7. Matematika Plus 3 Uzbenik

7/29/2019 7. Matematika Plus 3 Uzbenik

1/114


2/114

1000 .........................................................3

.......................................................................4

...............................................5

.......................................................................6

.........................................7

...............................................8

................................................................................9

I, V, X .......................................................................10

L, C, D, M .................................................................11

1000 .......13

100 ..........................................14

100 .......................................15

..................................................16

........................................17

(100 + 8) ..........18

(256 + 4) ..........19

(165 4) .....20 (308 7) .....21

(300 + 30) ..................22

(220 + 80) ..................23

(264 + 31) ...........24

(328 + 16) ...........25

(160 - 60) ..............26

(139 - 26) .......27

(174 - 46) .......28

(123 + 100) ...............................29

(235 + 114) ...............................30

(260 - 100) .............................31

(300 - 160) .............................32

..........33

................................34

..................................35

...........................................................................36

..............................................................37

..............................................................38

............................................................39

..............................................................40

................................................................................41

...................................................................................42

............................................................................43

(mm km) ...........................................................44

(kg, g, t) ....................................................................46

(l, dl, cl, ml, hl) ...............................................48

(, , ) ........................................50

1000 ..............51

........................................................52

10 100 ....................................................................53

10 100 .......................................................................53

.......................................55

(4 30) .............................................................56

(120 : 4) ..............................................................57

................................................................58

............................................................59

..........................60

.................................................61

.............................62

...........................63

.............................64

...............................65

.......................................................................66

........... .67

.......................................................................68

......................................................................69

............................................70

....................71

......................72

...............................................................73

..................................................................................74

............................................................................75 ...............................................................................................76

.................................................................................77

..........................................................78

...........................................................79

.....................................................................80

.....................................................81

a ..............................................................83

........................................................................................85

............................................................................86

................................................87

...................................................................................89

................................................................90

....... ...91

...92

.................................................................................................93

.....................................................................95

...............................................................................96

............................................................................................97

.............................................98

.................................................99

............................................................................100

................................................................................101

.....................................................................................103

........................................................................104

........................................................................106

........................................................................108

SADR@AJ

1_,2

1_,4

1_8

1_,3

1_,6

1_9

1_,5

1_,7

1_10


3/114


4/114

, !

.

.

. 1000, ,

, , .

,

.

, ,

.

. ,

.

, , .

,

.

.


5/114

1000

105

132

312

408

609

906

501

804 100J=

10D=1S


6/1144

ili

1S = 10D = 100J

100J = 10D = 1S

1 000J = 100D = 10S = 1H10 STOTINA ~ini 1 HIQADU

1 2 3

98 99 100

10 JEDINICA ~ine 1 DESETICU

1S 1S 1S 1S

1S 1S 1S 1S 1S

1 . 100 = 100 ~itamo sto ili jedna stotina

2 . 100 = 200 ~itamo dvesta ili dve stotine

3 . 100 = 300 ~itamo trista ili tri stotine

4 . 100 = 400 ~itamo ~etiristo ili ~etiri stotine

5 . 100 = 500 ~itamo petsto ili pet stotina

6 . 100 = 600 ~itamo {eststo ili {est stotina

7 . 100 = 700 ~itamo sedamsto ili sedam stotina

8 . 100 = 800 ~itamo osamsto ili osam stotina

9.100 = 900 ~itamo devetsto ili devet stotina

10 . 100 = 1 000 ~itamo hiqadu ili deset stotina

:

:


7/1145

.

100 200 300 400 500 600 700 800 900 1 000

:

100, 200, 300, 400, 500, 600, 700, 800, 900 1 000.

:

100 < 200 < 300 < 400 < 500 < 600 < 700 < 800 < 900 < 1 000,

1000 > 900 > 800 > 700 > 600 > 500 > 400 > 300 > 200 > 100.

2 1, 200 100. 2 3, 200 300.

