Question

Suprime los signos de agrupacion y realiza las operaciones
a) 2+{-1,5-3/4-[0,555...-1/6+(-2+5/3)]+8/9}-2= -17/12
b) -12+1,5-{6-[1/4+(2-7/8)+0,4]-1/2}-9/40+10= -89/20
c) 0,8333...+[0,5-1-(1/4-1/9+1 1/3)+1+(2+1/18+0,75)]=8/3
d) 1-{-1+3/4-2+[0,66..+0,166..-(1/3+2-0,5)-1/4+]+3}=3/2
e) 7/40+1-{-0,2+3/20+[-0,3-(-1-0,5)-0,375] }=1/10
f) -6+1,5{-4[1/2+(1-7/8)+0,4]-1/4}-7/40+2= -27/5
g) 5/5+[-1+0,75-(1 1/3+3/4-0,444...)+2+(5/18-0,5)+1/6]=8/9
h) 1-{0,3636...-[-1-0,5+(-2/3+1)]-3/11-(2,5-1/6)}-1/22=67/33
i) -0,58333...+3/5-{-3-[0,25-(1-5/6)]+3,333...-7/60}+1=53/60
j) -{-1+3/8-2+[0,666...+0,1666...-(1/3+2-0,5)-1/4]+3}+1/6=25/24
k) 12/3-(-2/21+1)-{-[0,666...-1/6+(-1+1/7)+5/14-(1,8333...-2/7)] }= - 131/42
AYUDA PORFAVOR

Answer 1

Al suprimir los signos de agrupación y resolver las operaciones nos queda:

Solución por pasos

se sabe que:

1,5 = 3/2 ; 0,555... = 5/9 ; 0,4 = 2/5 ; 0,8333... = 5/6 ; 0,5 = 1/2 ; 0,75 = 3/4; 0,66... =2/3; 0,166... = 1/6; 0,2  = 1/5 ; 0,3 = 3/10 ; 0,375 = 3/8 ; 0,44... = 4/9;

0,3636... = 4/11; 2,5 = 5/2; 0,58333... = 7/12; 0,25 = 1/4; 3,333... = 10/3; 1,833...=11/6.

Sustituir los valores en las operaciones

a) 2+{-3/2-3/4-[5/9-1/6+(-2+5/3)]+8/9}-2= -17/12

2+{-3/2-3/4-[5/9-1/6-1/3]+8/9}-2

2+{-3/2-3/4-1/18+8/9}-2

2+-17/12-2

-17/12

b) -12+3/2-{6-[1/4+(2-7/8)+2/5]-1/2}-9/40+10= -89/20

-12+3/2-{6-[1/4+9/8+2/5]-1/2}-9/40+10

-12+3/2-{6-71/40-1/2}-9/40+10

-12+3/2-149/40-9/40+10

-89/20

c) 5/6+[1/2-1-(1/4-1/9+1 1/3)+1+(2+1/18+3/4)]=8/3

5/6+[1/2-1-(1/4-1/9+4/3)+1+101/36]

5/6+[1/2-1-53/36+1+101/36]

5/6+11/6

8/3

d) 1-{-1+3/4-2+[2/3+1/6-(1/3+2- 1/2)-1/4+]+3}=3/2

1-{-1+3/4-2+[2/3+1/6-11/6-1/4+]+3}

1-{-1+3/4-2-5/4+3}

1-(-1/2)

1+1/2

3/2

e) 7/40+1-{- 1/5+3/20+[-3/10-(-1-1/2)-3/8] } =1/10

7/40+1-{- 1/5+3/20+[-3/10+3/2-3/8] }

7/40+1-{- 1/5+3/20+33/40 }

7/40+1-31/40

2/5

El resultado 1/10 esta errado.

f) -6+3/2{-4[1/2+(1-7/8)+2/5]-1/4}-7/40+2= -27/5

-6+3/2{-4[1/2+1/8+2/5]-1/4}-7/40+2

-6+3/2{-41/10-1/4}-7/40+2

-6-261/40-7/40+2

-107/10

El resultado -27/5 esta errado.

g) 5/5+[-1+3/4-(1 1/3+3/4-4/9)+2+(5/18- 1/2)+1/6]=8/9

5/5+[-1+3/4-(4/3+3/4-4/9)+2-2/9+1/6]

5/5+[-1+3/4-59/36+2-2/9+1/6]

5/5+1/18

19/18

El resultado -8/9 esta errado.

h) 1-{4/11-[-1-1/2+(-2/3+1)]-3/11-(5/2-1/6)}-1/22=67/33

1-{4/11-[-1-1/2+1/3]-3/11-7/3}-1/22

1-{4/11+7/6-3/11-7/3}-1/22

1+71/66-1/22

67/33

i) -7/12+3/5-{-3-[1/4-(1-5/6)]+ 10/3-7/60}+1=53/60

-7/12+3/5-{-3-[1/4-1/6]+ 10/3-7/60}+1

-7/12+3/5-{-3-1/12+ 10/3-7/60}+1

-7/12+3/5-2/15+1

53/60

j) -{-1+3/8-2+[2/3+1/6-(1/3+2-1/2)-1/4]+3}+1/6=25/24

-{-1+3/8-2+[2/3+1/6-11/6-1/4]+3}+1/6

-{-1+3/8-2-5/4+3}+1/6

7/8+1/6

25/24

k) 12/3-(-2/21+1)-{-[2/3-1/6+(-1+1/7)+5/14-(11/6-2/7)] }= - 131/42

12/3-19/21-{-[2/3-1/6-6/7+5/14-65/42] }

12/3-19/21-{--65/42 }

12/3-19/21-{65/42 }

12/3-19/21-65/42

65/42

El resultado -131/42 esta errado.