ГДЗ по Математике 5 Класс Номер 320 Дорофеев, Шарыгин, Суворова — Подробные Ответы

Преобразуйте произведение и вычислите его значение:
а) 75 ⋅ 14 ⋅ 18;
б) 16 ⋅ 125 ⋅ 4 ⋅ 35.

а) 75 ⋅ 14 ⋅ 18 = (25 ⋅ 5) ⋅ (7 ⋅ 2) ⋅ (2 ⋅ 9) = (25 ⋅ 2 ⋅ 2) ⋅ (3 ⋅ 7 ⋅ 9) = 100 ⋅ 189 = 18 900
б) 16 ⋅ 125 ⋅ 4 ⋅ 35 = (8 ⋅ 2) ⋅ 125 ⋅ 4⋅ (5 ⋅ 7) = (8 ⋅ 125) ⋅ (2 ⋅ 5) ⋅ (4 ⋅ 7) = 1 000 ⋅ 10 ⋅ 28 = 280 000

а) 75 ⋅ 14 ⋅ 18

1. Разложим числа на множители: 75 = 25 ⋅ 3, 14 = 7 ⋅ 2, 18 = 9 ⋅ 2.
2. Перегруппируем множители: (25 ⋅ 2 ⋅ 2) ⋅ (3 ⋅ 7 ⋅ 9).
3. Умножаем: 25 ⋅ 4 = 100 и 3 ⋅ 7 ⋅ 9 = 189.
4. Итоговое произведение: 100 ⋅ 189 = 18 900.

б) 16 ⋅ 125 ⋅ 4 ⋅ 35

1. Разложим числа на множители: 16 = 8 ⋅ 2, 125 = 5 ⋅ 5 ⋅ 5, 4 = 2 ⋅ 2, 35 = 5 ⋅ 7.
2. Перегруппируем множители: (8 ⋅ 125) ⋅ (2 ⋅ 5) ⋅ (4 ⋅ 7).
3. Умножаем: 8 ⋅ 125 = 1 000, 2 ⋅ 5 = 10, 4 ⋅ 7 = 28.
4. Итоговое произведение: 1 000 ⋅ 10 ⋅ 28 = 280 000.

Таким образом, мы можем упростить вычисления, разлагая числа на множители и перегруппировывая их.