:

200, 400, 600, 800 1 000,

100, 300, 500, 700 900.

10 .

:

1 = 10

10 100 , :

1 = 10 = 100

:

5 = 50, 7 = 70, 90 = 9, 1 = 100 = 10

1

3

5

7

9

2

4

6

8

10

1S


8/1146

1S

7S

8S

9S

10S

3S

2S

4S

5S

6S

101,

200.

201,

300.

301,

400.

401,

500.

901,

1 000.

801,

900.

701,

800.

601,

700.

501,

600.

1,

100.


9/1147

.

0, 9.

10.

10, 99. 90.

100, 999.

900.

1 000.

769 = 7 6 9 901 = 9 0 1 645 = 6 4 5 1 000 = 10 = 100

e e , .

, , , , 350,

452, 518 723 :

350

452

518

723

3 . 100

4 . 100

5 . 100

7 . 100

5 . 10

5 . 10

1 . 10

2 . 10

2 . 1

8 . 1

3 . 1

:

100 200 300 400 500 600 700 800 900 1 000

1S 2S 3S 4S 5S 6S 7S 8S 9S 10S

10 100 1 000.

1.

2.

3.

, , .

875 = 800 + 70 + 5 324 = 300 + 20 + 4 545 = 500 + 40 + 5 705 = 700 + 5


10/1148

, > < =,

.

,

.

1.

286 = 2 8 6 706 = 7 6 696 = 696

,

.

5.

5, 6 0, , :

650, 560, 605, 506.

:

506 < 560 < 605 < 650.

105,132, 312, 408, 501, 609, 804, 906 826, 743, 628, 437, 347

2.

520 > 320 438 < 5 3 8 899 < 998

3.

596 > 574 405 < 498 782 > 7 7 7

4.

8 3 5 < 836 669 > 664 958 < 959

,

.

,

.

A

B

105132

312826

347

437

628

743

408

609

906

501

804

6.

, B.

, B .


11/114

CD=400=500100

M

=1000

IX=9=

10-1 XL40=5010


12/11410

I, V, X

0, 1, 2, 3, 4, 5, 6, 7, 8 9 , .

. :

a:

I = 1 II = 1 +1 III = 1 +1 +1 X = 10 XX = 10 + 10 XXX = 10 +10 + 10

I X .

V = 5

V .

IV = 4 = 5 1 IX = 9 = 10 1

,

.

VI = 6 = 5+1 XV = 15 = 10 + 5 XXXVI = 36 = 30 + 5 + 1

XIV = 14 = 10 + (5 1) XIX = 19 = 10 + (10 1)

, .

(1) (5) (10)I V X

:

1 = I 6 = VI 7 = VII 8 = VIII 14 = XIV

19 = XIX 24 = XXIV 32 = XXXII 35 = XXXV 38 = XXXVIII

*

*

*

*

.


13/11411

L, C, D, M

I, X V, :

V, L D

, 7 :

(50) (100) (500) (1000)L C D MI

VXL

CDM

5 50 500

1.

IV = 4 = 5 1 L = 50 C = 100 D = 500

CD = 400 = 500 100 M = 1 000 IX = 9= 10 - 1 XL 40 = 50 10

XC = 90 = 100 10 CM = 900 = 1 000 100 XIV = 14 XLIV = 44

LIV = 54 XCIV = 94 XCIX = 99 CDXLIV = 444

CMXLIX = 949 CMXCIX = 999

2.

.

1 000 D 100 L 500 C 50 M

3.

:

XC, C, CI CXLIV, CXLV, CXLVI, CCCXXXIII, CCCXXXIV, CCCXXXV

DCXLVIII, DCXLIX, DCL CDXCIX, D, DI DCCLXXXVIII, DCCLXXXIX , DCCXC

DCCCXCIX , CM , CMI

1 10 100 1 000


14/11412

5.

