Вариант 1 №1 Найдите значение выражений: 4,2 a) 6,8 ⋅ 3,5+2,5. 6) 2,9−6,4 55 1 г)3 4 12. 33 8 11 д) 436 13 97 B) 20 35 12

a) 6,8 ⋅ 3,5+2,5

6,8 ⋅ 3,5 = 23,8

23,8 + 2,5 = 26,3

Ответ: 26,3

б) 2,9 − 6,4

2,9 − 6,4 = -3,5

Ответ: -3,5

в) \(\frac{13}{20} ⋅ \frac{9}{35} ⋅ \frac{7}{12}\)

\(\frac{13}{20} ⋅ \frac{9}{35} ⋅ \frac{7}{12} = \frac{13 ⋅ 9 ⋅ 7}{20 ⋅ 35 ⋅ 12} = \frac{13 ⋅ 9 ⋅ 7}{20 ⋅ 5 ⋅ 7 ⋅ 12} = \frac{13 ⋅ 9}{20 ⋅ 5 ⋅ 12} = \frac{13 ⋅ 3 ⋅ 3}{20 ⋅ 5 ⋅ 4 ⋅ 3} = \frac{13 ⋅ 3}{20 ⋅ 5 ⋅ 4} = \frac{39}{400}\)

Ответ: \(\frac{39}{400}\)

г) \(3\frac{5}{4} ⋅ \frac{5}{12}\)

Преобразуем смешанную дробь в неправильную:

\(3\frac{5}{4} = \frac{3 ⋅ 4 + 5}{4} = \frac{12 + 5}{4} = \frac{17}{4}\)

Умножаем дроби:

\(\frac{17}{4} ⋅ \frac{5}{12} = \frac{17 ⋅ 5}{4 ⋅ 12} = \frac{85}{48}\)

Преобразуем неправильную дробь в смешанную:

\(\frac{85}{48} = 1\frac{37}{48}\)

Ответ: \(1\frac{37}{48}\)

д) \(4\frac{3}{4} ⋅ \frac{8}{3} ⋅ \frac{11}{6}\)

Преобразуем смешанную дробь в неправильную:

\(4\frac{3}{4} = \frac{4 ⋅ 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4}\)

Умножаем дроби:

\(\frac{19}{4} ⋅ \frac{8}{3} ⋅ \frac{11}{6} = \frac{19 ⋅ 8 ⋅ 11}{4 ⋅ 3 ⋅ 6} = \frac{19 ⋅ 2 ⋅ 11}{3 ⋅ 6} = \frac{19 ⋅ 11}{3 ⋅ 3} = \frac{209}{9}\)

Преобразуем неправильную дробь в смешанную:

\(\frac{209}{9} = 23\frac{2}{9}\)

Ответ: \(23\frac{2}{9}\)