Treść zadania

Rozwiązania

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  sonar 10.9.2011 (15:02)

  zad 3 .
  a)
  -4 * (-2 -11) =
  = - 4 * (-13) =
  = 52
  b)
  -7 + 2* (-5) =
  = -7 + (-10)=
  = -7 -10=
  = -17
  c)
  -11- 12 : (-6) =
  =-11 - (-2)=
  = -11 + 2=
  = 13
  d)
  -8 – 5 * (-4) – 4 * (-6)=
  = -8 - (-20) - ( -24)=
  = -8 + 20 + 24=
  = 12 + 24=
  = 36
  e) I+I -> to jest znak miedzy ułamkami
  7+(-15) / -2 I+I -8/-3-1 =
  = 7-15 /2 I+I -8/-4=
  = -8/2 + 2=
  =-4 + 2=
  = 2
  f) I-I -> to jest znak między ułamkami
  -11-9 /-4 I–I 6-12 /-3 =
  = -20/-4 I-I -6/-3=
  =5 – 2=
  = 3
  
  zad4
  a) 1 i 7/8 * (-6) =
  = 15/8 * (-6/1) = (skracam 8 z 6)
  = 15/4 * (-2/1)=
  = - 30/4=
  = - 7 i 2/4=
  =-7 i ½
  
  b)-1 i 1/5 * 2 i 1/2=
  = - 6/5 * 5/2 = (skracam 6 z 2 oraz 5 z 5)
  = - 3/1 * 1/1=
  = -3/1=
  = -3
  
  c)- 1 i ¾ : 8=
  = - 7/4 * 1/8=
  = - 7/32
  
  d)1i 1/3 * 0,5=
  4/3 * ½ = (skracam 4 z 2)
  = 2/3 * 1/1=
  = 2/3
  
  e)5,25:(-1i 1/2)=
  = 5 i 25/100 : (-3/2)=
  = 5 i ¼ * (-2/3)=
  = 21/4 * (-2/3)= (skracam 21 z 3 oraz 4 z 2)
  = 7/2 * (-1/1)=
  = - 7/2=
  = - 3 i ½
  
  f)- 1,5 : (-2 i 1/3) =
  = - 1 i 5/10 : (-7/3)=
  = - 1 i ½ * (-3/7)=
  = - 3/2 * (-3/7) =
  = 9/14
  
  g)-1 i ¾ + 7 i 1/5= (sprowadzam ułamki do wspólnego mianownika -> 20)
  = - 1 i 15/20 + 7 i 4/20 =
  = 5 i 9/20
  
  h)- 2 i 3/8 – 1/12 = (sprowadzam ułamki do wspólnego mianownika -> 24)
  = - 2 i 9/24 - 2/24=
  = - 2 i 11/24
  
  i)- 13,1 – 2,5 = - 15,6
  
  j) 17,21 -20,03= - 2,82
  
  k)- 0,82 * (-0,3)= 0,246
  
  l)-0,75 – (1 i 2/3)=
  =- 75/100 – 1 i 2/3=
  = - ¾ – 1 i 2/3 = (sprowadzam ułamki do wspólnego mianownika -> 12)
  = - 9/12 – 1 i 8/12=
  = - 1 i 17/12=
  = - 2 i 5/12
  
  zad 5.
  a)
  ¾ + 2/3 : (-8/12)=
  = ¾ + 2/3 * (-12/8) = (skracam 2 z 8 oraz 3 z 12)
  = ¾ + 1/1 * (-4/4)=
  = ¾ + 1 * (-1)=
  = ¾ -1=
  = - ¼
  
  b)
  (2 – 1/7) * 3
  ---------------- =
  2 + 0,6
  
  
  '''''''2 i 6/7 * 3
  = -------------- =
  ''''''''2,6
  
  
  ''''20/7 * 3
  = --------- =
  ''''''''2 i 6/10
  
  
  '''''''60/7
  = --------- =
  ''''2 i 3/5
  
  
  ''''''60/7
  = --------- =
  '''''''13/5
  
  = 60/7 : 13/5=
  = 60/7 * 5/13=
  = 300/91=
  = 3 i 27/91
  
  c)
  (1/3 + 2/7) : (1 – 1/9) + 3/7=
  
  = (7/21 + 6/21) : 8/9 + 3/7=
  
  = 13/21 * 9/8 + 3/7= ( skracam 21 z 9)
  
  = 13/7 * 3/8 + 3/7=
  
  = 39/56 + 3/7=
  
  = 39/56 + 24/56=
  
  = 63/56=
  
  = 1 i 7/56=
  
  = 1 i 1/8
  
  d)V_ -> pierwiastek kwadratowy
  
  (2 – 5/6)^2 - ( 3^2 – V_ 1 i 7/9)=
  
  = ( 1 i 1/6)^2 - ( 9 – V_ 16/9) =
  
  = (7/6)^2 - ( 9 – 4/3)=
  
  = 47/36 - ( 9 – 1 i 1/3) =
  
  = 1 i 11/36 – 7 i 2/3=
  
  = 1 i 11/36 – 7 i 21/36=
  
  = - 6 i 10/36=
  
  = 6 i 5/18
  
  
  e)
  [(-2/3)^2 : 8/9]^ -1 =
  
  = [ 4/9 : 8/9] ^-1=
  
  = [ 4/9 * 9/8]^-1= (skracam 4 z 8 oraz 9 z 9)
  
  = [ 1/1 * ½]^-1=
  
  = 1/2^-1=
  
  = 2/1 ^1=
  
  = 2
  
  
  f)
  1,6 * 7/16 – 2,7/3^3=
  
  = 1 i 6/10 * 7/16 – 2,7 / 9=
  
  = 1 i 3/5 * 7/16 – 0,3=
  
  = 8/5 * 7/16 – 3/10=
  
  = 56/80 – 3/10 =
  
  = 56/80 – 24/80 =
  
  = 32/80=
  
  = 2/5
  
  
  zad 6
  
  ( 3 * 3,9 zł + 9,8 zł + 2* 8,3 zł + 2 * 6,6 zł ) :3=
  
  = (11,7 zł + 9,8 zł + 16,6 zł + 13,2 zł ) : 3=
  
  = 51,3 zł : 3=
  
  = 17,1 zł
  
  Każdy z nich zapłacił 17,1 zł.

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