Μαθηματικά Ε΄ 6.39. ΄΄...

Click here to load reader

  • date post

    13-Apr-2017
  • Category

    Education

  • view

    1.584
  • download

    1

Embed Size (px)

Transcript of Μαθηματικά Ε΄ 6.39. ΄΄...

  • :

    - 6 - 39

    ..

    http://e-taksh.blogspot.gr

    : http://e-taksh.blogspot.gr .1

  • 39

    :

    4

    17 +

    6

    17+

    5

    17=

    15

    17

    9

    14 -

    3

    14 =

    6

    14

    .

    , ( )

    ,

    ,

    ;

    , .

    , , , , , ... .

    , !

    .

    ;

    ...

    = =

    2

    3

    4

    5

    1

    2 + +

    + + 40

    60

    48

    60

    30

    60

    118

    60

    58

    60 = 1

    ,

    .

    ,

    .

    , ,

    , ,

    .

    20 12 30

    : http://e-taksh.blogspot.gr .2

    Xristos

  • , , , , .

    , , . , :

    1 : ...

    2 : ... .

    3 :

    ...

    =

    + + 5

    20

    12

    20

    4

    20

    21

    20

    1

    20 = 1

    1 : ...

    ... ( 4, 5, 10 ) = 20

    1

    4

    3

    5 + +

    2

    10

    2 :

    ... =

    3 : , ,

    .

    ... !

    / ...

    .

    / ,

    ,

    .. .

    . ,

    , (4) ...

    (20), 5. , .

    1

    4

    5 4 2

    : http://e-taksh.blogspot.gr .3

  • .

    ( ) .

    , , . , ;

    ... : ( , , 7 19).

    , , , .

    5

    9

    2

    3 + 1 + 2

    ,

    .

    .

    5

    9

    5

    3

    2

    1 + +

    ,

    .

    ...........................................

    ,

    !

    ...

    ,

    !

    ,

    !

    1 3 9

    : http://e-taksh.blogspot.gr .4

  • : http://e-taksh.blogspot.gr .5

  • ;

    .

    , .

    : http://e-taksh.blogspot.gr .6

  • ;

    : I. ... II. ... III. ,

    , . : http://e-taksh.blogspot.gr .7

  • 2 + 1 + 5 3 4 6 :

    : http://e-taksh.blogspot.gr .8

  • . ... 3 4 6 2

    3 2 3 2 3 1 3 3 1 1 1 ... (3, 4, 6) = 2*2*3 = 12

    : http://e-taksh.blogspot.gr .9

  • . ...

    :

    12 : 3 = 4 12: 4 = 3 12: 6 = 2

    : http://e-taksh.blogspot.gr .10

  • . ,

    2 + 1 + 5 = 2*4 + 1*3 + 5*2 = 8 + 3 + 10 = 3 4 6 3*4 4*3 6*2 12 12 12 : 8+3+10 = 21 = 1 9 12 12 12

    4 3 2

    : http://e-taksh.blogspot.gr .11

  • , www.atheo.gr -

    11

    20

    , . . . . ( ), .

    .. 61

    + 35

    + 21

    =

    2 3 6 2 ( 2 , 6 ) 1 3 3 3 ( 3 ) 1 1

    ... ( 2, 3, 6 ) = 2 3 = 6 , , , 6 . :

    21

    = 3231

    = 63

    35

    = 2325

    = 6

    10

    61

    = 1611

    = 61

    :

    61

    + 35

    + 21

    =

    63

    + 6

    10 +

    61

    = 6

    14 = 2

    62

    = 231

    : . .

    , .

    .. 2 + 21

    = 221

    21

    + 2 = 221

    ( )

    : http://e-taksh.blogspot.gr .12

  • , www.atheo.gr -

    12

    , :

    .. 221

    + 121

    = ( 2 + 1 ) + (21

    + 21

    ) = 3 + 1 = 4

    ,

    .

    1. :

    61 +

    64 =

    52 +

    54 =

    81 +

    83 =

    73 +

    215 =

    32 +

    61 =

    2. :

    61 +

    62 +

    63 =

    51 +

    21 +

    102 =

    81 +

    42 +

    21 =

    3. :

    2 + 61 = 5 +

    52 =

    83 + 4 =

    215 + 7 = 0,9 +

    102 =

    4. :

    261 + 3

    62 = 4

    51 + 3

    21 = 5

    81 + 3

    51 =

    5.

    32

    , 121

    261

    .

    ;

    6. 21

    ,

    52

    . 102

    .

    ;

    : http://e-taksh.blogspot.gr .13

  • &

    .

