ГДЗ по Математике 5 Класс Номер 313 Дорофеев, Шарыгин, Суворова — Подробные Ответы

Вычислите устно произведение и запишите, как вы рассуждали:
а) 13 ⋅ 5 ⋅ 2 ⋅ 7;
б) 5 ⋅ 5 ⋅ 6 ⋅ 4;
в) 7 ⋅ 2 ⋅ 5 ⋅ 2 ⋅ 5;
г) 2 ⋅ 9 ⋅ 5 ⋅ 5 ⋅ 4;
д) 8 ⋅ 4 ⋅ 125 ⋅ 25;
е) 5 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 6.

а) 13 ⋅ 5 ⋅ 2 ⋅ 7

(13 ⋅ 2) ⋅ (5 ⋅ 7) = 26 ⋅ 35 = 910.

Ответ: 910.

б) 5 ⋅ 5 ⋅ 6 ⋅ 4

(5 ⋅ 5) ⋅ (6 ⋅ 4) = 25 ⋅ 24 = 600.

Ответ: 600.

в) 7 ⋅ 2 ⋅ 5 ⋅ 2 ⋅ 5

(7 ⋅ 2) ⋅ (5 ⋅ 2 ⋅ 5) = 14 ⋅ 50 = 700.

Ответ: 700.

г) 2 ⋅ 9 ⋅ 5 ⋅ 5 ⋅ 4

(2 ⋅ 4) ⋅ (9 ⋅ 5 ⋅ 5) = 8 ⋅ 225 = 1800.

Ответ: 1800.

д) 8 ⋅ 4 ⋅ 125 ⋅ 25

(8 ⋅ 4) ⋅ (125 ⋅ 25) = 32 ⋅ 3125 = 100000.

Ответ: 100000.

е) 5 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 6

(5 ⋅ 5 ⋅ 5 ⋅ 5) ⋅ (2 ⋅ 2 ⋅ 2 ⋅ 2) ⋅ 6 = 625 ⋅ 16 ⋅ 6 = 60000.

Ответ: 60000.

Вычислим произведения для каждой из заданных задач, объясняя рассуждения.

а) 13 ⋅ 5 ⋅ 2 ⋅ 7

1. Удобно сгруппировать: (13 ⋅ 2) ⋅ (5 ⋅ 7).
2. Сначала вычислим 13 ⋅ 2 = 26.
3. Затем 5 ⋅ 7 = 35.
4. Теперь 26 ⋅ 35.
   • Можно разложить: 26 ⋅ 35 = 26 ⋅ (30 + 5) = 26 ⋅ 30 + 26 ⋅ 5 = 780 + 130 = 910.

Ответ: 910.

б) 5 ⋅ 5 ⋅ 6 ⋅ 4

1. Удобно сгруппировать: (5 ⋅ 5) ⋅ (6 ⋅ 4).
2. Сначала 5 ⋅ 5 = 25.
3. Затем 6 ⋅ 4 = 24.
4. Теперь 25 ⋅ 24.
   • Можно разложить: 25 ⋅ 24 = 25 ⋅ (20 + 4) = 25 ⋅ 20 + 25 ⋅ 4 = 500 + 100 = 600.

Ответ: 600.

в) 7 ⋅ 2 ⋅ 5 ⋅ 2 ⋅ 5

1. Удобно сгруппировать: (7 ⋅ 2) ⋅ (5 ⋅ 2 ⋅ 5).
2. Сначала 7 ⋅ 2 = 14.
3. Затем 5 ⋅ 2 = 10, и 10 ⋅ 5 = 50.
4. Теперь 14 ⋅ 50 = 700.

Ответ: 700.

г) 2 ⋅ 9 ⋅ 5 ⋅ 5 ⋅ 4

1. Удобно сгруппировать: (2 ⋅ 4) ⋅ (9 ⋅ 5 ⋅ 5).
2. Сначала 2 ⋅ 4 = 8.
3. Затем 9 ⋅ 5 = 45, и 45 ⋅ 5 = 225.
4. Теперь 8 ⋅ 225.
   • Можно разложить: 8 ⋅ 225 = 8 ⋅ (200 + 25) = 1600 + 200 = 1800.

Ответ: 1800.

д) 8 ⋅ 4 ⋅ 125 ⋅ 25

1. Удобно сгруппировать: (8 ⋅ 4) ⋅ (125 ⋅ 25).
2. Сначала 8 ⋅ 4 = 32.
3. Затем 125 ⋅ 25 = 3125 (так как 25 = 5², и 125 = 5³, тогда 125 ⋅ 25 = 5⁵ = 3125).
4. Теперь 32 ⋅ 3125.
   • Можно разложить: 32 ⋅ 3125 = 32 ⋅ (3000 + 125) = 96000 + 4000 = 100000.

Ответ: 100000.

е) 5 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5 ⋅ 5 ⋅ 6

1. Удобно сгруппировать: (5 ⋅ 5 ⋅ 5 ⋅ 5) ⋅ (2 ⋅ 2 ⋅ 2 ⋅ 2) ⋅ 6.
2. Сначала 5 ⋅ 5 ⋅ 5 ⋅ 5 = 625.
3. Затем 2 ⋅ 2 ⋅ 2 ⋅ 2 = 16.
4. Теперь 625 ⋅ 16 ⋅ 6.
   • Сначала 625 ⋅ 16 = 10000.
   • Затем 10000⋅ 6 = 60000.

Ответ: 60000.