Question

Вычислить наиболее удобным способом 3 3/8*3 1/5+3 1/5*1 5/12-4 1/6-3 5/12

Answer 1

$3 \frac{3}{8} \times 3 \frac{1}{5} + 3 \frac{1}{5} \times 1 \frac{5}{12} - 4 \frac{1}{6} - 3 \frac{5}{12} = 10 \frac{4}{5} + 4 \frac{8}{15} - 4 \frac{1}{6} - 3 \frac{5}{12} = 15 \frac{1}{3} - 4 \frac{1}{6} - 3 \frac{5}{12} = 11 \frac{1}{6} - 3 \frac{5}{12} = 7 \frac{3}{4}$

Пошаговое объяснение:

$3 \frac{3}{8} \times 3 \frac{1}{5} = \frac{3 + 3 \times 8}{8} \times \frac{1 + 3 \times 5}{5} = \frac{27}{8} \times \frac{16}{5} = \frac{27 \times 16}{8 \times 5} = \frac{432}{40} = \frac{54 \times 8}{5 \times 8} = \frac{54}{5} = \frac{10 \times 5 + 4}{5} = 10 \frac{4}{5}$

$3 \frac{1}{5} \times 1 \frac{5}{12} = \frac{1 + 3 \times 5}{5} \times \frac{5 + 1 \times 12}{12} = \frac{16}{5} \times \frac{17}{12} = \frac{16 \times 7}{5 \times 12} = \frac{272}{60} = \frac{68 \times 4}{15 \times 4} = \frac{68}{15} = \frac{4 \times 15 + 8}{15} = 4 \frac{8}{15}$

$10\frac{4}{5} + 4 \frac{8}{15} = 14 + \frac{4}{5} + \frac{8}{15} = 14 + \frac{4 \times 3}{5 \times 3} + \frac{8 \times 1}{15 \times 1} = 14 + \frac{12}{15} + \frac{8}{15} = 14 + \frac{12 + 8}{15} = 14 + \frac{20}{15} = 14 + \frac{4 \times 5}{3 \times 5} = 14 + \frac{4}{3} = 14 + \frac{1 \times 3 + 1}{3} = 15 \frac{1}{3}$

$15 \frac{1}{3} - 4 \frac{1}{6} = \frac{1 + 15 \times 3}{3} - \frac{1 + 4 \times 6}{6} = \frac{46}{3} - \frac{25}{6} = \frac{46 \times 2}{3 \times 2} - \frac{25 \times 1}{6 \times 1} = \frac{92}{6} - \frac{25}{6} = \frac{92 - 25}{6} = \frac{67}{6} = \frac{11 \times 6 + 1}{6} = 11 \frac{1}{6}$

$11\frac{1}{6} - 3 \frac{5}{12} = \frac{1 + 11 \times 6}{6} - \frac{5 + 3 \times 12}{12} = \frac{67}{6} - \frac{41}{12} = \frac{67 \times 2}{6 \times 2} - \frac{41 \times 1}{12 \times 1} = \frac{134}{12} - \frac{41}{12} = \frac{134 - 41}{12} = \frac{93}{12} = \frac{31 \times 3}{4 \times 3} = \frac{31}{4} = \frac{7 \times 4 + 3}{4} = 7 \frac{3}{4}$