Μαθηματικά Ε΄ 6.36. ΄΄...

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  • :

    - 6 - 36

    http://e-taksh.blogspot.gr

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

  • .. 4 x 6 = 24 24 4

    24 : 4 = 6 4 24

    .. 3 12 18,

    12 : 3 = 4 18 : 3 = 6

    .. 2 2 4 6 8 .

    .

    , ,

    .

    , ,

    () ,

    () .

    12 18

    3 3

    12 18. ,

    .

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

  • 5 5 10 15 20 .

    :

    ,

    . , 1 ( )

    :

    .. 1 x 4 = 4, 2 x 4 = 8, 3 x 4 = 12, 4 x 4 = 16, 5 x 4 = 20, .

    4, 8, 12, 16, 20 4 4

    , :

    4 : 4 = 1, 8 : 4 = 2, 12 : 4 = 3, 16 : 4 = 4, 20 : 4 = 5, .

    1. 2

    4 8:

    30, 32, 40, 48, 64, 70, 74, 80, 84, 90

    2 :

    4 :

    8 :

    2. 2

    5 10:

    20, 35, 40, 50, 65, 70, 85, 90, 105, 110

    2 :

    5 :

    10 :

    ! ,

    ! ( !!!!)

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

  • eva-edu

    .

    2 : 2x0=0

    2x1 =2

    2x2=4

    2x3=6

    2x4=8

    2x5=10

    2x6=12

    2x7=14

    2x8=16

    2 0, 2, 4, 6, 8, 10, 12, 14, 16

    3 4

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

  • : http://e-taksh.blogspot.gr .5

  • ;

    .. 8, 8 1, 2, 3, 4 5

    8, 16, 24, 32, 40

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

  • () .

    .

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

  • 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . 6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . 12, 24, 36, .

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

  • ;

    .

    .. 36 : 1, 2, 3, 4, 6, 9, 12, 18 36

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

  • , , .

    .. 180 : 180 = 2*90 = 2*2*45 = 2*2*3*15 = 2*2*3*3*5 .

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

  • 180

    2 * 90

    2 * 2 * 45

    2 * 2 * 3 * 15

    2 * 2 * 3 * 3 * 5

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

  • 180 2 2 180 90 90 2 2 90 45 45 3 2 45. 3 15 15 3 3 15 5 5 5 3 5. 5 1 1 180 = 2*2*3*3*5

    1

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

  • , www.atheo.gr -

    65

    16 , -

    . .. 7, 7 1, 2, 3, 4 5 7, 14, 21, 28 35.

    () . . .. 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, , 6 6, 12, 18, 24, 30, 36, 42, 48, 12, 24, 36, .

    .. 36 1, 2, 3, 4, 6, 9, 12, 18 36.

    ,

    .. 180 180 = 2 90 = 2 2 45 = 2 2 3 15 = 2 2 3 3 5. . (. ).

    1. :

    ( 3, 5 ) 100 ( 2, 4 ) 50 ( 4, 8 ) 50 ( 5, 10 ) 100

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

  • , www.atheo.gr -

    66

    2. :

    6 : ..

    10 : ...

    24 : ..

    30 : ..

    3. ( ) :

    12, 18, 32 15, 30, 45 10, 20, 40 12, 24, 48

    4. 25 ,

    . ;

    5. 25 ,

    . ; 6. 22 .

    ; 7. 48 , 60 24 .

    ; 8. 60 . 7

    5 . ;

    12 24 36 48 60

    9. 6 :

    3 : 3, 6,

    5 : 5,

    7 : 7,

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

  • 20 . .

    .

    .

    () .

    : 8 8, 16, 24, 32, 40, 48, ...

    12 12, 24, 36, 48, ...

    8 12 24, 48, ...

    24, (8,12)=24

    ( ) 2 , 1

    (..)

    .

    : 8 1, 2, 4, 8

    4 1, 2, 4

    8 12 1, 2, 4

    4 . (8,12)=4

    .

    ,

    .

    2, 3 .

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

  • 20 . .

    :

    22 0, 2, 4, 6, 8.

    ( )

    4 4 .. 324 4 24 4

    8

    8

    .. 5824 4 824 8.

    5 0 5

    10

    20 00 20 40 60 80

    25

    25

    . 375 25 75 25 (

    00 25 50 75)

    100

    3 3. . 324 3 3+2+4=9 9 3

    9 9 . 819 9 8+1+9=18 9 3

    6

    3

    . 3324 6

    3+3+2+4=12 12 3

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

  • 20 . .

