a)
[tex] \frac{1}{2} \div \frac{1}{3} \div \frac{1}{6} = \frac{1}{2} \times \frac{3}{1} \times \frac{6}{1} = \frac{18}{2} = 9[/tex]
b)
[tex] \frac{1}{2} \div ( \frac{1}{3} \div \frac{1}{6} ) = \frac{1}{2} \div ( \frac{1}{3} \times \frac{6}{1} ) = \frac{1}{2} \div \frac{6}{3} = \frac{1}{2} \times \frac{3}{6} = \frac{3}{12} = \frac{1}{4} [/tex]
c)
[tex] \frac{1}{2} \div ( \frac{1}{3} + \frac{1}{6} ) = \frac{1}{2} \div ( \frac{2}{6} + \frac{1}{6} ) = \frac{1}{2} \div \frac{3}{6} = \frac{1}{2} \times \frac{6}{3} = \frac{6}{6} = 1[/tex]
d)
[tex]( \frac{1}{2} + \frac{1}{3} ) \div \frac{1}{6} =( \frac{3}{6} + \frac{2}{6} ) \times \frac{6}{1} = \frac{5}{6} \times \frac{6}{1} = \frac{30}{6} = 5[/tex]
e)
[tex]( \frac{1}{2} - \frac{1}{3} ) \div \frac{1}{6} = ( \frac{3}{6} - \frac{2}{6} ) \times \frac{6}{1} = \frac{1}{6} \times \frac{6}{1} = \frac{6}{6} = 1[/tex]
f)
[tex] \frac{1}{2} \times \frac{1}{3} \div \frac{1}{6} = \frac{1}{6} \times \frac{6}{1} = \frac{6}{6} = 1[/tex]
