Математика: Вычислите те которые обведены простым карандашом

2.5 2.62.7 2.83.13.23.8 4.44.5...

Вычислите те которые обведены простым карандашом

Ответы

АртемGoloborshev 26.09.2021 14:20

2.5

$\frac{3}{1 - \frac{1}{2} } = \frac{3}{ \frac{2}{2} - \frac{1}{2} } = \frac{3}{ \frac{2 - 1}{2} } = \frac{3}{ \frac{1}{2} } = 3 \times 2 = 6$

2.6

$\frac{1 - \frac{1}{4} }{1 \frac{1}{2} } = \frac{ \frac{4}{4} - \frac{1}{4} }{ \frac{3}{2} } = \frac{ \frac{4 - 1}{4} }{ \frac{3}{2} } = \frac{ \frac{3}{4} }{ \frac{3}{2} } = \frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} = \frac{1}{2}$

2.7

$\frac{ \frac{2}{3} + \frac{1}{4} }{1 \frac{5}{6} } = \frac{ \frac{8}{12} + \frac{3}{12} }{ \frac{11}{6} } = \frac{ \frac{8 + 3}{12} }{ \frac{11}{6} } = \frac{ \frac{11}{12} }{ \frac{11}{6} } = \frac{11}{12} \times \frac{6}{11} = \frac{11 \times 6}{12 \times 11} = \frac{1}{2}$

2.8

$\frac{8 \frac{1}{3} }{ \frac{8}{9} - \frac{1}{3} } = \frac{ \frac{25}{3} }{ \frac{8}{9} - \frac{3}{9} } = \frac{ \frac{25}{3} }{ \frac{8 - 3}{9} } = \frac{ \frac{25}{3} }{ \frac{5}{9} } = \frac{25}{3} \times \frac{9}{5} = \frac{25 \times 9}{3 \times 5} = 5 \times 3 = 15$

3.1

$\frac{ \frac{5}{8} \times \frac{2}{3} }{ \frac{5}{9} } = \frac{ \frac{5 \times 2}{8 \times 3} }{ \frac{5}{9} } = \frac{ \frac{10}{24} }{ \frac{5}{9} } = \frac{10}{24} \times \frac{9}{5} = \frac{10 \times 9}{24 \times 5} = \frac{3}{4}$

3.2

$\frac{ \frac{3}{4} \times \frac{1}{3} }{ \frac{1}{2} } = \frac{ \frac{3 \times 1}{4 \times 3} }{ \frac{1}{2} } = \frac{ \frac{1}{4} }{ \frac{1}{2} } = \frac{1}{4} \times \frac{2}{1} = \frac{1 \times 2}{4 \times 1} = \frac{1}{2}$

3.8

$\frac{ \frac{3}{5} \times \frac{2}{15} \times \frac{1}{12} }{ \frac{1}{6} \times \frac{2}{5} \times \frac{3}{10} } = \frac{ \frac{3 \times 2 \times 1}{5 \times 15 \times 12} }{ \frac{1 \times 2 \times 3}{6 \times 5 \times 10} } = \frac{ \frac{1}{ 5\times 5 \times 6} }{ \frac{ 1}{2 \times 5 \times 5} } = \frac{ \frac{1}{25 \times 6} }{ \frac{1}{2 \times 25} } = \frac{1}{25 \times 6} \times \frac{2 \times 25}{1} = \frac{2 \times 25}{25 \times 6} = \frac{1}{3}$

4.4

$\frac{ \frac{3}{8} + \frac{1}{4} + \frac{5}{6} }{ \frac{1}{2} + \frac{2}{3} - \frac{1}{8} } = \frac{ \frac{9}{24} + \frac{6}{24} + \frac{20}{24} }{ \frac{12}{24} + \frac{16}{24} - \frac{3}{24} } = \frac{ \frac{9 + 6 + 20}{24} }{ \frac{12 + 16 - 3}{24} } = \frac{ \frac{35}{24} }{ \frac{25}{24} } = \frac{35}{24} \times \frac{24}{25} = \frac{35 \times 24}{24 \times 25} = \frac{35}{25} = \frac{7}{5}$

4.5

$\frac{ \frac{3}{8} + \frac{7}{12} + \frac{1}{2} }{ \frac{3}{4} - \frac{5}{8} + \frac{1}{6} } = \frac{ \frac{9}{24} + \frac{14}{24} + \frac{12}{24} }{ \frac{18}{24} - \frac{15}{24} + \frac{4}{24} } = \frac{ \frac{9 + 14 + 12}{24} }{ \frac{18 - 15 + 4}{24} } = \frac{ \frac{35}{24} }{ \frac{7}{24} } = \frac{35}{24} \times \frac{24}{7} = \frac{35 \times 24}{24 \times 7} = \frac{35}{7} = 5$