To find the quotient of \( \frac{5}{6} \) divided by \( 1 \frac{1}{2} \), we first need to convert \( 1 \frac{1}{2} \) to an improper fraction.
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Convert \( 1 \frac{1}{2} \): \[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \]
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Now we can rewrite the division as multiplication by the reciprocal: \[ \frac{5}{6} \div \frac{3}{2} = \frac{5}{6} \times \frac{2}{3} \]
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Multiply the fractions: \[ \frac{5 \times 2}{6 \times 3} = \frac{10}{18} \]
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Simplify \( \frac{10}{18} \): Both the numerator and the denominator can be divided by 2. \[ \frac{10 \div 2}{18 \div 2} = \frac{5}{9} \]
Thus, the quotient of \( \frac{5}{6} \div 1 \frac{1}{2} \) in simplified fraction form is \( \frac{5}{9} \).