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

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