ГДЗ по Математике 5 Класс Номер 321 Дорофеев, Шарыгин, Суворова — Подробные Ответы

При вычислении произведений помогает знание некоторых результатов.
Например, 37 ⋅ 3 = 111, 7 ⋅ 11 ⋅ 13 = 1001.
Пользуясь этими равенствами, вычислите:
а) 37 ⋅ 15;
б) 3 ⋅ 7 ⋅ 11 ⋅ 13 ⋅ 37;
в) 26 ⋅ 33 ⋅ 7;
г) 182 ⋅ 66.

а) 37 ⋅ 15 = 111 ⋅ 5 = 555

б) 3 ⋅ 7 ⋅ 11 ⋅ 13 ⋅ 37 = 1001 ⋅ 111 = 111111

в) 26 ⋅ 33 ⋅ 7 = 78 ⋅ 77 = 6006

г) 182 ⋅ 66 = 2002 ⋅ 6 = 12012

а) 37 ⋅ 15

• Разложим 15 на множители: 15 = 3 ⋅ 5.
• Используем известное 37 ⋅ 3 = 111.
• Тогда 37 ⋅ 15 = 111 ⋅ 5 = 555.

б) 3 ⋅ 7 ⋅ 11 ⋅ 13 ⋅ 37

• Известно, что 7 ⋅ 11 ⋅ 13 = 1001.
• Также знаем, что 37 ⋅ 3 = 111.
• Поэтому 3 ⋅ 7 ⋅ 11 ⋅ 13 ⋅ 37 = 1001 ⋅ 111 = 111111.

в) 26 ⋅ 33 ⋅ 7

• Разложим 33 на множители: 33 = 3 ⋅ 11.
• Тогда 26 ⋅ 33 ⋅ 7 = 26 ⋅ (3 ⋅ 11) ⋅ 7.
• Используем известное 7 ⋅ 11 = 77.
• 26 ⋅ 3 = 78.
• Поэтому 26 ⋅ 33 ⋅ 7 = 78 ⋅ 77 = 6006.

г) 182 ⋅ 66

• Разложим 66 на множители: 66 = 6 ⋅ 11.
• Тогда 182 ⋅ 66 = 182 ⋅ (6 ⋅ 11).
• 182 ⋅ 11 = 2002 (используем распределительное свойство: 182 = 180 + 2, 180 ⋅ 11 + 2 ⋅ 11 = 1980 + 22 = 2002).
• Теперь 2002 ⋅ 6 = 12012.