To determine if the ratios \( \frac{28}{35} \) and \( \frac{20}{25} \) are proportional, we can use the cross-products method. This method states that two ratios \( \frac{a}{b} \) and \( \frac{c}{d} \) are proportional if and only if the cross-products are equal, i.e., \( a \times d = b \times c \).
Step 1: Set up the ratios
First, identify the values from the ratios:
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For \( \frac{28}{35} \):
- \( a = 28 \)
- \( b = 35 \)
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For \( \frac{20}{25} \):
- \( c = 20 \)
- \( d = 25 \)
Step 2: Calculate the cross-products
Now, we will calculate the cross-products:
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Calculate \( a \times d \): \[ a \times d = 28 \times 25 \]
To calculate \( 28 \times 25 \): \[ 28 \times 25 = 700 \]
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Calculate \( b \times c \): \[ b \times c = 35 \times 20 \]
To calculate \( 35 \times 20 \): \[ 35 \times 20 = 700 \]
Step 3: Compare the cross-products
Since both cross-products are equal, we compare: \[ 28 \times 25 = 700 \quad \text{and} \quad 35 \times 20 = 700 \]
Conclusion
Since \( 28 \times 25 = 35 \times 20 \), the ratios \( \frac{28}{35} \) and \( \frac{20}{25} \) are proportional.
Thus, we conclude that the ratios \( 28:35 \) and \( 20:25 \) represent the same proportional relationship.