Question

Решить : 1. 7/10+7/9x27/35 2. 5/14+3/8x16/21 3. 3/16x4/7+5/8x6/35 4. 1+3/5x1 5/6 5. 5/12-8/21x7/16 6. 2-7/8x1 1/7

Answer 1

$\frac{7}{10} + \frac{7}{9} * \frac{27}{35} = \frac{7}{10} + \frac{7*(3*9)}{9*(5*7)}= \frac{7}{10} + \frac{3}{5} = \frac{7}{10} +\frac{3*2}{5*2} = \frac{7+6}{10} =\frac{13}{10} =1 \frac{3}{10} \\ \\ \frac{5}{14} + \frac{3}{8} * \frac{16}{21} = \frac{5}{14} + \frac{3*(2*8)}{8*(3*7)} = \frac{5}{14} + \frac{2}{7} = \frac{5}{14} + \frac{2*2}{7*2} = \frac{5+4}{14} = \frac{9}{14}$

$\frac{3}{16} * \frac{4}{7} + \frac{5}{8} * \frac{6}{35} = \frac{3*4}{(4*4)*7} + \frac{5*2*3}{(2*4)*(5*7)} = \frac{3*1}{1*4*7} + \frac{1*1*3}{4*7} = \\ \\ = \frac{3}{28} + \frac{3}{28} = \frac{6}{28} = \frac{6:2}{28:2} = \frac{3}{14} \\ \\ 1 + \frac{3}{5} * 1 \frac{5}{6} = 1 + \frac{3}{5} * \frac{1*6+5}{6} = 1 + \frac{3}{5} * \frac{11}{6} = 1+ \frac{11}{10} = 1 + 1\frac{1}{10} =2 \frac{1}{10}$

$\frac{5}{12} - \frac{8}{21} * \frac{7}{16} = \frac{5}{12} - \frac{8*7}{(3*7)*(2*8)} = \frac{5}{12} -\frac{1}{3*2} = \frac{5}{12} - \frac{1}{6} = \frac{5-2}{12}= \frac{3}{12} = \frac{1}{4} \\ \\ 2 - \frac{7}{8} *1 \frac{1}{7} = 2 - \frac{7}{8} * \frac{1*7+1}{7} =2 - \frac{7}{8} * \frac{8}{7} = 2 - 1 = 1$