Half (as noun) = one of two equal parts of a divisible whole: ‘Half an hour’
Half (as adjective) = partial: ‘He did only a half job.’
Do not use the before half except when talking about a particular half: ‘He spends half the week playing golf’, ‘I fell asleep during the second half of the concert.’
Number + and a half (NOT and half): ‘She can swim two lengths of the pool in four and a half minutes.’