CXCVI 196

CCCXCIX 399

CDXCIV 494

DCCXLVIII 748

DCCCLXXXVIII 888

CMLXXXIX 989

XCIV 94

DCXLIV 644

CMVII 907

MI 1001

4.

3 IIV III

8 IIX VIII

95 VC XCV

124 CXXIIII CXXIV

400 CD

449 CDXXXXVIIII CDXLIX

548 DXXXXVIII DXLVIII

800 CCM DCCC

819 DCCCXVIIII DCCCIX

900 D CM

6.

< > =.

CCVIII = 208 973 < CMLXXV CXVIII > 108

M > 999 DCCCLXXXIII < DCCCLXXXVI DI > CDIII


15/114

1000

0 100200300

+

500

400500600700800


16/11414

:

13+18 13 18.

13 , 8 .

13+18 31, 13+18=31.

.

1.

26 + 5 = 31 35 + 8 = 43 86 + 8 = 94 6 + 24 = 30 9 + 44 = 53 3 + 97 = 100

2.

26 + 34 = (20 + 30) + (6 + 4)= 50 + 10

= 60

26 + 34 :

26 + 34 = 26 + (30 + 4)

= (26 + 30) + 4

= 56 + 4

= 60

3.

37 34 6.

: (37 + 34) + 6.

: (37 + 34) + 6= 71 + 6 = 78.

4.

. 35 ,

17 . ?

35 .

17 , 35 + 17 .

:

35 + (35 + 17)= 35 + 52 = 87 .

:

87 .

SABIRAWE PRIRODNIH BROJEVA DO 100


17/11415

ODUZIMAWE PRIRODNIH BROJEVA DO 100

:

42 - 15 42 15.

42 , 15 .

42 - 15 27, 42 - 15 = 27.

.

1.

49 - 9 = 40 54 - 3 = 51 36 - 7 = 29 93 - 4 = 89

70 - 9 = 63 62 - 6 = 56 100 - 8 = 92

2.

57 - 25 = (50 - 20) + (7 - 5)

= 30 + 2

= 32

57 - 25 :

57 - 25 = 57 - (20 + 5)

= (57 - 20) - 5

= 37 - 5

= 32

3.

,

. .

: 98 - 31

: 98 - 31 = 67

4.

32 , 9

. ?

32 . 9 ,

32 - 9.

: 32 - 9 = 23

:

23 .


18/11416

. :

4 + 3 = 7 4 + 3 = 7 40 + 30 = 70

3 + 7 = 1 3 + 7 = 10 = 1 30 + 70 = 100 = 1

8 - 5 = 3 8 - 5 = 3 80 - 50 = 30

10 - 3 = 7 10 - 3 = 7 100 - 30 = 70

, :

4 + 3 = 7 9 - 4 = 5

400 + 300 = 700 1 = 10 = 100 900 - 400 = 500

7 = 70 = 700 9 = 90 = 900

1.

.

1 000 500 200 100

2.

:

200 + 500 = 700 600 - 500 = 100

3.

:

1000 - x = 200 700 + a = 900 y + 300 = 600 c - 200 = 400

= 1000 - 200 = 900 - 700 y = 600 - 300 = 400 + 200

x = 800 = 200 y = 300 = 600

SABIRAWE I ODUZIMAWE STOTINA

+ =

0 100 200 300

+ 500

400 500 600 700 800 0 100 200 300

- 500

400 500 600 700 800


19/11417

60 + 30 = 90 30 + 60 = 90 60 + 30 = 30 + 60

600 + 300 = 900 600 + 300 = 900 600 + 300 = 300 + 600

.

.

a b b a

a + b b + a

ZAMENA MESTA I ZDRU@IVAWE SABIRAKA

a + b = b + a

1.

