a) \(\displaystyle{\rm{}}{2 \over 3} + {1 \over 5}.{{10} \over 7} \)\(\displaystyle= {2 \over 3} + {{1.10} \over {5.7}} \)\(\displaystyle= {2 \over 3} + {2 \over 7} \)\(\displaystyle= {{14} \over {21}} + {6 \over {21}}\)\(\displaystyle= {{20} \over {21}};\)
b) \(\displaystyle{7 \over {12}} - {{27} \over 7}.{1 \over {18}} \)\(\displaystyle= {7 \over 2} - {{27.1} \over {7.18}} \)\(\displaystyle= {7 \over 2} - {3 \over {14}} \)\(\displaystyle= {{49} \over {14}} + {{ - 3} \over {14}} \)\(\displaystyle= {{46} \over {14}} = {{23} \over 7};\)
c) \(\displaystyle\left( {{{23} \over {41}} - {{15} \over {82}}} \right).{{41} \over {25}} \)\(\displaystyle= \left( {{{46} \over {82}} + {{ - 15} \over {82}}} \right).{{41} \over {25}} \)\(\displaystyle= {{31} \over {82}}.{{41} \over {25}} \)\(\displaystyle= {{31.41} \over {82.25}} = {{31} \over {50}};\)
d) \(\displaystyle{\rm{}}\left( {{4 \over 5} + {1 \over 2}} \right).\left( {{3 \over {13}} - {8 \over {13}}} \right) \)\(\displaystyle= \left( {{8 \over {10}} + {5 \over {10}}} \right).\left( {{3 \over {13}} + {{ - 8} \over {13}}} \right)\)\(\displaystyle= {{13} \over {10}}.{{ - 5} \over {13}} = {{13.( - 5)} \over {10.13}} = {{ - 1} \over 2}.\)
