№ 654 Алгебра = № 25.13 Математика
Умова:
Обчисліть значення виразу найзручнішим способом:
1) 157 · 37 + 29 · 157 + 143 · 42 + 24 · 143;
2) 9$\frac{2}{3}$ · 5$\frac{1}{2}$ − 16 · 4,5 + 10$\frac{1}{3}$ · 5$\frac{1}{2}$ − 16.
Розв'язок:
1) 157 ⋅ 37 + 29 ⋅ 157 + 143 ⋅ 42 + 24 ⋅ 143 = 157 ⋅ (37 + 29) + 143 ⋅ (42 + 24) = 157 ⋅ 66 + 143 ⋅ 66 = 66 ⋅ (157 + 143) = 66 ⋅ 300 = 19 800;
2) 9$\frac{2}{3}$ · 5$\frac{1}{2}$ − 16 · 4,5 + 10$\frac{1}{3}$ · 5$\frac{1}{2}$ − 16 = 5$\frac{1}{2}$ ⋅ (9$\frac{2}{3}$ + 10$\frac{1}{3}$) − 16 ⋅ (4,5 + 1) = 5$\frac{1}{2}$ ⋅ 20 − 5,5 ⋅ 16 = $\frac{11}{2}$ ⋅ 20 − 5,5 ⋅ 16 = 5,5 ⋅ 20 − 5,5 ⋅ 16 = 5,5 ⋅ (20 − 16) = 5,5 ⋅ 4 = 22.