To determine if the given ratios are proportional, we check if the cross-products are equal.
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For the proportion \( \frac{2.5}{2} = \frac{12}{24} \):
- Cross-multiply: \[ 2.5 \times 24 = 60 \] \[ 2 \times 12 = 24 \] Since \( 60 \neq 24 \), this means \( \frac{2.5}{2} \neq \frac{12}{24} \).
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For the proportion \( \frac{2.5}{10} = \frac{12}{48} \):
- Cross-multiply: \[ 2.5 \times 48 = 120 \] \[ 10 \times 12 = 120 \] Here, \( 120 = 120 \), which means \( \frac{2.5}{10} = \frac{12}{48} \).
Based on this assessment:
- \( \frac{2.5}{2} = \frac{12}{24} \) is not a proportion.
- \( \frac{2.5}{10} = \frac{12}{48} \) is a proportion.
So the final answer is that one of them is a proportion (specifically \( \frac{2.5}{10} = \frac{12}{48} \)), and the other is not. If the options provided are only "both are proportions" or "neither is a proportion," it would indicate the only valid choice is that neither of the pairs are proportions.
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