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a) $\frac{1}{6} \times \frac{2}{3} = \frac{{1 \times 2}}{{6 \times 3}} = \frac{2}{{18}} = \frac{1}{9}$
b) $\frac{6}{5} \times \frac{3}{8} = \frac{{6 \times 3}}{{5 \times 8}} = \frac{{18}}{{40}} = \frac{9}{{20}}$
c) $\frac{4}{3} \times \frac{8}{9} = \frac{{4 \times 8}}{{3 \times 9}} = \frac{{32}}{{27}}$
d) $\frac{5}{{12}} \times \frac{{12}}{5} = \frac{{5 \times 12}}{{12 \times 5}} = \frac{{60}}{{60}} = 1$
a) $\frac{1}{6} + \frac{2}{3} = \frac{1}{6} + \frac{4}{6} = \frac{{1 + 4}}{6} = \frac{5}{6}$
b) $\frac{3}{5} + \frac{9}{{20}} = \frac{{12}}{{20}} + \frac{9}{{20}} = \frac{{12 + 9}}{{20}} = \frac{{21}}{{20}}$
c) $\frac{3}{8} + \frac{3}{{24}} = \frac{9}{{24}} + \frac{3}{{24}} = \frac{{9 + 3}}{{24}} = \frac{{12}}{{24}} = \frac{1}{2}$
a) $\frac{1}{6}:\frac{3}{7} = \frac{1}{6} \times \frac{7}{3} = \frac{7}{{18}}$
b) $\frac{5}{{12}}:\frac{1}{4} = \frac{5}{{12}} \times \frac{4}{1} = \frac{{5 \times 4}}{{12 \times 1}} = \frac{{5 \times 4}}{{4 \times 3 \times 1}} = \frac{5}{3}$
c) $\frac{4}{{15}}:\frac{8}{3} = \frac{4}{{15}} \times \frac{3}{8} = \frac{{4 \times 3}}{{15 \times 8}} = \frac{{4 \times 3}}{{5 \times 3 \times 4 \times 2}} = \frac{1}{{10}}$
d) $\frac{{18}}{5}:\frac{9}{{10}} = \frac{{18}}{5} \times \frac{{10}}{9} = \frac{{18 \times 10}}{{5 \times 9}} = \frac{{9 \times 2 \times 5 \times 2}}{{5 \times 9}} = 4$
a) $\frac{3}{2} - \frac{1}{6} - \frac{5}{6} = \frac{9}{6} - \frac{1}{6} - \frac{5}{6} = \frac{{9 - 1 - 5}}{6} = \frac{3}{6} = \frac{1}{2}$
b) $1 - \frac{1}{3} - \frac{2}{3} = \frac{3}{3} - \frac{1}{3} - \frac{2}{3} = \frac{{3 - 1 - 2}}{3} = 0$
a) $\frac{1}{{10}} + \frac{3}{{10}} = \frac{{1 + 3}}{{10}} = \frac{4}{{10}} = \frac{2}{5}$
b) $\frac{5}{{12}} + \frac{1}{{12}} = \frac{{5 + 1}}{{12}} = \frac{6}{{12}} = \frac{1}{2}$
c) $\frac{3}{2} + \frac{1}{2} = \frac{{3 + 1}}{2} = \frac{4}{2} = 2$
a) $\frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}$
b) $\frac{2}{3} - \frac{4}{{15}} = \frac{{10}}{{15}} - \frac{4}{{15}} = \frac{6}{{15}} = \frac{2}{5}$
c) $\frac{3}{5} - \frac{{10}}{{25}} = \frac{{15}}{{25}} - \frac{{10}}{{25}} = \frac{5}{{25}} = \frac{1}{5}$
a) $\frac{2}{3} - \frac{1}{3} = \frac{{2 - 1}}{3} = \frac{1}{3}$
b) $\frac{7}{{12}} - \frac{5}{{12}} = \frac{{7 - 5}}{{12}} = \frac{2}{{12}} = \frac{1}{6}$
c) $\frac{{17}}{{21}} - \frac{{10}}{{21}} = \frac{{17 - 10}}{{21}} = \frac{7}{{21}} = \frac{1}{3}$
a) $1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{{3 - 1}}{3} = \frac{2}{3}$
b) $1 - \frac{6}{9} = \frac{9}{9} - \frac{6}{9} = \frac{{9 - 6}}{9} = \frac{3}{9} = \frac{1}{3}$
c) $2 - \frac{2}{5} = \frac{{10}}{5} - \frac{2}{5} = \frac{{10 - 2}}{5} = \frac{8}{5}$
a) $\frac{1}{6} + \frac{3}{2} + \frac{1}{2} = \frac{1}{6} + \left( {\frac{3}{2} + \frac{1}{2}} \right) = \frac{1}{6} + \frac{4}{2} = \frac{1}{6} + \frac{{12}}{6} = \frac{{13}}{6}$
b) $\frac{3}{8} + \frac{1}{2} + \frac{1}{8} = \left( {\frac{3}{8} + \frac{1}{8}} \right) + \frac{1}{2} = \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1$
c) $\frac{2}{5} + \frac{6}{{10}} + \frac{3}{5} = \frac{2}{5} + \frac{3}{5} + \frac{3}{5} = \frac{{2 + 3 + 3}}{5} = \frac{8}{5}$