To determine which of the given ratios is equivalent to \( \frac{3}{2} \), we can compare each option with \( \frac{3}{2} \).
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Option A: \( 1 \)
\( 1 = \frac{1}{1} \), which is not equivalent to \( \frac{3}{2} \). -
Option B: \( \frac{9}{4} \)
To compare \( \frac{9}{4} \) with \( \frac{3}{2} \), we can find a common denominator (which is 4): \[ \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4} \] Since \( \frac{9}{4} \neq \frac{6}{4} \), these are not equivalent. -
Option C: \( \frac{9}{6} \)
Simplifying \( \frac{9}{6} \): \[ \frac{9}{6} = \frac{3 \times 3}{3 \times 2} = \frac{3}{2} \] So, this option is equivalent to \( \frac{3}{2} \). -
Option D: \( \frac{2}{3} \)
Comparing \( \frac{2}{3} \) with \( \frac{3}{2} \): \( \frac{2}{3} \) is not equivalent to \( \frac{3}{2} \).
Thus, the only option that is equivalent to \( \frac{3}{2} \) is:
C. \( \frac{9}{6} \)