Question

вычислить 8 21/27 + (21 5/14 * 1/6) : (10 13/42 - 9 13/28 + 2 5/24) - (8/9 *1/9) :2
/ - дробная черта
* - умножение

Answer 1

$8 frac {21}{27} + (21 frac{5}{14} cdot frac{1}{6}) : (10 frac {13}{42} - 9 frac{13}{28} + 2 frac{5}{24}) - (frac{8}{9} cdot frac{1}{9}) :2 = \ 8+ frac {21}{27} + frac {299}{84}: (10-9+2+ frac {13}{2 cdot 3 cdot 7} - frac{13}{2 cdot 2 cdot 7 } + frac{5}{2 cdot 2 cdot 2 cdot 3}) - frac{4}{81} = \ 8+ frac {21 cdot 3 -4}{27} + frac {299}{84}: (10-9+2+ frac{5 cdot 7 - 13 cdot 6 + 13 cdot 4 }{2 cdot 2 cdot 2 cdot 3 cdot 7}) =$
$8+ frac {59}{27} + frac {299}{84}: (3+ frac{3}{2 cdot 2 cdot 2 cdot 3 cdot 7}) = 8+ frac {59}{27} + frac {299}{84}: ( frac{2 cdot 2 cdot 2 cdot 7+1}{2 cdot 2 cdot 2 cdot 7}) = \ 8+ frac {59}{27} + frac {299}{84}: ( frac{57}{56}) = 8+ frac {59}{27} + frac {299}{84} cdot frac{56}{57} = 8+ frac {59}{27} + frac {598}{171} = \ 8+ frac {59}{27} + frac {598}{171} = 11 + frac {59}{27} + frac {85}{171} = 11 + frac {59}{3^3} + frac {85}{3^2 cdot 19} =$
$11 + frac {59 cdot 19+85 cdot 3 cdot 19}{3^3 cdot 19} = 11 + frac {5016}{513} = 11 + frac {88}{9} = 11 + 8 + frac {7}{9} = 19 frac {7}{9}$