Математика 6 класс

Упражнение 1472

Условие Виленкин 6 кл:

Найдите значение выражения:
1) (3,5 + 2 1/3) : (3,5 - 2 1/3);
2) (5,6 - 3 1/3) : (1,5 + 1 1/3);
3) (16 - 8 1/3) : (-2 5/9);
4) (15 - 9 2/3) : (-3 5/9).

 

ГДЗ Ответ:

1) (3,5 + 2 1/3) : (3,5 - 2 1/3) = 3,5 • 3,5 - 2 1/3 • 3,5 + 2 1/3 • 3,5 - 2 1/3 • 2 1/3 =
= (3,5)2 - (2 1/3)2 = (35/10)2 - (7/3)2 = (7/2)2 - (7/3)2 = 72 • (1/4 - 1/9) =
= 49 • (9/36 - 4/36) = 49 5/36 = 245/36 = 6 29/36;

2) (5,6 - 3 1/3) : (1,5 + 1 1/3) = (5 9/15 - 3 5/15) : (1 3/6 + 1 2/6) =
= 2 4/15 : 1 5/6 = 34/15 • 6/11 = 1 13/55;

3) (16 - 8 1/3) : (-2 5/9) = (15 3/3 - 8 1/3) : (-2 5/9) = 7 2/3 : (-2 5/9) =
= 23/3 • (-9/23) = -9/3 = -3;

4) (15 - 9 2/3) : (-3 5/9) = (14 3/3 - 9 2/3) : (-3 5/9) = 5 1/3 : (-32/9) =
= -16/3 • 9/32 = -1 1/2 = -1,5.

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