To determine if the ratios form a proportion, we need to check if the cross-products are equal for each pair of fractions. A proportion is established if \( \frac{a}{b} = \frac{c}{d} \), which implies that \( a \cdot d = b \cdot c \).
Let's analyze each case:
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For \( \frac{2.25}{10} \) and \( \frac{9}{40} \):
- Cross-multiplying gives: \[ 2.25 \cdot 40 \quad \text{and} \quad 10 \cdot 9 \]
- Calculate: \[ 2.25 \cdot 40 = 90 \] \[ 10 \cdot 9 = 90 \]
- Since \( 90 = 90 \), this is a proportion.
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For \( \frac{2.5}{10} \) and \( \frac{90}{40} \):
- Cross-multiplying gives: \[ 2.5 \cdot 40 \quad \text{and} \quad 10 \cdot 90 \]
- Calculate: \[ 2.5 \cdot 40 = 100 \] \[ 10 \cdot 90 = 900 \]
- Since \( 100 \neq 900 \), this is not a proportion.
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For \( \frac{2.25}{12} \) and \( \frac{90}{40} \):
- Cross-multiplying gives: \[ 2.25 \cdot 40 \quad \text{and} \quad 12 \cdot 90 \]
- Calculate: \[ 2.25 \cdot 40 = 90 \] \[ 12 \cdot 90 = 1080 \]
- Since \( 90 \neq 1080 \), this is not a proportion.
Summary:
- Proportion found: \( \frac{2.25}{10} = \frac{9}{40} \)
- Not proportions: \( \frac{2.5}{10} = \frac{90}{40} \), \( \frac{2.25}{12} = \frac{90}{40} \)
Final answer: None of these sets of ratios is a proportion, except for the first one. However, since the question was whether any of the sets are a proportion, the solution is:
2.25/10 = 9/40 is a proportion.