First, let's convert the mixed numbers to improper fractions to make the calculations easier.
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Convert the total hours worked:
- \( 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2} \) hours.
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Convert the time taken to build one airplane:
- \( 1 + \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5} \) hours.
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Now, we need to find out how many model airplanes Jeremy built. To do this, we'll divide the total hours worked by the hours taken to make one airplane: \[ \text{Number of models} = \frac{\text{Total hours worked}}{\text{Hours per model}} = \frac{\frac{17}{2}}{\frac{7}{5}}. \]
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To divide fractions, multiply by the reciprocal: \[ \frac{17}{2} \times \frac{5}{7} = \frac{17 \times 5}{2 \times 7} = \frac{85}{14}. \]
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Calculating \(\frac{85}{14}\) gives us:
- Dividing \( 85 \) by \( 14 \) gives us \( 6 \) with a remainder:
- \( 85 \div 14 = 6\) with a remainder of \( 1 \):
- So, \( \frac{85}{14} = 6 + \frac{1}{14} \).
Therefore, Jeremy built \( 6 + \frac{1}{14} \) models.
The correct response is:
6 + 1/14 models