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Transcript of Μαθηματικά Ε΄ 6.36. ΄΄...

• :

- 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

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• , , .

.. 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,

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• 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

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