z z z z z NÚMEROS z ENTEROS z z z z z z z z I.E.S. Pablo Serrano

Presentación del tema: "z z z z z NÚMEROS z ENTEROS z z z z z z z z I.E.S. Pablo Serrano"— Transcripción de la presentación:

1 z z z z z NÚMEROS z ENTEROS z z z z z z z z I.E.S. Pablo Serrano
Mariano Benito

2 Sumas en Z 9+3=12 (-9)+(-3)= -9-3=-12 (+9)+(+3)= 7 -5+(-3)= -5-3=-8
5+2= 6-3= 3 6+(+3)= 6+3=9 6+(-3)= -7+3= -4 7+2 = 9 (-7)+(+3)= (+7)+2= -6-4=-10 6-4= 2 -6+(-4)= 6+(-4)= (-8)+(+4)= -8+4=-4 -8+(+4)= -8+4= -4 6+(-2)= 6-2= 4 -6+(+3)= -6+3=-3 7+3 = 10 (+7)+3= -7+3= -4 (-5)+(-4)= -5-4= -9 -5+(-4)= -5-4= -9

3 Restas en Z -9+3 =-6 9-5 = 4 (-9)-(-3)= (+9)-5= -5+2 =-3 -5-3 = -8
9-5 = 4 (-9)-(-3)= (+9)-5= -5+2 =-3 -5-3 = -8 -5-(-2)= -5-(+3)= 6+2 = 8 6+3 = 9 6-(-2)= 6-(-3)= -7-3= -10 7+3 =10 (-7)-(+3)= (+7)-(-3)= -6+1 =-5 6+4 = 10 -6-(-1)= 6-(-4)= -8-(-4)= -8+4 =-4 -8-1= -9 6-(+2)= 6-2 =4 6-(+3)= 6-3 = 3 (+7)-3= 7-3 = 4 (-7)-2= -7-2 = -9 (-5)-(-1)= -5+1 =-4 (-5)-(-4)= -5+4 = -1

4 Sumas y restas en Z 17 -17 -(-9)+5-(-3)= -(+9)-5-(+3)= -10 -6
-5+(-3)-2= -5-(+3)+2= 11 7 6+(+3)-(-2)= 6-(-3)+(-2)= 2 -2 -(-7)-(+3)-2= -(+7)-(-3)+2= -9 9 -6+(-4)-(-1)= 6-(-4)-(+1)= -8+(-4)+1= -11 -8+(+4)-1= -5 6-(-3)-(+2)= 7 6-(+3)+(-2)= 1 -(+7)-3-2= -12 -(-7)+3-2= 8 -(-5)+(-4)-(-1)= 2 (-5)-(-4)-(-1)=

5 Más sumas y restas en Z; más ..
-6 (-9+5-1)-(3-2)= -(2+9)-(5+3-4)= -15 -2 -(-5)+(-3-2)= 5-( )= 9 -(2-6-3)+2= -(6-2-3)-(-3+2)= 4 -9 -(-7-1+3)-(+3-2)= -(4+7-3)+(-2+1)= -5 (1-6-4)-(-1-3)= (-1+6-4)-(+1)= -8+(6-4+1)= -5 (+4-1-5)= -11 -(6-2)-(-3+2-1)= -2 (6-2-7)+(-2)= -5 -(2+7-3)-2= -8 -(-4-7+8)-(6-2)= -1 -(-5-4+3)-(-1+5)= 2 -(-5)-(-4-1+9)= 1

6 Productos y cocientes en Z
5 -2 15:3= -(+10):5= -5 6 25:(-5)= (+3)·2= 18 6 6·(+3)= (-12):(-2)= 1 -6 -(-7):(+7)= (-3)·2= 4 -4 (-4)·(-1)= 16:(-4)= -8:(-4)= 2 (+4)·(-2)= -8 6·(-3)= -18 6:(+3)= 2 -(+9):3= -3 -(-7)·3= 21 -(-5)·(-4)= -20 (-4):(-2)= 2

7 Operaciones combinadas en Z
14 -5 -(-9)+15:3= -(+10):5-(+3)= -7 -11 25:(-5)-2= -5-(+3)·2= 20 6·(+3)-(-2)= 6-(-12):(-2)= -1 -1 -(-7):(+7)-2= -(+7)-(-3)·2= -2 -5 -6+(-4)·(-1)= 16:(-4)-(+1)= -8:(-4)+1= 3 -8+(+4)·(-2)= -16 6·(-3)-(+2)= -20 6:(+3)+(-2)= -(+9):3-2= -5 -(-7)·3-2= 19 -(-5)·(-4)-(-1)= -19 (-5)-(-4):(-2)= -7

8 Operaciones combinadas en Z, más largas
-(-9)·2+15:3-(-3):3= 9·2+15:3+3:3 = = 24 2·5-(-5)-2·(-7)= 29 6·(+3)-22:(-2)-3= 26 -(-7):7-2·(-6)+(-3)·(-1)= 16 -6:(-3)+(-4)·(-1)-6= -8:(-4)+10:(-5)-3= -3 6·(-3)-(+2):2+4·3= -7 -1 -(+9):3-22:(-11)= -(-5)·(-4)-(-1)+10:2= -14

9 Operaciones combinadas en Z, más largas..
-9·2-15:3-(+3):3= -9·2-15:3-3:3 = = -24 -2·5-(+5)-2·(-7)= -1 -6·(+3)-16:(-2)-3= -13 (-7):7-2·(+6)+3·(-1)= -16 6:(-3)+4·(-1)-6= -12 8:(-4)-10:(-5)+3= 3 -6·(-3)-(-2):2+4·3= 31 -1 -(-9):3-22:(-11)-6= -(-5)·4-(-1)-10:(-2)= 26

10 Operaciones con paréntesis, en Z
-9·2-15:( )= -9·2-15:(-5) = = -13 15 -2·( )-2·(-7)= 4 -( ):5-16:(-2)-3= -13 (-7):( )-2·(+6)= -21 6:(-3+1)+4·(-1+3-5)-6= 8:(-4)-10:(-5+2+1)= 3 (2-6-3):7-(-2):2= -7 -(-9):(3-13+1)-6= -1 -(-5+4-1)·(-3)-10:(-2)=

11 Propiedad distributiva
-9·2-15·2+7·2 = ( )·2 = -17·2= -34 2 -2·( ) =-2·5+2·3+2·1+2·2= = 15 3·( )= -35 2·5-3·5+(-6)·5 = 6·(-3+1)+4·(-1+3-5)= -24 8:(-4)-10·(-5+2+1)= -22 -48 (2-6-3)·7-(-2):2= -3·6+7·6+(-4)·6= -(-5+4-1)·(-3)-14:(-2)= 1