300 + 200 = 200 + 300 = 500 200 + 700 = 700 + 200 = 900 100 + 900 = 900 + 100 = 1000

:

a b c 200 + 300 + 400 a + b + c

200 300 400

a b c (200 + 300)+ 400 = 500 + 400 = 900 (a + b) + c

a b c 200 + (300 + 400) = 200 + 700 = 900 a + (b + c)

a b c (200 + 400) + 300 = 600 + 300 = 900 (a + c) + b

(200 + 300) + 400 = 200 + (300 + 400) = (200 + 400) + 300

(a + b) + c = a + (b + c) = (a + c) + b

,

.

2

:

700, 200, 100 (700 + 200) + 100 = 700 + (200 + 100) = (700 + 100) + 200

300, 500, 100 (300 + 500) + 100 = 300 + (500 + 100) = (300 + 100) + 500

200, 300, 400 (200 + 300) + 400 = 200 + (300 + 400) = (200 + 400) + 300


20/11418

SABIRAWE TROCIFRENOG I JEDNOCIFRENOG BROJA

(100 + 8; 124 + 3)

.

1.

100 8:

1 + 8

100 8 :

1 + 8

2.

124, 3

1 2 4 + 3

3.

5 872

872 + 5 = 877

4.

273 5

272 + 5 = 277

100 + 8 = 108

124 + 3 = 127

+

2 7 2

5

2 7 7


21/11419

SABIRAWE TROCIFRENOG I JEDNOCIFRENOG BROJA

(256 + 4; 236 + 7)

1.

256 4 :

256 + 4 = 250 + (6 + 4)

= 250 + 10

= 260

256 + 4

0, 1 . .

2. 236 7.

236 + 7 = (236 + 4) + 3

= 240 + 3

= 243

236 + 7

3.

:

695 + 5 = 700 517 + 6 = 523 517 996 + 4 = 1 000 996

+ 6 + 4

523 1 000

4.

548 9.

5 4 8

: 548 + 9 = 557

+ 9

5 5 7 5.

700 300 9.

: (700 300) + 9 = 400 + 9 = 409

695

+ 5

700_____ _____

_____


22/11420

ODUZIMAWE JEDNOCIFRENOG BROJA OD TROCIFRENOG

(165 - 4; 106 - 8; 300 - 6; 180 - 6)

1. 165 4 :

65 - 4 = 61

165 - 4 = 161

165 - 4

106 - 8

106 - 8 = 106 - (6 + 2)

= (106 - 6) - 2

= 100 - 2

= 98

6 8. 1 .

0, 10 .

10 . 16 .

16 - 8 = 8.

9 .

3. o :

300 - 6

300 - 6 = (200 + 100) - 6

= 200 + (100 - 6)

= 200 + 94

= 294

180 - 6

180 - 6 = (100 + 80) - 6

= 100 + (80 - 6)

= 100 + 74

= 174

4.

265 540 700 607 402 957

- 4 - 7 - 6 - 8 - 9 - 5

261 533 694 599 393 952__________ _____ _____ _____ _____

2. 106 8 :


23/11421

3.

ODUZIMAWE JEDNOCIFRENOG BROJA OD TROCIFRENOG

(308 - 7; 146 - 8; 264 - 4)

:

1.

308 - 7

46 - 8 = 38

146 8 = 138

8 - 7 = 1

308 - 7 = 301

2. 6 8.

14

. 16

8.

3 ,

1. 13.

3,

1 .

264 - 4

64 - 4 = 60

264 - 4 = 260

4.

693, .

.

: 693 - 9 = 684 6 9 3

- 9

6 8 4


24/11422

SABIRAWE TROCIFRENOG BROJA I DESETICA

(330 + 30; 250 + 50)

.

1.

300 + 30

300 + 30 = 330

2.

250 + 50 = (200 + 50) + 50

= 200 + (50 +50)

= 200 + 100

= 300

250 + 50

560 900 820 950 720 660 370

+ 40 + 80 + 80 + 50 + 60 + 40 + 30

600 980 900 1000 780 700 400

3.

1 000 300 20 70.

