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МатематикаВопрос:
1144. Выполните умножение: 2 a) ⋅ (-5 1/4); 7 б) -4 1/2 ⋅ (-1 1/3); в) 3,6 ⋅ (-2/3); г) -4/7 ⋅ 4,2;
Ответ:
Краткое пояснение: Представим смешанные числа в виде неправильных дробей и выполним умножение.
- a) \(\frac{2}{7} ⋅ (-5 \frac{1}{4}) = \frac{2}{7} ⋅ (-\frac{21}{4}) = -\frac{2 ⋅ 21}{7 ⋅ 4} = -\frac{2 ⋅ 3}{1 ⋅ 4} = -\frac{6}{4} = -\frac{3}{2} = -1\frac{1}{2}\)
- б) \(-4 \frac{1}{2} ⋅ (-1 \frac{1}{3}) = -\frac{9}{2} ⋅ (-\frac{4}{3}) = \frac{9 ⋅ 4}{2 ⋅ 3} = \frac{3 ⋅ 2}{1 ⋅ 1} = \frac{6}{1} = 6\)
- в) \(3,6 ⋅ (-\frac{2}{3}) = \frac{36}{10} ⋅ (-\frac{2}{3}) = \frac{12}{5} ⋅ (-\frac{2}{1}) = -\frac{12 ⋅ 2}{5 ⋅ 1} = -\frac{24}{5} = -4\frac{4}{5}\)
- г) \(-\frac{4}{7} ⋅ 4,2 = -\frac{4}{7} ⋅ \frac{42}{10} = -\frac{4 ⋅ 6}{1 ⋅ 10} = -\frac{24}{10} = -2,4\)
Ответ: а) -1 1/2; б) 6; в) -4 4/5; г) -2,4
