To find the quotient of \(\frac{3}{4}\) and \(\frac{5}{6}\), you can follow these steps:
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Dividing by a fraction is equivalent to multiplying by its reciprocal. So, we rewrite the expression: \[ \frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \times \frac{6}{5} \]
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Multiply the fractions: \[ = \frac{3 \times 6}{4 \times 5} = \frac{18}{20} \]
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Simplify the fraction: Both the numerator and the denominator can be divided by 2: \[ = \frac{18 \div 2}{20 \div 2} = \frac{9}{10} \]
Thus, the quotient of \(\frac{3}{4}\) and \(\frac{5}{6}\) is \(\frac{9}{10}\).
The answer is: \(\frac{9}{10}\)