:

4.5 = 4 5/10 = 4 1/2 = 9/2
4/4.5 = 4/(9/2) = 4/1 * 2/9 = 8/9

The correct result would be 8/9.
[tex] \frac{8}{9} [/tex]

First remove the decimal in the denominator by multiply both numerator and denominator by 10.
Then simply dividing both numerator and denominator by 5