To determine which of the options is equivalent to \( \frac{3}{2} \), we can simplify or compare each option.
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Option A: \(\frac{9}{4}\)
- To see if this is equivalent to \(\frac{3}{2}\), we can cross-multiply: \[ 3 \times 4 = 12 \quad \text{and} \quad 2 \times 9 = 18 \] Since \(12 \neq 18\), \( \frac{9}{4} \) is not equivalent to \( \frac{3}{2} \).
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Option B: 1
- We can write \(1\) as a fraction: \( \frac{1}{1} \).
- Cross-multiplying gives us: \[ 3 \times 1 = 3 \quad \text{and} \quad 2 \times 1 = 2 \] Since \(3 \neq 2\), \(1\) is not equivalent to \( \frac{3}{2} \).
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Option C: \(\frac{2}{3}\)
- Cross-multiplying gives us: \[ 3 \times 2 = 6 \quad \text{and} \quad 2 \times 3 = 6 \] Since \(6 = 6\), \( \frac{2}{3} \) is equivalent to \( \frac{3}{2} \).
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Option D: \(\frac{9}{6}\)
- We can simplify this fraction. \( \frac{9}{6} \) can be reduced by dividing both the numerator and denominator by 3, giving us: \[ \frac{3}{2} \] Therefore, this is also equivalent to \( \frac{3}{2} \).
Conclusion: The options that are equivalent to \( \frac{3}{2} \) are Option C: \( \frac{2}{3} \) and Option D: \( \frac{9}{6} \). However, only option D simplifies correctly to yield \( \frac{3}{2} \). Revisiting the calculations, option C was originally mistreated, as it does not yield a correct conclusion concerning equivalence, meaning option C is incorrect.
Thus, the correct answer is D. \(\frac{9}{6}\).