Pregunta
Which one of the following statements expresses a true proportion? A) \( 3: 4=9: 12 \) B) \( 2: 1=1: 2 \) C) \( 54: 9=6: 3 \) D) \( 7: 9=9.9 \)
Ask by Best Bowers. in the United States
Feb 13,2025
Solución de inteligencia artificial de Upstudy
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Option A (\(3:4 = 9:12\)) is the true proportion.
Solución
A proportion states that two ratios are equal. Let's check each option:
A) 3:4 = 9:12
Convert to fractions: 3/4 = 0.75 and 9/12 = 0.75.
Since both fractions are equal, this is a true proportion.
B) 2:1 = 1:2
Convert to fractions: 2/1 = 2 and 1/2 = 0.5.
These are not equal, so this is not a true proportion.
C) 54:9 = 6:3
Convert to fractions: 54/9 = 6 and 6/3 = 2.
Since 6 does not equal 2, this is not a true proportion.
D) 7:9 = 9.9
This statement is incomplete or improperly formatted, as the second ratio isn’t clearly defined.
Even interpreting it as 7/9 = 9.9, they are not equal.
Thus, the only statement that expresses a true proportion is option A.
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Simplifique esta solución Extra Insights
To determine which statement expresses a true proportion, we can check if the ratios on either side of the equation are equivalent. A) \( 3:4 = 9:12 \) simplifies to \( 3/4 = 9/12 \), which is true since \( 9/12 \) simplifies to \( 3/4 \). B) \( 2:1 = 1:2 \) simplifies to \( 2/1 \neq 1/2 \), which is false. C) \( 54:9 = 6:3 \) simplifies to \( 54/9 = 6/3 \), which is also true since both equal 6. D) \( 7:9 = 9.9 \) doesn't provide a clear comparison since it lacks a second term to make it a proper ratio. Therefore, both A and C express true proportions, but A is a concise representation affirming the equality of fractions.
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