To determine whether \( \frac{2.5}{10} = \frac{12}{48} \) or \( \frac{2.5}{2} = \frac{12}{48} \) is a proportion, we need to simplify both fractions and see if they are equal.
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For \( \frac{2.5}{10} \):
\[ \frac{2.5}{10} = \frac{25}{100} = \frac{1}{4} \quad \text{(dividing both numerator and denominator by 25)} \]
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For \( \frac{12}{48} \):
\[ \frac{12}{48} = \frac{1}{4} \quad \text{(dividing both numerator and denominator by 12)} \]
Now we can compare the two:
\[ \frac{2.5}{10} = \frac{1}{4} \quad \text{and} \quad \frac{12}{48} = \frac{1}{4} \]
Since both fractions simplify to \( \frac{1}{4} \), we have:
\[ \frac{2.5}{10} = \frac{12}{48} \]
Therefore, \( \frac{2.5}{10} \) is equal to \( \frac{12}{48} \).
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Now for \( \frac{2.5}{2} \):
\[ \frac{2.5}{2} = 1.25 \]
As a decimal, we can also express \( \frac{12}{48} \):
\[ \frac{12}{48} = \frac{1}{4} = 0.25 \]
Since \( 1.25 \neq 0.25 \), we find that:
\[ \frac{2.5}{2} \neq \frac{12}{48} \]
Conclusion:
- \( \frac{2.5}{10} = \frac{12}{48} \) is a proportion.
- \( \frac{2.5}{2} = \frac{12}{48} \) is not a proportion.
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