1. Запишите в буквенном виде равенство, выражающее:

a. сочетательное свойство умножения;

b. распределительное свойство умножения относительно сложения;

c. распределительное свойство умножения относительно вычитания.

2. Вычислите наиболее удобным

a. 25 ⋅ 78 ⋅ 4;

b. 49 ⋅ 9 + 21 ⋅ 9;

c. 2 ⋅ 49 ⋅ 50;

d. 316 ⋅ 5 − 216 ⋅ 5.

e. 3 ⋅ 5 ⋅ 8 ⋅ 3;

f. 239 ⋅ 47 + 239 ⋅ 53.

3. Упростите выражение:

a. 2 ⋅ x ⋅ 15, если х=3

b. 27x − 19x, если х=6

c. 6 ⋅ a ⋅ 13 ⋅ b;

d. 32y − 14y + y, если у=5

4. Верно ли неравенство:

a. 5 ⋅ 324 ⋅ 20 5 ⋅ 7 ⋅ 9 ⋅ 5 ⋅ 2;

c. 2 ⋅ 2 ⋅ 5 ⋅ 57 ⋅ 5 > 5 ⋅ 56 ⋅ 20;

d. 14 ⋅ 3 ⋅ 25 ⋅ 5 ⋅ 8 < 7 ⋅ 3 ⋅ 3 ⋅ 10 ⋅ 25 ⋅ 4

5. Выполните умножение:

a. 2 км 56 м ⋅ 68;

b. 3 т 5 ц 65 кг ⋅ 5;

c. 4 сут 6 ч 12 мин ⋅11

1. Равенства, выражающие свойства умножения:
a. Сочетательное свойство умножения: a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c
b. Распределительное свойство умножения относительно сложения: a ⋅ (b + c) = a ⋅ b + a ⋅ c
c. Распределительное свойство умножения относительно вычитания: a ⋅ (b - c) = a ⋅ b - a ⋅ c

2. Решение примеров:
a. 25 ⋅ 78 ⋅ 4 = (25 ⋅ 4) ⋅ 78 = 100 ⋅ 78 = 7800
b. 49 ⋅ 9 + 21 ⋅ 9 = (49 + 21) ⋅ 9 = 70 ⋅ 9 = 630
c. 2 ⋅ 49 ⋅ 50 = 2 ⋅ (49 ⋅ 50) = 2 ⋅ 2450 = 4900
d. 316 ⋅ 5 − 216 ⋅ 5 = (316 − 216) ⋅ 5 = 100 ⋅ 5 = 500
e. 3 ⋅ 5 ⋅ 8 ⋅ 3 = (3 ⋅ 3) ⋅ (5 ⋅ 8) = 9 ⋅ 40 = 360
f. 239 ⋅ 47 + 239 ⋅ 53 = 239 ⋅ (47 + 53) = 239 ⋅ 100 = 23900

3. Упрощение выражений:
a. 2 ⋅ x ⋅ 15, если x = 3: 2 ⋅ 3 ⋅ 15 = 6 ⋅ 15 = 90
b. 27x − 19x, если x = 6: 27 ⋅ 6 − 19 ⋅ 6 = 162 − 114 = 48
c. 6 ⋅ a ⋅ 13 ⋅ b = 6 ⋅ 13 ⋅ a ⋅ b = 78 ⋅ a ⋅ b
d. 32y − 14y + y, если y = 5: 32 ⋅ 5 − 14 ⋅ 5 + 5 = 160 − 70 + 5 = 95

4. Проверка неравенств:
a. 5 ⋅ 324 ⋅ 20 > 5 ⋅ 7 ⋅ 9 ⋅ 5 ⋅ 2: 5 ⋅ 324 ⋅ 20 = 8100 > 5 ⋅ 7 ⋅ 9 ⋅ 5 ⋅ 2 = 3150 (верно)
b. 2 ⋅ 2 ⋅ 5 ⋅ 57 ⋅ 5 > 5 ⋅ 56 ⋅ 20: 2 ⋅ 2 ⋅ 5 ⋅ 57 ⋅ 5 = 1140 > 5 ⋅ 56 ⋅ 20 = 5600 (неверно)
c. 14 ⋅ 3 ⋅ 25 ⋅ 5 ⋅ 8 < 7 ⋅ 3 ⋅ 3 ⋅ 10 ⋅ 25 ⋅ 4: 14 ⋅ 3 ⋅ 25 ⋅ 5 ⋅ 8 = 4200 < 7 ⋅ 3 ⋅ 3 ⋅ 10 ⋅ 25 ⋅ 4 = 6300 (верно)

5. Умножение:
a. 2 км 56 м ⋅ 68 = (2 ⋅ 1000 + 56) ⋅ 68 = 2056 ⋅ 68 = 139648
b. 3 т 5 ц 65 кг ⋅ 5 = (3 ⋅ 1000 + 5 ⋅ 100 + 65) ⋅ 5 = 35065 ⋅ 5 = 175325
c. 4 сут 6 ч 12 мин ⋅ 11 = (4 ⋅ 24 + 6) ⋅ 11 = 102 ⋅ 11 = 1122