To determine how much money Christian is giving to his brother for graduation, we can follow these steps:
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Calculate the amount he has left after paying his neighbor: \[ \text{Amount left} = \text{Total amount} - \text{Amount owed to neighbor} = 600 - 45 = 555 \text{ dollars} \]
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Determine half of the amount left: \[ \text{Gift for brother} = \frac{1}{2} \times \text{Amount left} = \frac{1}{2} \times 555 = 277.50 \text{ dollars} \]
Thus, Christian is giving his brother $277.50 for graduation.