ГДЗ по Математике 5 Класс Номер 331 Дорофеев, Шарыгин, Суворова — Подробные Ответы

Задача

Правильно ли выполнены преобразования?
Если нет, то объясните, в чём ошибка, и дайте верный ответ:
1) 38 ⋅ 5 = (30 + 8) ⋅ 5 = 30 ⋅ 5 + 8;
2) (27 — 14) ⋅ 9 = 27 ⋅ 9 — 14 ⋅ 9;
3) 6 ⋅ (a — b) = 6 ⋅ a — 6 ⋅ b;
4) (2 + a) ⋅ 6 = 2 ⋅ 6 + a ⋅ 6 = 12 + 6 ⋅ a;
5) (b + 4) ⋅ 3 = b ⋅ 3 + 4;
6) 5 + 5 ⋅ 4 + 7 ⋅ 5 = 5 ⋅ (4 + 7);
7) 3 ⋅ 23 — 17 ⋅ 3 = 3 ⋅ (23 — 17);
8) 5 + 5 ⋅ a = 5 ⋅ (1 + a);
9) b ⋅ 7 + b ⋅ 9 = b ⋅ (7 + 9);
10) 4 ⋅ a + 12 = 4 ⋅ a + 4 ⋅ 3 = 4 ⋅ (a + 3).

Краткий ответ:

1) 38 ⋅ 5 = (30 + 8) ⋅ 5 = 30 ⋅ 5 + 8 – неверно, так как 8 не умножили на 5
38 ⋅ 5 = (30 + 8) ⋅ 5 = 30 ⋅ 5 + 8⋅ 5
2) (27 − 14) ⋅ 9 = 27 ⋅ 9 − 14 ⋅ 9 – верно
3) 6 ⋅ (a − b) = 6 ⋅ a − 6 ⋅ b – верно
4) (2 + a) ⋅ 6 = 2 ⋅ 6 + a ⋅ 6 = 12 + 6 ⋅ a – верно
5) (b + 4) ⋅ 3 = b ⋅ 3 + 4 – неверно, так как 4 не умножили на 3
(b + 4) ⋅ 3 = b ⋅ 3 + 4 ⋅ 3
6) 5 + 5 ⋅ 4 + 7 ⋅ 5 = 5 ⋅ (4 + 7) – неверно, так как забыли третье слагаемое, когда выносили 8 за скобку
5 + 5 ⋅ 4 + 7 ⋅ 5 = 5 ⋅ 1 + 5 ⋅ 4 + 7 ⋅ 5 = 5 ⋅ (1 + 4 + 7)
7) 3 ⋅ 23 − 17 ⋅ 3 = 3 ⋅ (23 − 17) – верно
8) 5 + 5 ⋅ a = 5 ⋅ (1 + a) – верно
9) b ⋅ 7 + b ⋅ 9 = b ⋅ (7 + 9) — верно
10) 4 ⋅ a + 12 = 4 ⋅ a + 4 ⋅ 3 = 4 ⋅ (a + 3) – верно

Подробный ответ:

Рассмотрим каждое преобразование:

1) 38 ⋅ 5 = (30 + 8) ⋅ 5 = 30 ⋅ 5 + 8

Ошибка:

Здесь не применено распределительное свойство правильно. 8 нужно было умножить на 5.
Верное преобразование: 38 ⋅ 5 = (30 + 8) ⋅ 5 = 30 ⋅ 5 + 8 ⋅ 5.

2) (27 − 14) ⋅ 9 = 27 ⋅ 9 − 14 ⋅ 9

Верно:

Это правильное применение распределительного свойства: (a — b) ⋅ c = a ⋅ c — b ⋅ c.

3) 6 ⋅ (a − b) = 6 ⋅ a − 6 ⋅ b

Верно:

Это также правильное применение распределительного свойства.

4) (2 + a) ⋅ 6 = 2 ⋅ 6 + a ⋅ 6 = 12 + 6 ⋅ a

Верно:

Распределительное свойство применено правильно.

5) (b + 4) ⋅ 3 = b ⋅ 3 + 4

Ошибка:

4 не умножено на 3.
Верное преобразование: (b + 4) ⋅ 3 = b ⋅ 3 + 4 ⋅ 3.

6) 5 + 5 ⋅ 4 + 7 ⋅ 5 = 5 ⋅ (4 + 7)

Ошибка:

При вынесении общего множителя 5 за скобку забыли учесть первое слагаемое.
Верное преобразование: 5 + 5 ⋅ 4 + 7 ⋅ 5 = 5 ⋅ 1 + 5 ⋅ 4 + 7 ⋅ 5 = 5 ⋅ (1 + 4 + 7).

7) 3 ⋅ 23 − 17 ⋅ 3 = 3 ⋅ (23 − 17)

Верно:

Это правильное применение распределительного свойства: a ⋅ c — b ⋅ c = c ⋅ (a — b).

8) 5 + 5 ⋅ a = 5 ⋅ (1 + a)

Верно:

Общий множитель 5 вынесен за скобку правильно.

9) b ⋅ 7 + b ⋅ 9 = b ⋅ (7 + 9)

Верно:

Общий множитель b вынесен за скобку правильно.

10) 4 ⋅ a + 12 = 4 ⋅ a + 4 ⋅ 3 = 4 ⋅ (a + 3)

Верно:

Общий множитель 4 вынесен за скобку правильно.

Оцени решение