To find out how much time Carrington has left for the remaining part of the exam, we first need to determine how much time he has used.
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An hour is divided into 2 halves: \[ \text{One-half of an hour} = \frac{1}{2} , \text{hour} \]
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Three-fourths of that half hour: \[ \text{Three-fourths of One-half of an hour} = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8} , \text{hour} \]
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Now, subtract the time used from the total time allotted for the exam, which is one hour: \[ \text{Time left} = 1 , \text{hour} - \frac{3}{8} , \text{hour} \]
To perform this subtraction, convert 1 hour into eighths: \[ 1 , \text{hour} = \frac{8}{8} , \text{hour} \]
Now, subtract: \[ \text{Time left} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} , \text{hour} \]
So Carrington has \(\frac{5}{8}\) of an hour left for the remaining part of the exam.
The answer choices given do not include \(\frac{5}{8}\) of an hour directly, but based on the context, the closest reasoning can state that Carrington effectively still has time left for the remaining portion. However, none of the answer choices directly correspond to \(\frac{5}{8}\) of an hour, which means we might have to infer or reevaluate the choices provided. In this case, you might not be provided the right answer if emphasis is on fractions of hours.
Thus, the conclusion stands - Carrington has \(\frac{5}{8}\) of an hour remaining for the exam.
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