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) \(\frac{{ - 2}}{7}:\frac{4}{7} = \frac{{ - 2}}{7}.\frac{7}{4} = \frac{{ - 2}}{4} = \frac{{ - 1}}{2}\)      

b) \(\frac{{ - 4}}{5}:\frac{{ - 3}}{{11}} = \frac{{ - 4}}{5}.\frac{{11}}{{ - 3}} = \frac{{ - 44}}{{ - 15}} = \frac{{44}}{{15}}\)

c) \(4:\frac{{ - 2}}{5} = 4.\frac{5}{{ - 2}} = \frac{{20}}{{ - 2}} =  - 10\)

d) \(\frac{{15}}{{ - 8}}:6 = \frac{{15}}{{ - 8}}.\frac{1}{6} = \frac{{ - 15}}{{48}}= \frac{{ - 5}}{{16}}\).

a) \(\dfrac{-2}{7}:\dfrac{4}{7}=\dfrac{-2}{7}.\dfrac{7}{4}=\dfrac{-2.7}{7.4}=\dfrac{-1}{2}\)

b) \(\dfrac{-4}{5}:\dfrac{-3}{11}=\dfrac{-4}{5}.\dfrac{-11}{3}=\dfrac{-4.\left(-11\right)}{5.3}=\dfrac{44}{15}\)

c) \(4:\dfrac{-2}{5}=4.\dfrac{-5}{2}=\dfrac{4.\left(-5\right)}{2}=-10\)

d) \(\dfrac{15}{-8}:6=\dfrac{-15}{8}.\dfrac{1}{6}=\dfrac{-15}{8.6}=\dfrac{-5}{16}\)

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) $\frac{3}{5} - \frac{{10}}{{25}} = \frac{{15}}{{25}} - \frac{{10}}{{25}} = \frac{5}{{25}} = \frac{1}{5}$