: (1000 - 300) + (70 + 20) = 700 + 90 = 790.

4.

__________ _____ __________ _____ _____


25/11423

SABIRAWE TROCIFRENOG BROJA I DESETICA

(220 + 80; 146 + 20; 185 + 30)

.

1.

220 + 80 = (220 + 20) + 80= 200 + (20 + 80)

= 200 + 100

= 300

220 + 80

2.

146 + 20 = (100 + 46) + 20

= 100 + (46 + 20)

= 166

146 + 20

3.

185 + 30

185 + 30 = (100 + 85) + 30

= 100 + (85 + 30)

= 100 + 115

= (100 + 100) + 15

= 200 + 15

= 215

4.

620 80 30 60.

: (620 + 80) + (30 + 60) = 700 + 90 = 790.

258 9 70 20.

: (258 + 9) + (70 + 20) = 267 + 90 = 357.


26/11424

SABIRAWE TROCIFRENOG I DVOCIFRENOG BROJA

(264 + 31; 223 + 67)

.

1.

264 + 31

264 + 31 = 200 + (64 + 31)

= 200 + 95

= 295

2.

223 + 67 = (223 + 60) + 7

= 283 + 7

= 290

223 + 67

3.

112 48 .

: (112 + 48) + 10 = 160 + 10 = 170

4.


27/11425

SABIRAWE TROCIFRENOG I DVOCIFRENOG BROJA

(328 + 16)

328 + 16 = 300 + (28 + 16)

= 300 + 44

= 344

.

1.

54 + 27 = 81 39 + 52 = 91,

2.

3.

__________ _____ _____

_____ _____ __________

506 + 34 = 500 + (6 + 34) = 500 + 40 = 540

49 + 226 = (49 + 26) + 200 = 75 + 200 = 275

222 13 446 46

+ 33 + 777 + 24 + 309

255 790 470 355

708 424 16 661

+ 88 + 39 + 175 + 22

796 463 191 683


28/11426

ODUZIMAWE DESETICA OD TROCIFRENOG BROJA

(160 - 60; 166 - 30; 300 - 50; 348 - 60)

:

15 - 10 = 5 45 - 40 = 5 50 - 35 = 15 66 - 30 = 36 90 - 55 = 35 60 - 60 = 0

:

160 - 60 = (100 + 60) - 60 = 100 + (60 - 60) = 100 + 0 = 100

166 - 60 = (160 + 6) - 30 = (160 - 30) + 6 = 130 + 6 = 136.

1.

100 - 50 = 50 300 - 50 = 250 900 - 70 = 830 340 - 60 = 280

2.

348 - 60 = 348 - (40 + 20)

= (348 - 40) - 20

= 308 - 20

= 288

3..

186 - 30 = (180 + 6) 30 = (180 - 30) + 6 = 150 + 6 = 156

875 - 70 = (870 + 5) - 70 = (870 - 70) + 5 = 800 + 5 = 805

140 - 60 = 140 - (40 + 20) = (140 - 40) - 20 = 100 - 20 = 80

548 - 60 = (540 - 60) + 8 = 480 + 8 = 488

657 - 90 = (650 - 90) + 7 = 560 + 7 = 567


29/11427

ODUZIMAWE DVOCIFRENOG OD TROCIFRENOG BROJA

(139 - 26; 300 - 36)

.

1.

139 - 26

139 - 26 = (100 + 39) - 26

= 100 + (39 - 26 )

= 100 + 13

= 113

2.

300 - 36

100 - 30 = 70 100 - 36 = 100 - (30 + 6) 300 - 36 = 300 - (30 + 6)

= 100 - 30 - 6 = 300 - 30 - 6

= 70 - 6 = 270 - 6

= 64 = 264

649 - 24 = 600 + (49 - 24) = 600 + 25 = 625

787 - 66 = 700 + (87 - 66) = 700 + 21 = 721

444 - 33 = 400 + (44 - 33) = 400 + 11 = 411

3.

