Вычислите а)1/2*4/5*5/6 б)7/8*4/35*9/10 в)42/56*8/21*15/36 г)14/19*95/96*16/35 досконально и с деяниями.

Вычислим значения:

а) 1/2 * 4/5 * 5/6 = 1/3;

1) 1/2 * 4/5 = (1 * 4)/(2 * 5) = (2 * 2)/(2 * 5) = 2/5;

2) 2/5 * 5/6 = (2 * 5)/(5 * 6) = 2/6 = 2/(2 * 3) = 1/3.

б) 7/8 * 4/35 * 9/10 = 9/100;

1) 7/8 * 4/35 = (7 * 4)/(8 * 35) = (7 * 4)/(4 * 2 * 7 * 5) = 1/(2 * 5) = 1/10;

2) 1/10 * 9/10 = (1 * 9)/(10 * 10) = 9/100.

в) 42/56 * 8/21 * 15/36 = 5/42;

1) 42/56 * 8/21 = (42 * 8)/(56 * 21) = (2 * 21 * 8)/(7 * 8 * 21) = 2/7;

2) 2/7 * 15/36 = (2 * 15)/(7 * 36) = (2 * 3 * 5)/(7 * 2 * 3 * 6) = 5/(7 * 6) = 5/42.

г) 14/19 * 95/96 * 16/35 = 1/3;

1) 14/19 * 95/96 = (14 * 95)/(19 * 96) = (2 * 7 * 5 * 19)/(19 * 2 * 48) = 35/48;

2) 35/48 * 16/35 = (35 * 16)/(48 * 35) = (35 * 16)/(3 * 16 * 35) = 1/3.