You multiply two halves, the equivalent of four, by four to get a product of 8 halves. Then add the "extra" half from the original "four and one half" to get nine halves.
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One half and four fifths can't be written as improper fractions.
5 1/2 is 11/2 as an improper fraction
improper fraction f0r three wholes and one half = 7/2
improper fraction of 5 and one half = 11/2
3/2