4.

, < = > .

377 - 16 < 400 - 29 486 - 54 > 500 - 78 984 - 62 = 1000 - 78


30/11428

ODUZIMAWE DVOCIFRENOG OD TROCIFRENOG BROJA

(174 - 46; 232 - 46)

.

1.

174 - 46 = 100 + (74 - 46)

= 100 + 28

= 128

2.

232 - 46 = 100 + (132 - 32 - 14)

= 100 + (100 - 14)

= 100 + 86

= 186

283 - 77 = 200 + (83 - 77) = 200 + 6 = 206

588 - 49 = 500 + (88 - 49) = 500 + 39 = 539

412 - 58 = 300 + (112 - 12 - 46) = 300 + 54 = 354

3.

4.

712, 134 89. :

712 - (134 - 89) = 712 - 45 = 667


31/11429

SABIRAWE TROCIFRENIH BROJEVA

(123 + 100; 283 + 324)

.

1.

2.

123 + 100 = (100 + 23) + 100

= (100 + 100) + 23

= 200 + 23

283 + 324 = (283 + 300) + 24

= 583 + 24

= 607

716 + 200 = 916 627 + 192 = (627 + 100) + 92 = 727 + 92 = 819

546 + 300 = 846 563 + 245 = (563 + 200) + 45 = 763 + 45 = 808

253 200 735 829 392

+ 400 + 688 + 181 + 100 + 376

653 888 916 929 768

3.

_____ _____ _____ _____ _____


32/11430


(235 + 114; 218 + 135; 279 + 143)


(235 + 114; 218 + 135; 279 + 143)

235 + 114 = (235 + 100) + 14

= 335 + 14

= 349

218 + 135 = (218 + 100) + 35

= 318 + 35

= 353

279 + 143 = (279 + 100) + 43

= (379 + 40) + 3

= 422


33/11431

ODUZIMAWE TROCIFRENIH BROJEVA

(260 - 100; 256 - 116)

1.

260 - 100 = (200 - 100) + 60

= 100 + 60

= 160

2.

256 - 116 = 256 - 100 - 16= 156 - 16

= 140

830 - 100 = (800 - 100) + 30 = 700 + 30 = 730

839 - 629 = (839 - 600) - 29 = 239 - 29 = 210

3.

648 963 815 437 602

- 237 - 162 - 504 - 237 - 201

411 801 311 200 401_____ _____

_____ _____ _____

4.

782 542.

: 982 242 = (982 - 200) - 42 = 782 42 = 740

5.

500 , 100 20 . 310 .

?

: (500 + 100 + 20) - 310 = (620 + 300)- 10 = 320 - 10 = 310

.


34/11432

ODUZIMAWE TROCIFRENIH BROJEVA

(300 - 160; 276 - 139; 484 - 286)

1.

300 - 160 = (300 - 100) - 60 = 200 - 60 = 140

2.

276 - 139 = (276 - 100) - 39 = 176 - 39 = 137

3.

484 - 286 = (300 +184) - (200 + 86)

= (300 + 184) - (200 + 86)= 100 + 98

= 198

4.


35/11433

a + b = c

K :

40 ; (230 + 40) + 190 = 270 + 190 = 460

50 ; 230 + (190 + 50) = 230 + 240 = 270

30 ; (230 - 30) + 190 = 200 + 190 = 390

90 ; 230 + (190 - 90) = 230 + 100 = 330

60,

60 ; (230 + 60) + (190 - 60) = 290 + 130 = 420

10,

10 ? (230 - 10) + (190 + 10) = 220 + 200 = 200

, . , .

, ,

.

630.

m, n. m + n = 630.

30. (m + 30) + n = 630 + 30, 30 .

70. m + (n + 70) = 630 + 70, 70.

40. (m - 40) + n = 630 - 40, 40.

50. m + (n - 50) = 630 50, 50.