    1. : 81, 9225, 312, 800 530

    10: 25:

    5: 2:

    3: 100:

    9: 8:

    4: 20:

    2. : 432, 140, 1005, 132 120

    2 5: 3 5: 2 3: 2 9:

    2, 5 8: 2,3,4,5,8,10:

    2,3 10: 2, 5 20

    3.

    :

    ) 534 __ 2 5 ) 841__ 2 3

    ) 93__ 3 5 ) 342__ 5, 9 20

    ) 181__ 2 9 ) 5__3__ 3 4

    ) 547__ 3 25 ) 5__ __3__ 2, 3, 5 9

    ..

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

  • (09/12)

    ;

    , 0

    .

    .. 4 : 2 = 2 0 -- 5 : 3 = 1 2 -- 132 : 11 = 12 0

    0, ,

    .

    .. 4 : 2 = 2 0, 0, 2

    4

    5 : 3 = 1 2, 0 ( 2), 3

    5

    132 : 11 =12 0, 0, 11 132.

    .

    ;

    .. 5. 2, 10.

    10 5.

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

    http://sainia.gr/mathimatika-e/922-diaieretes-kai-pollaplasia

  • .. 26. 7, 152.

    152 26.

    .. 12. 6, 72.

    72 12.

    .. 16. 9, 144.

    144 16.

    .. 54. 2, 108.

    108 54

    ,

    . , , .

    ;

    6 :

    6 (61 = 6), 12 (62 = 12), 18 (63 = 18), 24 (64 = 24), 30 (65 = 30), 36 (66 = 36), 42

    (67 = 42), 48 (68 = 48)... .

    3 :

    3 (31 = 3), 6 (32 = 6), 9 (33 = 9), 12 (34 = 12), 15 (35 = 15), 18 (36 = 18), 21 (37 = 21), 24 (38 = 24), 27 (39 = 27), 30 (310) = 30...

    6

    3, 6, 12, 18, 24 30

    6 3. 6, 12, 18, 24 30 6 3.

    .

    : http://e-taksh.blogspot.gr .19

  • : .

    6 6;

    21;

    , 48 .

    ;

    40 =..

    50 =

    75 = .

    81 =

    320 = ..

    3 6, 9 12:

    6:

    9:

    12:

    8500;

    2 8500:2=4250 - 50

    5 67

    23 100

    500 641

    .

    7 : 7, 14, 21, 28, 35, 42, 49, 56 7, ( 0)

    .

    . 36 1,2,3,4,6,9,12,18,36 1 .

    , . .. 180 180 = 2 x 90 = 2 x 2 x 45= 2 x 2 x 3 x 15 = 2 x 2 x 3 x 3 x 5. H

    : http://e-taksh.blogspot.gr .20

  • . . . 10, 18 24 : 10: 1, 2, 5, 10 18: 1, 2, 3, 6, 9, 18 24: 1, 2, 3, 4, 6, 8, 12, 24 , . . . 2 3 : 2: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24... 3: 0, 3, 6, 9, 12, 15, 18, 21, 24, 27...

    (0)

    . . . 6, 12, 18, 24 ...

    100, (1) (2) .( ) , 28, 2009

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

    http://egpaid.blogspot.com/http://www.tki.org.nz/r/wick_ed/maths/interactives_matrix.phphttp://www.jamit.com.au/htmlFolder/app1004.htmlhttp://illuminations.nctm.org/ActivityDetail.aspx?ID=12http://www.blogger.com/profile/14801585743634627041http://egpaid.blogspot.com/2009/03/blog-post_28.html

  • kyra_daskala

    A M 1

    ( ) : . : 26/10/09

    8 8;

    15;

    , 36, : 36= 2 x 3 x 6. ;

    60 =..

    50 =

    45 = .

    72 =

    840 = ..

    3 6, 9 12:

    . (.. 5

    7 7,14,21,28,35)

    .

    :

    1. 2. 3. .

    . (.. 36 1,2,3,4,6,9,12,18,36)

    ,

    . .. 180 180 = 2 x 90 = 2 x 2 x 45=

    2 x 2 x 3 x 15 = 2 x 2 x 3 x 3 x 5. H -

    : http://e-taksh.blogspot