    : http://e-taksh.blogspot.gr .14

    http://eclass31.weebly.com/uploads/8/3/3/4/8334101/1978238_orig.png?219

  • .

    .

    .

    : http://e-taksh.blogspot.gr .15

    http://eclass31.weebly.com/uploads/8/3/3/4/8334101/162070_orig.png?163http://eclass31.weebly.com/uploads/8/3/3/4/8334101/1668375_orig.pnghttp://eclass31.weebly.com/uploads/8/3/3/4/8334101/5124317_orig.png?259

  • .

    .

    : http://e-taksh.blogspot.gr .16

    http://eclass31.weebly.com/uploads/8/3/3/4/8334101/4283188_orig.png?386http://eclass31.weebly.com/uploads/8/3/3/4/8334101/2330227_orig.png?230

  • &

    ,

    . .

    ,

    .

    : http://e-taksh.blogspot.gr .17

    http://eclass31.weebly.com/kappalambda940sigmamualphataualpha-07.htmlhttp://eclass31.weebly.com/uploads/8/3/3/4/8334101/5312466_orig.png?277

  • .

    :

    (...). (), , , ,

    ... ( ).

    ( ) "". , .

    : http://e-taksh.blogspot.gr .18

    http://eclass31.weebly.com/kappalambda940sigmamualphataualpha-08.htmlhttp://eclass31.weebly.com/uploads/8/3/3/4/8334101/9559607_orig.png?152

  • : http://e-taksh.blogspot.gr .19

    http://eclass31.weebly.com/uploads/8/3/3/4/8334101/2692100_orig.png?211

  • : http://e-taksh.blogspot.gr .20

    Xristos

  • 1

    2.4 1. : 2. : 1 3. : 4. : 3 5. :

    1. ) .. . ) 1 ) . ) . ) 1 . ) .

    : http://e-taksh.blogspot.gr .21

  • 2

    2. .

    ) 5 + 1

    4 =

    21

    4 , ) 2

    1

    3= 2

    1

    3 , )

    5

    6

    2

    6 > 1 ,

    ) 3

    4 +

    2

    5 > 1 , )

    3

    4 +

    7

    4 +

    9

    4 +

    1

    4 = 5

    )

    5 + 1

    4 =

    5 4

    4

    +

    1

    4 =

    20

    4+

    1

    4 =

    21

    4

    )

    21

    3=

    2 3

    3

    1

    3=

    6

    3

    1

    3=

    5

    3 =

    3 1 2

    3

    + =

    3 1

    3

    +

    2

    3 = 1 +

    2

    3 = 1

    2

    3

    ) 5

    6

    2

    6 =

    3

    6 =

    1

    2 < 1

    ) 3

    4 +

    2

    5 =

    3 5

    4 5

    +

    2 4

    4 5

    =

    15

    20 +

    8

    20=

    23

    20 > 1

    ) 3

    4 +

    7

    4 +

    9

    4 +

    1

    4 =

    3 + 7 + 9 + 1

    4 =

    20

    4= 5

    3.

    21

    4< 3

    2

    5

    21

    4 = 2 +

    1

    4=

    2 4

    4

    +

    1

    4=

    8

    4+

    1

    4 =

    9

    4 =

    9 5

    4 5

    =

    45

    20

    32

    5 = 3 +

    2

    5 =

    3 5

    5

    +

    2

    5 =

    15

    5+

    2

    5=

    17

    5 =

    17 4

    5 4

    =

    68

    20

    45 < 68 , 45

    20<

    68

    20 2

    1

    4< 3

    2

    5

    : http://e-taksh.blogspot.gr .22

  • 3

    4.

    ) 1

    8 +

    6

    8 +

    2

    8 )

    2

    11 +

    5

    11+

    4

    11 )

    2

    5 +

    5

    6 )

    4

    7+

    2

    14 + 2

    ) 1

    8 +

    6

    8 +

    2

    8 =

    1 + 6 + 2

    8 =

    9

    8

    ) 2

    11 +

    5

    11+

    4

    11 =

    2 + 5 + 4

    11 =

    11

    11= 1

    ) 2

    5 +

    5

    6 =

    2 6

    5 6

    +

    5 5

    6 5

    =

    12

    30 +

    25

    30 =

    37

    30

    ) 4

    7+

    2

    14 + 2 =

    4

    7+

    1

    7 +

    14

    7 =

    4+1+14

    7 =

    19

    7

    5. ; 6.

    ) 7

    12

    5

    12 )

    7

    12 1 )

    7

    2

    4

    12 )

    15