Μαθηματικά Ε΄ 6.36. ΄΄...
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.. 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 .
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12 18
3 3
12 18. ,
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5 5 10 15 20 .
:
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:
.. 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 :
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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
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;
.. 8, 8 1, 2, 3, 4 5
8, 16, 24, 32, 40
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() .
.
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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, .
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;
.
.. 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 .
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180
2 * 90
2 * 2 * 45
2 * 2 * 3 * 15
2 * 2 * 3 * 3 * 5
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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
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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
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66
2. :
6 : ..
10 : ...
24 : ..
30 : ..
3. ( ) :
12, 18, 32 15, 30, 45 10, 20, 40 12, 24, 48
4. 25 ,
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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
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2, 3 .
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20 . .
:
22 0, 2, 4, 6, 8.
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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
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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
..
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;
, 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.
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.. 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.
.
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: .
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
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. . . 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
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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 -
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