Question

помогите пожалуйста111111

Answer 1

1. Выполните действия:

1)

$7 \frac{7}{9} - 4 \frac{1}{12} + 2 \frac{3}{4} = 7 \frac{28}{36} - 4 \frac{3}{36} + 2 \frac{27}{36} = (7 + \frac{28}{36}) - (4 + \frac{3}{36} ) + (2 + \frac{27}{36} ) = 7 + \frac{28}{36} - 4 - \frac{3}{36} + 2 + \frac{27}{36} = 5 + \frac{28 - 3 + 27}{36} = 5 + \frac{52}{36} = 5 + \frac{13}{9} =5 + 1 \frac{4}{9} = 5 + 1 + \frac{4}{9} = 6 + \frac{4}{9} = 6 \frac{4}{9}$

2)

$17 \frac{2}{3} - 6 \frac{1}{36} + 4 \frac{3}{8} = 17 \frac{48}{72} - 6 \frac{2}{72} + 4 \frac{27}{72} = (17 + \frac{48}{72} ) - (6 + \frac{2}{72} ) + (4 + \frac{27}{72} ) = 17 + \frac{48}{72} - 6 - \frac{2}{72} + 4 + \frac{27}{72} = 15 + \frac{48 - 2 + 27}{72} = 15 + \frac{73}{72} = 15 + 1 \frac{1}{72} = 15 + 1 + \frac{1}{72} = 16 \frac{1}{72}$

3)

$10 \frac{9}{16} - (3 \frac{11}{12} + 4 \frac{4}{9} ) = 10 \frac{9}{16} - 3 \frac{11}{12} - 4 \frac{4}{9} = 10 \frac{81}{144} - 3 \frac{132}{144} - 4 \frac{64}{144} = (10 + \frac{81}{144} ) - (3 + \frac{132}{144} ) - (4 + \frac{64}{144} ) = 10 + \frac{81}{144} - 3 - \frac{132}{144} - 4 - \frac{64}{144} = 3 + \frac{81 - 132 - 64}{144} = 3 + ( - \frac{ 115}{144} ) = 3 - \frac{115}{144} = 2 + \frac{144}{144} - \frac{115}{144} = 2 + \frac{144 - 115}{144} = 2 + \frac{29}{144} = 2 \frac{29}{144}$

4)

$(20 - 7 \frac{23}{36} ) - (14 \frac{4}{27} - 6 \frac{1}{18} ) = (19 \frac{36}{36} - 7 \frac{23}{36} ) - (14 \frac{8}{54} - 6 \frac{3}{54} ) = (19 + \frac{36}{36} - 7 - \frac{23}{36} ) - (14 + \frac{8}{54} - 6 - \frac{3}{54} ) = (12 + \frac{36 - 23}{36} ) - (8 + \frac{8 - 3}{54} ) = (12 + \frac{13}{36} ) - (8 + \frac{5}{54} ) = 12 + \frac{39}{108} - 8 - \frac{10}{108} = 4 + \frac{36 - 10}{108} = 4 + \frac{26}{108} = 4 + \frac{13}{54} = 4 \frac{13}{54}$

2. Найдите значение выражения:

1)

$(9 \frac{3}{7} + 2 \frac{9}{16} ) - 5 \frac{3}{7} = 9 \frac{3}{7} + 2 \frac{9}{16} - 5 \frac{3}{7} = (9 \frac{3}{7} - 5 \frac{3}{7} ) + 2 \frac{9}{16} = (9 + \frac{3}{7} - 5 - \frac{3}{7} ) + 2 \frac{9}{16} = 4 + 2 \frac{9}{16} = 4 + 2 + \frac{9}{16} = 6 + \frac{9}{16} = 6 \frac{9}{16}$

2)

$10 \frac{5}{14} - (3 \frac{5}{14} + 2 \frac{9}{34} ) = 10 \frac{5}{14} - 3 \frac{5}{14} - 2 \frac{9}{34} = (10 \frac{5}{14} - 3 \frac{5}{14} ) - 2 \frac{9}{34} = (10 + \frac{5}{14} - 3 - \frac{5}{14} ) - 2 \frac{9}{34} = 7 - 2 \frac{9}{34} = 6 \frac{34}{34} - 2 \frac{9}{34} = 6 + \frac{34}{34} - 2 - \frac{9}{34} = 4 + \frac{34 - 9}{34} = 4 + \frac{25}{34} = 4 \frac{25}{34}$

