Вариант 4 1.Выполните действие: a) 4,6 (-2,5); (-3,6); 5 ; 16 6)-25,344: B)-11:11: (-3). 2. Решите уравнение: 8 a) -1,4-x = 4,27; 6) -6,2 : y = 31. 7 11 13 By+1= 18 3.Выполните действие: a) (15,54: (-4,2) - 2,5) 1,4 + 1,08. 4*. Найдите значение выражения (0,4)(1)-(-0,5):121 7 7 18 6

1. Выполните действие:

a) 4,6 ⋅ (-2,5); (-3,6);

4,6 \(\cdot\) (-2,5) = -11,5

-25,344 : (-3,6) = 7,04

б) -25,344 : (-3,6);

в) -1\(\frac{1}{7}\) \(\cdot\) 1\(\frac{5}{16}\);

-1\(\frac{1}{7}\) = -\(\frac{8}{7}\)

1\(\frac{5}{16}\) = \(\frac{21}{16}\)

-\(\frac{8}{7}\) \(\cdot\) \(\frac{21}{16}\) = -\(\frac{8 \cdot 21}{7 \cdot 16}\) = -\(\frac{1 \cdot 3}{1 \cdot 2}\) = -\(\frac{3}{2}\) = -1,5

г) 1\(\frac{1}{8}\) : (-3\(\frac{3}{8}\)).

1\(\frac{1}{8}\) = \(\frac{9}{8}\)

-3\(\frac{3}{8}\) = -\(\frac{27}{8}\)

\(\frac{9}{8}\) : (-\(\frac{27}{8}\)) = \(\frac{9}{8}\) \(\cdot\) (-\(\frac{8}{27}\)) = -\(\frac{9 \cdot 8}{8 \cdot 27}\) = -\(\frac{1 \cdot 1}{1 \cdot 3}\) = -\(\frac{1}{3}\)

2. Решите уравнение:

a) -1,4x = 4,27;

x = 4,27 : (-1,4)

x = -3,05

б) -6,2 : y = 31.

y = -6,2 : 31

y = -0,2

в) \(\frac{7}{9}\) + \(\frac{11}{12}\) = \(\frac{13}{18}\)

y = \(\frac{13}{18}\) - \(\frac{11}{12}\) - \(\frac{7}{9}\)

Приведем к общему знаменателю 36:

y = \(\frac{13 \cdot 2}{18 \cdot 2}\) - \(\frac{11 \cdot 3}{12 \cdot 3}\) - \(\frac{7 \cdot 4}{9 \cdot 4}\)

y = \(\frac{26}{36}\) - \(\frac{33}{36}\) - \(\frac{28}{36}\)

y = \(\frac{26 - 33 - 28}{36}\) = -\(\frac{35}{36}\)

3. Выполните действие:

a) (15,54 : (-4,2) - 2,5) ⋅ 1,4 + 1,08.

15,54 : (-4,2) = -3,7

(-3,7 - 2,5) \(\cdot\) 1,4 + 1,08

-6,2 \(\cdot\) 1,4 + 1,08

-8,68 + 1,08 = -7,6

4*. Найдите значение выражения

(0,4 - \(\frac{11}{15}\)) \(\cdot\) (1\(\frac{2}{7}\)) - (\(\frac{7}{18}\) - 0,5) : 1\(\frac{1}{6}\)

0,4 = \(\frac{4}{10}\) = \(\frac{2}{5}\)

1\(\frac{2}{7}\) = \(\frac{9}{7}\)

1\(\frac{1}{6}\) = \(\frac{7}{6}\)

\(\frac{2}{5}\) - \(\frac{11}{15}\) = \(\frac{2 \cdot 3}{5 \cdot 3}\) - \(\frac{11}{15}\) = \(\frac{6}{15}\) - \(\frac{11}{15}\) = -\(\frac{5}{15}\) = -\(\frac{1}{3}\)

\(\frac{7}{18}\) - 0,5 = \(\frac{7}{18}\) - \(\frac{1}{2}\) = \(\frac{7}{18}\) - \(\frac{1 \cdot 9}{2 \cdot 9}\) = \(\frac{7}{18}\) - \(\frac{9}{18}\) = -\(\frac{2}{18}\) = -\(\frac{1}{9}\)

-\(\frac{1}{3}\) \(\cdot\) \(\frac{9}{7}\) - (-\(\frac{1}{9}\)) : \(\frac{7}{6}\)

-\(\frac{1}{3}\) \(\cdot\) \(\frac{9}{7}\) = -\(\frac{1 \cdot 9}{3 \cdot 7}\) = -\(\frac{1 \cdot 3}{1 \cdot 7}\) = -\(\frac{3}{7}\)

-\(\frac{1}{9}\) : \(\frac{7}{6}\) = -\(\frac{1}{9}\) \(\cdot\) \(\frac{6}{7}\) = -\(\frac{1 \cdot 6}{9 \cdot 7}\) = -\(\frac{1 \cdot 2}{3 \cdot 7}\) = -\(\frac{2}{21}\)

-\(\frac{3}{7}\) - (-\(\frac{2}{21}\)) = -\(\frac{3}{7}\) + \(\frac{2}{21}\) = -\(\frac{3 \cdot 3}{7 \cdot 3}\) + \(\frac{2}{21}\) = -\(\frac{9}{21}\) + \(\frac{2}{21}\) = -\(\frac{7}{21}\) = -\(\frac{1}{3}\)

Ответ: 1. a) -11,5; 7,04; б) -1,5; г) -\(\frac{1}{3}\); 2. a) -3,05; б) -0,2; в) -\(\frac{35}{36}\); 3. a) -7,6; 4. -\(\frac{1}{3}\)

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