Question

прошу !решите по действиям а) (2/7+ 3 1/3)-(11/14+13/28) б) (8 7/12-2 5/8)-(3 7/12-1 1/3) ​

Answer 1

Пошаговое объяснение:

а)

$( \frac{2}{7} + 3 \frac{1}{3} ) - ( \frac{11}{14} + \frac{13}{28} ) = 3 \frac{13}{21} - 1 \frac{1}{4} = 2 \frac{31}{84}$

$1) \frac{2}{7} + 3 \frac{1}{3} = 3 + \frac{2}{7} + \frac{1}{3} = 3 + \frac{2 \times 3}{7 \times 3} + \frac{1 \times 7}{3 \times 7} = 3 + \frac{6}{21} + \frac{7}{21} = 3 + \frac{6 + 7}{21} = 3 + \frac{13}{21} = 3 \frac{13}{21}$

$2) \frac{11}{14} + \frac{13}{28} = \frac{11 \times 2}{14 \times 2} + \frac{13 \times 1}{28 \times 1} = \frac{22}{28} + \frac{13}{28} = \frac{22 + 13}{28} = \frac{35}{28} = \frac{5 \times 7}{4 \times 7} = \frac{5}{4} = \frac{1 \times 4 + 1}{4} = 1 \frac{1}{4}$

$3)3 \frac{13}{21} - 1 \frac{1}{4} = \frac{13 + 3 \times 21}{21} - \frac{1 + 1 \times 4}{4} = \frac{76}{21} - \frac{5}{4} = \frac{76 \times 4}{21 \times 4} - \frac{5 \times 21}{4 \times 21} = \frac{304}{84} - \frac{105}{84} = \frac{304 - 105}{84} = \frac{199}{84} = \frac{2 \times 84 + 31}{84} = 2 \frac{31}{84}$

б)

$(8 \frac{7}{12} - 2 \frac{5}{8} ) - (3 \frac{7}{12} - 1 \frac{1}{3} ) = 5 \frac{23}{24} - 2 \frac{1}{4} = 3 \frac{17}{24}$

$1)8 \frac{7}{12} - 2 \frac{5}{8} = \frac{7 + 8 \times 12}{12} - \frac{5 + 2 \times 8}{8} = \frac{103}{12} - \frac{21}{8} = \frac{103 \times 2}{12 \times 2} - \frac{21 \times 3}{8 \times 3} = \frac{206}{24} - \frac{63}{24} = \frac{206 - 63}{24} = \frac{143}{24} = \frac{5 \times 24 + 23}{24} = 5 \frac{23}{24}$

$2)3 \frac{7}{12} - 1 \frac{1}{3} = \frac{7 + 3 \times 12}{12} - \frac{1 + 1 \times 3}{3} = \frac{43}{12} - \frac{4}{3} = \frac{43 \times 1}{12 \times 1} - \frac{4 \times 4}{3 \times 4} = \frac{43}{12} - \frac{16}{12} = \frac{43 - 16}{12} = \frac{27}{12} = \frac{9 \times 3}{4 \times 3} = \frac{9}{4} = \frac{2 \times 4 + 1}{4} = 2 \frac{1}{4}$

3) 5 \frac{23}{24} - 2 \frac{1}{4} = \frac{23 + 5 \times 24}{24} - \frac{1 + 2 \times 4}{4} = \frac{143}{24} - \frac{9}{4} = \frac{143 \times 1}{24 \times 1} - \frac{9 \times 6}{4 \times 6} = \frac{143}{24} - \frac{54}{24} = \frac{143 - 54}{24} = \frac{89}{24} = \frac{3 \times 24 + 17}{24} = 3 \frac{17}{24}