Treść zadania

Najlepsze rozwiązanie

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  sonar 31.3.2011 (22:19)

  a)
  1/6 * 3 i 3/4 * 100 * 4/15 * 24/25=
  
  = 1/6 * 15/4 * 100 * 4/15 * 24/25 = (skracam 6 z 15, 4 ze 100)
  
  = 1/2 * 5/1 * 25 * 4/15 * 24/25= (skracam 25 z 15)
  
  = 5/2 * 5 * 4/3 * 24/25= (skracam 3 z 24)
  
  = 25/2 * 4/1 * 8/25=
  
  = 100/2 * 8/25 = (skracam 100 z 25 oraz 2 z 8)
  
  = 4/1 * 4/1=
  
  = 16/1=
  
  = 16
  
  
  
  b)
  0,4 * 1,4 * 3/4 * 1/7 * 10=
  
  = 4/10 * 1 i 4/10 * 3/4 * 1/7 * 10 =
  
  = 4/10 * 14/10 * 3/4 * 1/7 * 10 = (skracam 4 z 10 oraz 10 z 14)
  
  = 2/5 * 7/5 * 3/4 * 1/7 * 10 =
  
  = 14/25 * 3/4 * 1/7 * 10 = (skracam 14 z 4)
  
  = 7/ 25 * 3/2 * 1/7 * 10 =
  
  = 21/50 * 1/7 * 10 = (skracam 21 z 7)
  
  = 3/50 * 1/1 * 10 =
  
  = 3/50 * 10=
  
  = 30/50=
  
  = 3/5
  
  
  
  c)
  6,6 * 9/40 * 5/6 * 8/11 * 1/3=
  
  = 6 i 6/10 * 9/40 * 5/6 * 8/11 * 1/3=
  
  = 66/10 * 9/40 * 5/6 * 8/11 * 1/3= (skracam 66 z 40 )
  
  = 33/10 * 9/20 * 5/6 * 8/11 * 1/3 = (skracam 20 z 5 oraz 6 z 8)
  
  = 33/10 * 9/4 * 1/3 * 4/11 * 1/3 = (skracam 9z 3)
  
  = 33/10 * 3/4 * 1/1 * 4/11 * 1/3=
  
  = 33/10 * 3/4 * 4/11 * 1/3= (skracam 4 z 4)
  
  = 33/10 * 3/1 * 1/11 * 1/3 =
  
  = 99/10 * 1/33 = ( skracam 99 z 33)
  
  = 3 /10 * 1/1=
  
  = 3/10
  
  
  
  d)
  3,6/7 * 0,08/1,1 * 2,2/1,2 * 2,1/0,6=
  
  = 3 i 6/10 / 7 * 8/100 / 1 i 1/10 * 2 i 2/10 / 1 i 2/10 * 2 i 1/10 / 6/10=
  
  = 36/10 :7 * 2/25 / 11/10 * 22/10 / 12/10 * 21/10 / 6/10 =
  
  = 36/10 * 1/7 * 2/25 * 10/11 * 22/10 * 10/12 * 21/10 * 10/6= (skracam 25 z 10, 11 z 22, 10 z 10 , 12 z 21, 10z10)
  
  = 36/10 * 1/7 * 2/5 * 2/1 * 2/1 * 1/4 * 3/1 * 1/6 = (skracam 2 z 4 oraz 3 z 6)
  
  = 36/10 * 1/7 * 2/5 * 2/1 * 1/1 * 1/2 * 1/1 * 1/2 =
  
  = 36/70 * 4/5 * 1/4= (skracam 4 z 4)
  
  = 36/70 * 1/5 * 1/1 =
  
  = 36/350 =
  
  = 18/ 175

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