a_1.pdf
TRANSCRIPT
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1
1
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: 0,1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, .
. , .
(): 1, 3, 5, 7, 9, 11 ..
(): 0, 2, 4, 6, 8, 10, 12,.
. . .
0,7 -, 0,23 , 0,149 , .. 2,4, 16,38, 3,123.
.. 0,4 0,17 0,12567.
.. 5,133
:
1 = 10 = 100 = 1000 1 = 10 = 100 = 1000
1 = 10 = 100 = 1000 - .
. 10 (10 ) . :
, .
, .
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2
, ( ) - . 12,28 = 12,280000 11,200 =11,2. , .
:
1. 0, 1, 2, 3, 4 - .
2. 5, 6, 7, 8, 9 - - .
: , ..., .
,
, , . - .
.
.
. + 12 = 20,
+12 20 . 8 .
, - ' .
.
: 1. , .. 12 +8 =20, 20 12+8 = 8+12 .
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3
2. .
, - , :
= + =
: 1. ,
. 2.
.
, - , . .. 3*5 = 5+5+5 = 15 3*5 = 3+3+3+3+3 = 15. 15 5, 3 .
,
.
: 1. 10, 100, 1000 .,
1, 2, 3 . . 2. 10, 100, 1000 .,
1, 2, 3 . . 3. 0,1 0,01 0,001 ., -
1, 2, 3 ., .
3 ,
() : 0.3=0, 1.3=3, 2.3=6, 3.3=9 . 0, 3, 6, 9, 3 -
3 3 = {0, 3, 6, 9, ...}.
= {0, , 2, 3, 4,...}
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4
6: 6 = {0, 6, 12, 18, 24, 30, 36, 42, 48 ..} 5: 5 = {0, 5, 10, 15, 20, 25, 30, 35, 40, 45, .} 6 5 : {0, 30, } 30, , : (5, 6) = 30
1, : = . . ...
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. 2 , 3 . 10 , 1 .
..: 102=100, 103=1000, 104=10.000, 105=100.000.
, : x+x = x (+) x (+)=x+x
, : xx = x () x ()=x x
, ( )
( ) , -.
, , :
: = = . . 0 : = 1, :1 = 0:=0.
, ,
, - , : = . + & <
.
1. 0, . 2. = 0, = . . .
-
5
&
16: 16 = {1, 2, 4, 8,16}
24: 24 = {1, 2, 3, 4, 6, 8, 12, 24}
16 24 : {1, 2, 4, 8} 8, ,
(16, 24) = 8
10 100 .
10 100 1000 ., . 10, 100, 1000 .
: 260:10 = 26 260:100 = 2,6 260:1000 = 0,26
18,1:10= 1,81 18,1:100 = 0,181 18,1:1000 = 0,0181
1. . .. 7 - , 0, 7, 14, 21, 28,...
2. . .. 27 9, 27 9.
3. , . .. 5 15, , : , 15, 30, 45, 60, ..
4. , . .. 6 18 36, : 18+36 = 54 36-18= 18.
10, 100, ... 10, 100, ..., 1, 2, ...
. 2
2, 0, 2, 4, 6, 8 - . 5
5, 0 5. 3 9
3 9, 3 9.
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6
1
2 . :
. , -
1.
!
. ... ... , .
1. ... , , .
2. ... , , .
.. 144 = 24 32, 160 = 25 5, : ... (144, 160) = 25 32 5 = 3295 = 1.440 ... (144, 160) = 24 = 16
, 10 , , - .
: 36,45 : 4,5 = (36,45.10) : (4,510)= 364,5 : 45 = 8
, .
. , - , .
: 70 : 22 = 3,181818.. 70:22 = 3,18.
1 1 . 2 1 .
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7
1. .
2. .
1. : . .
. .
. .
2. . .
.
.
.
: 1. : 15+7+12+3+5=42 ( 15+5=20, 7+3=10, 20+10+12=42)
2. : 13 + 2 - 5 + 7= 15 - 5 + 7 = 10 + 7 = 17 13 + 2 - 5 + 7= 15 - 5 + 7 = 15 12 =....
:
. + () -
. - () . [] [] -
. .. 13 + 2 - 5 + 72 = (13+2+7) - (5+2) = 22 7 = 15
3. -:
35+7=15+7=22 35+7=312=36 46 - 54 + 52=24 -20+10 =4+10=14 46 - 54 + 52 = 4192=..... 12:3 + 25 + 3 = 4+10+3=17 12:3 + 25 + 3 = 12:55+3=...
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.
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8
/ ! 208:4 = 20 (8:4) = 202 = 40 8:420 = (8:4) 20 = 220 = 40 8:420 = 8:80=...
4.
.
(122+8:2)+3 = (24+4)+3 = 28+3=31 (3+5)2 = 82 = 64 (3+5)2 = 32 + 52 = 9+25 =...
5.
.
: 12:3 + 25 + 3 = 4+10+3 = 17 12:3 + 25 + 3 =12:3=4+25=10 .......
