To determine if the ratios \( \frac{2.5}{10} \) and \( \frac{12}{48} \) or \( \frac{2.5}{2} \) and \( \frac{12}{24} \) are equivalent, we'll simplify each fraction and see if they are equal.
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For \( \frac{2.5}{10} \) and \( \frac{12}{48} \):
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Simplifying \( \frac{2.5}{10} \): \[ \frac{2.5}{10} = \frac{25}{100} = \frac{1}{4} \quad (\text{dividing both numerator and denominator by } 25) \]
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Simplifying \( \frac{12}{48} \): \[ \frac{12}{48} = \frac{1}{4} \quad (\text{dividing both numerator and denominator by } 12) \]
Since \( \frac{1}{4} = \frac{1}{4} \), the two fractions are equivalent. Therefore, \( \frac{2.5}{10} = \frac{12}{48} \) is a proportion.
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For \( \frac{2.5}{2} \) and \( \frac{12}{24} \):
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Simplifying \( \frac{2.5}{2} \): \[ \frac{2.5}{2} = \frac{25}{20} = \frac{5}{4} \quad (\text{dividing both numerator and denominator by } 5) \]
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Simplifying \( \frac{12}{24} \): \[ \frac{12}{24} = \frac{1}{2} \quad (\text{dividing both numerator and denominator by } 12) \]
Since \( \frac{5}{4} \neq \frac{1}{2} \), the two fractions are not equivalent. Therefore, \( \frac{2.5}{2} \neq \frac{12}{24} \) is not a proportion.
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In summary:
- \( \frac{2.5}{10} = \frac{12}{48} \) is a proportion.
- \( \frac{2.5}{2} \neq \frac{12}{24} \) is not a proportion.