Question

7
657. Вычислите:
1
1 2
1) 3- +5
6 5
2
3
:11
2
; 3)
1 2
+
8 9
1) 5-
2
1
+
3 6
5
9​

Answer 1

Ответ:

1)

$(3 \frac{1}{3} + 5 \frac{1}{6} ) \times \frac{2}{5} - 2 \frac{3}{4} \div (1 \frac{1}{2} - \frac{2}{5} ) =0.9 \\ 1)3 \frac{1}{3} + 5 \frac{1}{6} = \frac{3 \times 3 + 1}{3} + \frac{6 \times 5 + 1}{6} = \\ \frac{10}{3} + \frac{31}{6} = \frac{10 \times 2 + 31}{6} = \frac{51}{6} \\ 2) \frac{51}{6} \times \frac{2}{5} = \frac{51}{15} \\ 3)1 \frac{1}{2} - \frac{2}{5} = \frac{2 \times 1 + 1}{2} - \frac{2}{5} = \frac{3}{2} - \frac{2}{5} = \\ \frac{3 \times 5 - 2 \times 2}{10} = \frac{15 - 4}{10} = \frac{11}{10} \\ 4)2 \frac{3}{4} \div \frac{11}{10} = \frac{4 \times 2 + 3}{4} \div \frac{11}{10} = \frac{11}{4} \div \frac{11}{10} = \\ \frac{11}{4} \times \frac{10}{11} = \frac{5}{2} \\ 5) \frac{51}{15} - \frac{5}{2} = \frac{51 \times 2 - 5 \times 15}{30} = \frac{102 - 75}{30} = \\ \frac{27}{30} = \frac{9}{10} = 0.9$

2)

$( \frac{1}{8} + \frac{2}{9} - \frac{1}{4} ) \times 5 \frac{1}{7} \div ( \frac{7}{9} - \frac{2}{3} + \frac{1}{6} ) = 1 \frac{4}{5} \\ 1) \frac{1}{8} + \frac{2}{9} = \frac{1 \times 9 + 2 \times 8}{72} = \frac{9 + 16}{72} = \frac{25}{72} \\ 2) \frac{25}{72} - \frac{1}{4} = \frac{25 - 1 \times 18}{72} = \frac{25 - 18}{72} = \frac{7}{72} \\ 3) \frac{7}{72} \times 5 \frac{1}{7} = \frac{7}{72} \times \frac{7 \times 5 + 1}{7} = \frac{7}{72} \times \frac{36}{7} = \frac{1}{2} \\ 4) \frac{7}{9} - \frac{2}{3} = \frac{7 - 2 \times 3}{9} = \frac{7 - 6}{9} = \frac{1}{9} \\ 5) \frac{1}{9} + \frac{1}{6} = \frac{1 \times 2 + 1 \times 3}{18} = \frac{5}{18} \\ 6) \frac{1}{2} \div \frac{5}{18} = \frac{1}{2} \times \frac{18}{5} = \frac{9}{5} = 1 \frac{4}{5}$