The expression \( \frac{3}{5} \div -\frac{2}{5} \) represents a division scenario that is typically involved in comparing how many times one quantity is larger than another, especially when the second quantity is negative.
Looking at the options:
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A describes a comparison of how much land is used for different purposes, which involves subtraction, not division.
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B describes a situation where we want to find out how many times further down the miner went on the second day compared to the first day. This scenario matches the division of two quantities.
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C also involves a comparison between the tuna and sardine, but it incorrectly states a division that results in the sardine being further down than the tuna, leading to an inappropriate use of the negative sign.
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D compares time spent studying versus watching television. Again, this involves subtraction rather than division.
The correct answer is B: "On the first day of mining a metal, a miner goes \( \frac{2}{5} \) of a kilometer below ground level. On the second day, he goes \( \frac{3}{5} \) of a kilometer below ground level. How many times further below ground level does the miner go on the second day than on the first day?"
This scenario is appropriately modeled by the expression \( \frac{3}{5} \div -\frac{2}{5} \).
11 answers