Let's analyze the student's work step by step to find the error.
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Convert ounces to pounds: The correct conversion from ounces to pounds is: \[ 1 \text{ pound} = 16 \text{ ounces} \Rightarrow \frac{1 \text{ pound}}{16 \text{ ounces}}. \] To convert ounces to pounds, you should multiply by \(\frac{1 \text{ pound}}{16 \text{ ounces}}\).
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Convert pounds to kilograms: The correct conversion from pounds to kilograms is: \[ 1 \text{ kilogram} = 2.2 \text{ pounds} \Rightarrow \frac{1 \text{ kilogram}}{2.2 \text{ pounds}}. \] To convert pounds to kilograms, you also need to use the conversion factor correctly, which typically would involve multiplying by \(\frac{1 \text{ kilogram}}{2.2 \text{ pounds}}\).
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Need to convert grams to kilograms: Since \(1 \text{ kilogram} = 1,000 \text{ grams}\), if you are converting to kilograms directly, you would indeed need to incorporate a step to convert grams to kilograms if you were calculating grams first.
Now, looking at what the student did:
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The student used \( \frac{16 \text{ pounds}}{1 \text{ ounce}} \) instead of \( \frac{1 \text{ pound}}{16 \text{ ounces}} \) to convert ounces to pounds. This is incorrect.
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The student does attempt to convert pounds to kilograms using \( \frac{1 \text{ kilogram}}{2.2 \text{ pounds}} \), which is technically correct for the conversion from pounds to kilograms.
However, since the conversion from ounces to pounds was performed incorrectly, the immediate error in the process led to the wrong result.
Therefore, the answer is: The student multiplied by \( \frac{16 \text{ pounds}}{1 \text{ ounce}} \) instead of \( \frac{1 \text{ pound}}{16 \text{ ounces}} \).
1 answer