, - .
: 9 000 000 = 9106 12 000 000 = 1,2107. -
, 1 10, 10,
10.
/
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9
1 1. , ...
:
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1234,123 1 2 3 4 1 2 3 44,32
0,12345 235.789
44444,44444 21.346,01200 333.123,13 11,34789
0,45
2. . : , -
, , , , , :
5.124,367 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..
7.365,124 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..
2.143,765 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..
4.217,356 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..
3.546,271 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..
3. 1 .
23.240,45
90.910,99
43.209,18
11.249,91
77.231,65
27.216,35
97.385,84
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10
4. :
5. :
95 (48 31)= (92 43) 24= 69 (18+11)=
(89 18) 14= (55+25) 15= (78 44) +49=
3855 + 9764 2345 1769= 0,234 + 75,32 2,09 11,023=
32,54 13,83 +77,32 2,56= 24,89 + 0,341 5,23 0,28 + 2,01=
6. = 0,01, = 0,1, = 1, = 10, = 100
1456,24 = 2498 = 0,5864 =
7. : ! = () = () 23 5 2= 18 2 15= 250 23,454= 26,175850=
8. :
9 + 45 +212= 318+11 + 42,5= 312,52 53 + 142,5= 27,5 33 + 5,25= 14 32,2 +128= 44,25 11,50,5 + 23,2310=
9. 1.850 3,5 .
225 ;
10. 5 . 8 10
, 12 3 9 11 , 15
75 ;
11. 4 . 16,5 , 14,25
18 . 3,2 ;
356 + 349 =
7356 + 1987 =
1300 + 3357 =
3,567 + 13,023 =
139 + 12,7 =
789,34 + 19,38 =
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11
12. .
5 . 6 . -
;
13. :
24 204 0,24 103 1003 0,13
32 302 0,32 15 0,15 0,012
14. . ;
(34)2 (22)3 2333 (22+32) 2223 (43)2 (23)2 (23)3 (2+3)2 25
15. :
5104+2103+8102+5101+4100= 2105+4103+8102+3100=
16. :
(10+8)2 (73)3= (153 18)2 802=
8,42 + (34,57 24,47)3= (33 23)5 (57 37) 3.5= 33+32+31+30= 110+18+16+14+12+10=
152142+132122+112102= (15 14)2+(13 12)2+(11 10)2=
17. :
(7+28+5+13+12) 25= 338+228+178+288= (13,25+26+37,5+23,25) 12,34= 4,835+4,815+2,226,7+2,273,3=
18.
3+4,5+2,5 =2,345 23,67+35+41,33 =0,3456 2+2+7,5+7,5+120+120 +=20
19. 50
40 . ;
20. 36 3 .
2;
-
12
21. 630 . 3
270 . -
;
22. , = 2 + 4 (-), = 2( + 1) + 6 + 1 ().
23. 60 = 60. ;
24. 33.
;
25. :
] 3 + 45 26= ] 20:2 + 342= ] 48 7 + 311= ]57 23 + 4:2= ] 42:6 + 39 52= ]11526:3+88:11= ] 65:13 + 726 322= ] 712 9 + 124 42:6= ] 1,25 3,4:1,7 + 8= ] 3,3:0,55 + 60,3 + 3,30,2 2=
26. :
] 54:9 + 253 62:12= ] 57 26:16 + 245 + 63= ] 3324 126:9= ] 32 24 + 12:22 + 334= ] 25:8 + 432 18:9= ] 352 532 + 223 28= 27. :
=24,83 + 2323 125:252= =33:11 + 128:42 18:32= =2812:23 + 1113 100 (0,1)2 + 72533=
= 7,32 (23 0,80,5) 0,62 0,127= = (9,6:8 + 0,9) (6:10+42) + 732= = 6,4:22 +(33 +33,3) 72 3220,33= = 132(82 +52)+(52 1294)(12510 542)+13= = 2433 36:223 +(21+24) 32= = 352 532 + 2 (24 8) + 33:9=
28. :
] 1810:2,5 22 (23 7)= ] 72322 32,2 + 25 (3443) + 9= ] 24 (62 + 82) :10 + 2,21,1= ] (6 + 8)2 :(24 23) + (32 8,5)2= ] (0,12 + 0,72) 102 + (2,8 1,2)2= ] (62 + 34 47)59 + (33 +3 39)5=
29. :
=82 + (8)2= =49 + (7)2= =2 + 322 +72= ] =0,9 ] =3,2 ] =3 ( )
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13
30. : = 2 + 2 + 2 =( + )2
] =5 & =6 ]=9 & =7 ]=7,3 & =0,1
() , ; -
.
31. :
52 + 62 83 + 32 + 4 3(2 + 6)
3,5
32
0,1
-
1 . 14
2
: ()
. , . = = =
... 1 .. 0 1 2 3 4 5 6 7 ()
() - .
, - . - 4 , 4, . -: = 4.
. -
. ( ).
