Question

Resuelve las siguientes operaciones:
1,33..... - 0,666.. - 3030.....
(3/5 - 0,4) - 0,4 + 1/3 - 5
(2,5 + 3/2 + 0,25 - 0,875) - ( 0,6 + 3/4)

Answer 1

Resuelve las siguientes operaciones:
1,33..... - 0,666.. - 3030... =

{ 1,33= 1 33.../99...= 1 1/3;
0,666= 666.../999...= 2/3;
0,303030= 3030../9999..= 10/33;}

= 1 1/3- 2/3 - 10/33= (3•1+1)/3 -2/3 -10/33= 4/3- 2/3 -10/33= 2/3 - 10/33= (2•11)/(3•11) - 10/33= 22/33- 10/33= 12/33= (12:3)/(33:3)= 4/3= 1 1/3= 1,33333....


{ 0,4= 4/10= (4:2)/(10:2)= 2/5}


(3/5 - 0,4) - 0,4 + 1/3 - 5 = (3/5- 2/5) - 2/5+ 1/3- 5= 1/5 - 2/5 + 1/3 -5= - (2/5- 1/5) + 1/3- 5= - 1/5 + 1/3- 5= 1/3 - 1/5- 5= (1•5)/(3•5) - (1•3)/(5•3) -5= 5/15- 3/15 -5= 2/15 -5= -( 5 -2/15)= - (4 15/15- 2/15)= - 4 13/15;

________ (3/5- 0,4)- 0,4+ 1/3- 5= 3/5 - 0,4 - 0,4 + 1/3 - 5= 3/5+ 1/3 - ( 0,4+ 0,4+ 5)= (3•3)/(5•3) + (1•5)/(3•5) - 5,8= 9/15+ 5/15= 14/15 - 5,8= 14/15 - 5 8/10= 14/15- 5 (8:2)/(10:2)= 14/15- 5 4/5= 14/15- 5 (4•3)/(5•3)= 14/15 - 5 12/15= - (5 12/15 - 14/15)= -( 4 (15•1+12)/15 - 14/15) = - (4 27/15- 14/15)= - 4 13/15;



(2,5 + 3/2 + 0,25 - 0,875) - ( 0,6 + 3/4) = (2,5+ 1,5 + 0,25 - 0,875)- (0,6+ 0,75)= 4,25- 0,875 - 0,6 - 0,75= 4,25- (0,875+ 0,75+ 0,6)= 4,25 - 2,225= 2,025.