To evaluate the expression \( \frac{3}{2} \div \frac{3}{4} \), you can multiply by the reciprocal of the second fraction. Here are the steps:
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Write the expression: \[ \frac{3}{2} \div \frac{3}{4} \]
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Multiply by the reciprocal of \( \frac{3}{4} \): \[ \frac{3}{2} \times \frac{4}{3} \]
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Multiply the numerators and the denominators: \[ \frac{3 \times 4}{2 \times 3} = \frac{12}{6} \]
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Simplify \( \frac{12}{6} \) by dividing both the numerator and the denominator by 6: \[ \frac{12 \div 6}{6 \div 6} = \frac{2}{1} = 2 \]
Thus, the final simplified answer is: \[ \boxed{2} \]