18. Найдите значение числового выражения: a) (0,018+0,982): (8·0,5-0,8); б) (0,008 +0,992): (5·0,6-1,4); в) (6-7\frac{1}{8})·(2\frac{2}{9}+3); г) (15-4\frac{1}{8})·(3\frac{14}{15}-2\frac{3}{5}); д) \frac{1,05+\frac{3}{4}}{(7,5-3\frac{1}{3})·0,6}; e) \frac{(7,5+6\frac{2}{3})·0,12}{4,5+\frac{3}{5}}.

Решение задания №18

Найдем значение каждого числового выражения:

а) (0,018 + 0,982) : (8 \(\cdot\) 0,5 – 0,8)

(0,018 + 0,982) = 1

(8 \(\cdot\) 0,5 – 0,8) = 4 – 0,8 = 3,2

1 : 3,2 = 1 : \(\frac{32}{10}\) = \(\frac{10}{32}\) = \(\frac{5}{16}\) = 0,3125

б) (0,008 + 0,992) : (5 \(\cdot\) 0,6 – 1,4)

(0,008 + 0,992) = 1

(5 \(\cdot\) 0,6 – 1,4) = 3 – 1,4 = 1,6

1 : 1,6 = 1 : \(\frac{16}{10}\) = \(\frac{10}{16}\) = \(\frac{5}{8}\) = 0,625

в) (6 – 7\(\frac{1}{8}\)) \(\cdot\) (2\(\frac{2}{9}\) + 3)

(6 – 7\(\frac{1}{8}\)) = (\(\frac{48}{8}\) – \(\frac{57}{8}\)) = -\(\frac{9}{8}\)

(2\(\frac{2}{9}\) + 3) = (\(\frac{20}{9}\) + \(\frac{27}{9}\)) = \(\frac{47}{9}\)

- \(\frac{9}{8}\) \(\cdot\) \(\frac{47}{9}\) = -\(\frac{47}{8}\) = -5,875

г) (15 – 4\(\frac{1}{8}\)) \(\cdot\) (3\(\frac{14}{15}\) – 2\(\frac{3}{5}\))

(15 – 4\(\frac{1}{8}\)) = (\(\frac{120}{8}\) – \(\frac{33}{8}\)) = \(\frac{87}{8}\)

(3\(\frac{14}{15}\) – 2\(\frac{3}{5}\)) = (\(\frac{59}{15}\) – \(\frac{13}{5}\)) = (\(\frac{59}{15}\) – \(\frac{39}{15}\)) = \(\frac{20}{15}\) = \(\frac{4}{3}\)

\(\frac{87}{8}\) \(\cdot\) \(\frac{4}{3}\) = \(\frac{87}{2}\) \(\cdot\) \(\frac{1}{3}\) = \(\frac{29}{2}\) = 14,5

д) \(\frac{1,05 + \frac{3}{4}}{(7,5 – 3\frac{1}{3}) \cdot 0,6}\)

1,05 + \(\frac{3}{4}\) = 1,05 + 0,75 = 1,8

(7,5 – 3\(\frac{1}{3}\)) = (7,5 – \(\frac{10}{3}\)) = (\(\frac{15}{2}\) – \(\frac{10}{3}\)) = (\(\frac{45}{6}\) – \(\frac{20}{6}\)) = \(\frac{25}{6}\)

(\(\frac{25}{6}\) \(\cdot\) 0,6) = \(\frac{25}{6}\) \(\cdot\) \(\frac{6}{10}\) = \(\frac{25}{10}\) = 2,5

\(\frac{1,8}{2,5}\) = \(\frac{18}{25}\) = 0,72

е) \(\frac{(7,5 + 6\frac{2}{3}) \cdot 0,12}{4,5 + \frac{3}{5}}\)

7,5 + 6\(\frac{2}{3}\) = \(\frac{15}{2}\) + \(\frac{20}{3}\) = \(\frac{45}{6}\) + \(\frac{40}{6}\) = \(\frac{85}{6}\)

(\(\frac{85}{6}\) \(\cdot\) 0,12) = \(\frac{85}{6}\) \(\cdot\) \(\frac{12}{100}\) = \(\frac{85}{1}\) \(\cdot\) \(\frac{2}{100}\) = \(\frac{170}{100}\) = 1,7

4,5 + \(\frac{3}{5}\) = \(\frac{9}{2}\) + \(\frac{3}{5}\) = \(\frac{45}{10}\) + \(\frac{6}{10}\) = \(\frac{51}{10}\) = 5,1

\(\frac{1,7}{5,1}\) = \(\frac{17}{51}\) = \(\frac{1}{3}\) \(\approx\) 0,3333

Ответ: a) 0,3125; б) 0,625; в) -5,875; г) 14,5; д) 0,72; е) 0,3333

Отлично, ты хорошо умеешь находить числовые выражения! Продолжай в том же духе!