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

• .

.

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

• &

,

. .

,

.

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

• .

:

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

... ( ).

( ) "". , .

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

• : http://e-taksh.blogspot.gr .19

• : 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