I
noun
BAD : He agreed to give her the half of the money.
GOOD : He agreed to give her half of the money.
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Do not use the before half except when talking about a particular half. Compare: 'He spends half the week playing golf.' 'During the second half of the concert I could hardly stay awake.'
II
pronoun
1
BAD : We will stay in Bangkok for two and half days.
GOOD : We will stay in Bangkok for two and a half days.
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number + and a half (NOT and half ): 'She can swim two lengths of the pool in four and a half minutes.'
2
BAD : We have a break of one and a half hour for lunch.
GOOD : We have a break of one and a half hours for lunch.
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number greater than one + plural form: 'three and a half minutes', 'twelve and a half miles'
Note the alternative: 'We have a one and a half hour break for lunch.'