$(1)\frac {9}{10}÷[\frac {1}{2}×(\frac {6}{5}-\frac {7}{10})]$
$=\frac {9}{10}÷(\frac {1}{2}×\frac {5}{10})$
$=\frac {9}{10}÷\frac {1}{4}$
$=\frac {9}{10}×4$
$=\frac {18}{5}$
$(2)\frac {14}{15}×(\frac {5}{14}+\frac {5}{21})+\frac {2}{3}$
$=\frac {14}{15}×\frac {5}{14}+\frac {14}{15}×\frac {5}{21}+\frac {2}{3}$
$=\frac {1}{3}+\frac {2}{9}+\frac {2}{3}$
$=(\frac {1}{3}+\frac {2}{3})+\frac {2}{9}$
$=1+\frac {2}{9}$
$=\frac {11}{9}$
$(3)\frac {4}{11}×\frac {5}{19}+\frac {5}{11}×\frac {7}{19}$
$=\frac {5}{11}×\frac {4}{19}+\frac {5}{11}×\frac {7}{19}$
$=\frac {5}{11}×(\frac {4}{19}+\frac {7}{19})$
$=\frac {5}{11}×\frac {11}{19}$
$=\frac {5}{19}$
$(4)(\frac {1}{16}+\frac {3}{49})×16+\frac {1}{49}$
$=\frac {1}{16}×16+\frac {3}{49}×16+\frac {1}{49}$
$=1+\frac {48}{49}+\frac {1}{49}$
$=2$
$(5)2.5×7.2×0.4$
$=(2.5×0.4)×7.2$
$=1×7.2$
$=7.2$
$(6)375-47+25-153$
$=(375+25)-(47+153)$
$=400-200$
$=200$
$(7)42×\frac {42}{43}$
$=(43-1)×\frac {42}{43}$
$=42-\frac {42}{43}$
$=41\frac {1}{43}$
$(8)8×(\frac {1}{4}+\frac {2}{9})×9$
$=8×\frac {1}{4}×9+\frac {2}{9}×9×8$
$=18+16$
$=34$
