To determine if the given ratios are equal, we can simplify both sides of the proposed equalities.
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First comparison: \( \frac{2.5}{10} \) and \( \frac{12}{48} \)
Let's simplify both fractions:
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For \( \frac{2.5}{10} \): \[ \frac{2.5}{10} = \frac{25}{100} = \frac{1}{4} \quad (\text{by multiplying numerator and denominator by 10}) \]
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For \( \frac{12}{48} \): \[ \frac{12}{48} = \frac{1}{4} \quad (\text{by dividing numerator and denominator by 12}) \]
Since \( \frac{2.5}{10} = \frac{1}{4} \) and \( \frac{12}{48} = \frac{1}{4} \), we have: \[ \frac{2.5}{10} = \frac{12}{48} \]
Therefore, the first comparison is a proportion.
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Second comparison: \( \frac{2.5}{2} \) and \( \frac{12}{24} \)
Let's simplify both fractions:
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For \( \frac{2.5}{2} \): \[ \frac{2.5}{2} = 1.25 \]
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For \( \frac{12}{24} \): \[ \frac{12}{24} = \frac{1}{2} \quad (\text{by dividing numerator and denominator by 12}) \]
Since \( 1.25 \) is not equal to \( 0.5 \), we have: \[ \frac{2.5}{2} \neq \frac{12}{24} \]
Therefore, the second comparison 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.