3. Упростите выражение:

1)

$\frac{3a}{8b} - \frac{a}{5b} = \frac{3}{8} \times \frac{a}{b} - \frac{1}{5} \times \frac{a}{b} = \frac{a}{b} ( \frac{3}{8} - \frac{1}{5} ) = \frac{a}{b} ( \frac{15}{40} - \frac{8}{40} ) = \frac{a}{b} \times \frac{7}{40} = \frac{7a}{40b}$

2)

$\frac{4m}{9n} + \frac{5m}{12n} = \frac{4}{9} \times \frac{m}{n} + \frac{5}{12} \times \frac{m}{n} = \frac{m}{n} ( \frac{4}{9} + \frac{5}{12} ) = \frac{m}{n} ( \frac{16}{36} + \frac{15}{36} ) = \frac{m}{n} \times \frac{31}{36} = \frac{31m}{36n}$

3)

$\frac{7x}{6y} - \frac{4x}{15y} = \frac{7}{6} \times \frac{x}{y} - \frac{4}{15} \times \frac{x}{y} = \frac{x}{y} ( \frac{7}{6} - \frac{4}{15} ) = \frac{x}{y} ( \frac{35}{30} - \frac{8}{30} ) = \frac{x}{y} \times \frac{27}{30} = \frac{x}{y} \times \frac{9}{10} = \frac{9x}{10y}$

4. Решить уравнения:

1)

$(x + \frac{5}{12} ) - \frac{9}{20} = \frac{11}{15}$

$x = \frac{11}{15} - \frac{5}{12} + \frac{9}{20}$

$x = \frac{44}{60} - \frac{25}{60} + \frac{27}{60}$

$x = \frac{46}{60}$

$x = \frac{23}{30}$

2)

$(x - \frac{7}{15} ) + \frac{5}{8} = \frac{17}{24}$

$x = \frac{17}{24} + \frac{7}{15} - \frac{5}{8}$

$x = \frac{85}{120} + \frac{56}{120} - \frac{75}{120}$

$x = \frac{66}{120}$

$x = \frac{11}{20}$

3)

$\frac{4}{5} - (x + \frac{1}{60} ) = \frac{2}{3}$

$\frac{4}{5} - x - \frac{1}{60} = \frac{2}{3}$

$x = \frac{4}{5} - \frac{1}{60} - \frac{2}{3}$

$x = \frac{48}{60} - \frac{1}{60} - \frac{40}{60}$

$x = \frac{7}{60}$

4)

$4 \frac{3}{4} - (x - 2 \frac{5}{8} ) = 3 \frac{5}{6}$

$4 \frac{3}{4} - x + 2 \frac{5}{8} = 3 \frac{5}{6}$

$x = 4 \frac{3}{4} + 2 \frac{5}{8} - 3 \frac{5}{6}$

$x = 4 + \frac{3}{4} + 2 + \frac{5}{8} - 3 - \frac{5}{6}$

$x = 3 + ( \frac{3}{4} + \frac{5}{8} - \frac{5}{6} )$

$x = 3 + ( \frac{18}{24} + \frac{15}{24} - \frac{20}{24} )$

$x = 3 + \frac{13}{24}$

$x = 3 \frac{13}{24}$

5)

$9 \frac{9}{28} - (4 \frac{5}{21} - x) = 6 \frac{2}{7}$

$9 \frac{9}{28} - 4 \frac{5}{21} + x = 6 \frac{2}{7}$

$x = 6 \frac{2}{7} - 9 \frac{9}{28} + 4 \frac{5}{21}$

$x = 6 + \frac{2}{7} - 9 - \frac{9}{28} + 4 + \frac{5}{21}$

$x = 1 + ( \frac{2}{7} - \frac{9}{28} + \frac{5}{21} )$

$x = 1 + ( \frac{24}{84} - \frac{27}{84} + \frac{20}{84} )$

$x = 1 + \frac{17}{84}$

$x = 1 \frac{17}{84}$