Question

Вычислите 14*(1/2+1/3+1/4)= 1/3*6/7-1/7*3/4= 1/2*2/3*3/4*5/6*23/24*24/25=

Answer 1

$14* ( \frac{1}{2} + \frac{1}{3} + \frac{1}{4} ) = 14* ( \frac{1*6}{2*6} + \frac{1*4}{3*4} + \frac{1*3}{4*3} ) = \\ \\ = \frac{14}{1}* \frac{13}{12} = \frac{7*13}{1*6} = \frac{91}{6} = 15 \frac{1}{6}$

$\frac{1}{3} * \frac{6}{7} - \frac{1}{7} * \frac{3}{4} = \frac{1*6}{3*7} - \frac{1*3}{7*4} = \\ \\ =\frac{2}{7} - \frac{3}{28} = \frac{2*4}{7*4} - \frac{3}{28} = \frac{5}{28}$

$\frac{1}{2} * \frac{2}{3} * \frac{3}{4} * \frac{5}{6} * \frac{23}{24} * \frac{24}{25} = \frac{1*2*3*5*23*24}{2*3*4*6*24*25} = \\ \\ = \frac{1*1*5*23*1}{1*1*4*6*25} = \frac{1*23}{4*6*5} = \frac{23}{120}$