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$4 \frac{1}{2} :6= \frac{9}{2} * \frac{1}{6} = \frac{9}{12} = \frac{3}{4}$
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$5 \frac{1}{4} :7= \frac{21}{4} * \frac{1}{7} = \frac{3}{4}$
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$5 \frac{1}{7} :12= \frac{36}{7} * \frac{1}{12} = \frac{3}{7}$
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$6 \frac{1}{2} :1 \frac{6}{7} = \frac{13}{2} : \frac{13}{7} = \frac{13}{2} * \frac{7}{13} = \frac{7}{2} =3 \frac{1}{2}$
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$6 \frac{2}{3} :2 \frac{7}{9} = \frac{20}{3} : \frac{25}{9} = \frac{20}{3} * \frac{9}{25} = \frac{12}{5} =2 \frac{2}{5}$