Expressões numericas
Autor: Eduardo Santos | Publicado: 2014-07-27T21:58:00-03:00



1) As operações de adição e de subtração são efetuadas na ordem em que aparecem

Exemplos

a) 7-3+1-2=
&nbsp;&nbsp;&nbsp; =4+1-2=
&nbsp;&nbsp;&nbsp; =5-2=
&nbsp;&nbsp;&nbsp; =3

B) 15-1-2+5=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =14-2+5=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =12+5=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =17

2) Existem expressões onde aparecem os sinais de associação e que devem ser eliminados nesta ordem

1º) parênteses ( )
2º) colchetes [ ]
3º) Chaves { }

exemplo
&nbsp;&nbsp;&nbsp;
74+{10-[5-(6-4)+1]}=
&nbsp;&nbsp;&nbsp; =74+{10-[5-2+1]}=
&nbsp;&nbsp; &nbsp;=74+{10-[3+1]}=
&nbsp;&nbsp; &nbsp;=74+{10-4}=
&nbsp;&nbsp;&nbsp; =74+6=
&nbsp;&nbsp;&nbsp; =80 






3º) multiplicações e divisões

4º) adições e subtrações

Se houver sinais de associação (parênteses, colchetes e chaves) devemos proceder da seguinte maneira:

5º) As contas dentro dos parênteses seguindo a ordem acima colocada

6º) As contas dentro dos colchetes seguindo a ordem acima colocada

7º) As contas dentro das chaves seguindo a ordem acima colocada


EXEMPLOS

1º) 15+[(3x6-2)-(10-6:2)+1]=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 15+[(18-2)-(10-3)+1]=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =15+[16-7+1]=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =15+[9+1]=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =15+10=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =25

2º) 50-{40-3x[5-(10-7)]}=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 50-{40-3x[5-3]}=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 50-{40-3x2}=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 50-{40-6}=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = 50-34=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; =16

EXERCÍCIOS

1) Calcule as expressões

a) 3x75+3x25 = (R:300)
b) 5x97+5x3 = (R:500 )
c) 4x101+4x99 = (R:800)
d) 20x47+80x47 = (R:4700)
e) 12+16:8x3-5 = (R:13)
f) 100-6x7+8:2 = (R:62)
g) 64:8+5x5-3 = (R: 30)
h) 1+3+5x7-9:3 = (R:36)

2) Calcule o valor das expressões:

a) 7+15:3 = (R:12)
b) 4x5+1 = (R:21)
c) 10:2+8 = (R:13) 
d) 32+12:2 = (R:38)
e) 20:10+10 = (R:12)
f)7x3-2x5 = (R:11)
g)40-2x4+5 = (R:37)
h)4x3+10:2 = (R:17)
i)50-16:8+7 = (R:55)
j)32:4:2:2 = (R:2) 

3) Calcule o valor das expressões

a) (13+2)x3+5 = (R:50)
b)(7+2)x(3-1) = (R:18)
c)(4+2x5)-3 = (R:11)
d) 20-(15+6:3) = (R:3)
e)15+[6+(8-4:2)] = (R:27)
f)40-[3+(10-2):2] = (R:33)
g)[30+2x(5-3)]x2-10 = (R:58)
h) 10+[4+(7x3+1)]-3 = (R:33)

4) Calcule o valor das expressões

a) (3+2)x(5-1)+4 = (R:24)
b) 82-8x7:(4-1x3) = (R:26)
c) 25-[10-(2x3+1)] = (R:22)
d) 70-[12+(5x2-1)+6] = (R:43)
e)8:2+[15-(4x2+1)] = (R:10)
f)9+[4+2x(6-4)+(2+5)]-8 = (R:16)
g) 50+{10-2x[(6+4:2)-(10-3)]} = (R:58)
h)180:{10+2x[20-45:(13-2x5)]} = (R:9)


5) Calcule o valor das expressões:

a) 70:7-1= (R:9)
b) 20+3x2= (R:26)
c) 30+10:10 = (R:31) 
d) 150-7x12= (R:66)
e) 48:16+20:4 = (R:8)
f) 10-8:2+3 = (R:9)
g) 30:5-1+2x3 = (R:11)

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Bibliografias



BIANCHINI, E. Matemática. São Paulo:
Moderna, 1999. 5ª serie.

BONGIOVANI, V., VISSOTO, O. R. LAUREANO, J.L.T. Matemática e
vida. São Paulo: Ática, 1997. 5ª serie.
GIOVANI, J.R.,
CASTRUCCI, B.; GIOVANI JR., J.R. A conquista da matemática. São Paulo: FTD,
1998. 5ª serie.