, m. m,
000.000.40
1 .
:
(dam) 1 dam = 10 m (hm) 1 hm = 100 m (km) 1 km = 1000 m
: (dm) 1 dm = 1/10 m (cm) 1 cm = 1/100 m (mm) 1mm = 1/1000 m
:
(yrd), 3 (ft) 1 12 (in). O 0,75m = 75 cm. 1609 m 1852 m 15,43 m (1 = 120 )
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1 . 15
: , , , ( ), . - () -
.
- :
7,8 m
x 10 m 7,8 m
78 dm x 10 dm : 10 78 dm
780 cm
x 10 cm : 10 780 cm
7.800 mm mm : 10 7.800 mm
-
( ) . - , . - , .
-
. ( ).
, m2. 1 m. :
. (dam2) 1 dam2 = 100 m2 ( ) . (hm2) 1 hm2 = 10.000 m2 ( ) . (km2) 1 km2 = 100.000 m2
: . (dm2) 1 dm2 = 1/100 m2 . (cm2) 1 cm2 = 1/10.000 m2 . (mm2) 1mm2 = 1/1.000.000 m2
: 1 = 1000 m2 ( ).
m2 :
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1 . 16
7,8 m2
x 100 m2 7,8 m2
780 dm2
x 100 dm2 : 100 780 dm2
78.000 cm2
x 100 cm2 : 100 78.000 cm2
7.800.000 mm2 mm2 : 100 7.800.000 mm2
, -, .
. -
, . ..: = 6m = 2m, E = = 6m2m =12 m2
- , .
..: = 6m , E = (= 2) = 6m6m =36 m2
, .
, ( ) . - ( ) .
-
. ( ). , m3.
1 m.
(dam3) 1 dam3 = 1.000 m3 (hm3) 1 hm3 = 1.000.000 m3 (km3) 1 km3 = 1.000.000.000 m3
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1 . 17
(dm3) 1 dm2 = 1/1.000 m2 (cm3) 1 cm2 = 1/1.000.000 m2 (mm2) 1mm2 = 1/1.000.000.000 m2
(l), 1l = 1.000ml.
1dm3. ml=1cm2
.
! , ;
m3 - :
7,8 m3
x 1.000 m3 7,8 m3
7.800 dm3
x 1.000 dm3 : 1.000 7.800 dm3
7.800.000 cm3
x 1.000 cm3 : 1.000 7.800.000 cm3
7.800.000.000 mm3 mm3 : 1.000 7.800.000.000 mm3
, - - . ,
, V = ,
, V = = 3 .
(sec).
(min) 1min = 60 sec (h) 1h = 60 min = 3.600 sec.
(d) 1d = 24 h 1 =
365 366 , , 1 = 100 .
( ) (Kg). O (ton) 1ton = 1.000Kg. (gr), 1.000 gr = 1Kg.
. ; ( -)
-
1 . 18
2001 ().
1/1/2002 , ().
100 : ) : 1, 2, 5, 10, 20, 50 , 1 & 2 ) : 5, 10, 20, 50, 100, 200, 500.
,
!
-
1 . 19
1. 6,4 m 25 dm
3850 mm. (. 61,6 m3) 2. 28dm ] m 3, ] dm3, ] cm 3 (. 21,952m3, 21.952dm3, 21.952.000cm3) 3. 64 . . (V=512 m3) 4. 70 dm, 5 m. 217
m3, . (=6,2 ) 5. 2,9 ,
1,5 0,72 . 1725 ;
(. 3.132 l 5.402.700 ) 6. 1,8 m ,
1,2 m 8,5 dm, 37cm, 15 cm , 17 cm. ; (. 195 /)
7. 8 m3 .
34 6,5 m 3,5 m. (. 11,956 m)
8. 80 cm,
45cm 60 cm. ] . ] 120 ;
(. 216dm3, 33,33 cm ) 9. 184.800 . 15,4 . 7000 , ;
(. 84.000 ) 10. : 10 cm, 5 cm
13,2 cm. 0,1 dm ;
(. 3,2 cm ) 11. . : ] . ] . (. 8, 27)
-
1 . 20
. 1. 0,68m 50cm. (. =2,36 m, =0,34 m2 ) 2. 1,28 km 360m.
, . (. =280m, E=100800m2)
3. 7,8 m 50,7 m2.
. (. 6,5m, =28,6m) 4. 36,8m. (. =84,64m2) 5. 20 . -
25 , . (. 16 ) 6. 65dm 3,4 m 25.480 . -
; ( . 563.108 ) 7. 6
3,6 . 40 cm. 856 ; (. 135 , 115.560 )
8. 48,5 250.000
1.455.000 . . (. =5820 m2, =120 m)
9. 120 m 6240 m2 . -
. ; (. 3.536 m2)
10.
80 . 45.000 . (. =256m2, 11.520.000 drx)
11. 70 m
150 cm. - 50 cm 30 cm.
(. 2.860 ) 12. , 88 dam.