30, . (m +30) + (n 30) = 630,

.

230 + 190 = 420

230 , 190. :


36/11434

a - b = c

155 - 75 = 80

155 . 75 .

?

:

50 ; (155 + 50) - 75 = 205 - 75 = 130

50 . (155 - 50) - 75= 105 -75 = 30

.

1.

400.

a b.

- b = 400.

b 166?

( + 166) - b

: 400 + 166 = 566, 166.

b 215?

( - 215) - b

: 400 - 215 = 385, 215.

2.

O , :

(288 + ) - 158 = 190.

190. 288 - 158 = 130,

= 190 130

= 60.

(288 - ) - 158 = 100

100. 288 - 158 = 130,

= 190 100

= 90.


37/11435

a - b = c

760 - 420 = 340

760 . 420. ?

:

20 ; 760 - (420 - 20) = 760 - 400 = 360

20 . 760 - (420 + 20) = 760 - 440 = 320

, .

, .

1.

375.

b.

- b = 375 b 75?

- (b + 75) : 375 - 75 = 300 75.

b 75?

- (b - 75) : 375 + 75 = 450 75.

2.

860 - 400 = 460, .

860 - (400 + ) = 410

410, = 460 - 410, = 50.

860 - (400 - ) = 500

500, = 500 - 460, = 40.

3.

217.

:

110; 217 110 = 107

110; 217 + 110 = 327.


38/11436

370, 260. 110.

370 260 = 110 100?

(370 +100) - (260 + 100) = 470 360 = 110

.

100?

(370 - 100) - (260 - 100) = 470 360 = 110

.

.

1.

800 - 396 = (800 + 4) - (396 + 4) = 804 - 400 = 404

675 - 505 = (675 - 5) - (505 - 5) = 670 - 500 = 170

2.

550, 120, 430. :

100; (550 - 100) - (120 - 100) = 430

100. (550 + 100) - (120 + 100) = 430

3.

, , , :

825 - 675 = 850 - 700 25.

719 489 = 700 - 470 19.

.


39/11437

380 + 220 400 - 126 .

:

200 + 30

300 + 30

600 + 30

900 + 40

900 + 50

900 + 60 b :

+ 30 900 - b

200, 300, 600. b 40, 50, 60.

2.

712.

.

= 1, = 3, = 5, = 7, = 9,

:

+ 712.

+ 712 .

1 + 712 = 713, 3 + 712 = 715, 5 +712 = 717,

7 + 712 = 719, 9 + 712 = 721.

107 - m, a m .

: 11, 12, 13, 14, 15, 16, 17, 18, 19 20.

107 - m m .

1.

117 , , 900, 788, 120.

900 117 = 783

788 117 = 671

120 117 = 3.

m 11 12 13 14 15 16 17 18 19 20

107 - m 96 95 94 93 92 91 90 89 88 87

3.


40/11438

169 . , 215 .

?

169 .

x, m, y, a, t . .

n,

169 + n = 215.

.

.

!

169 + n = 215

n = 215 169

n = 146

: 169 + 146 = 215

1. 46 900?

. : + 46 = 900.

:

+ 46 = 900

= 900 - 46

= 854.

: 854 + 46 = 900

2. 650 175,

.

: + ( 650 + 175) = 1 000

+ 725 = 1000

= 1 000 725

= 275

: 275 + 725 = 1 000

3. 109 . , 212 ?

:

109 + m = 212

m = 212 - 109

m = 103.

: 109 + 103 = 212

: 103 .

1 6 9 ?

? 46

2 1 5

900


41/11439

714 kg.

685 , 279 ? , 578 kg?

- 685 = 279

= 279 + 685

= 964

: 964 - 685 = 279

714 - = 578

= 714 - 578

= 136

: 714 - 136 = 578

. .

! !

3. 722 245 100. ?

: - (722 - 245) = 100

- 477 = 100

= 477 + 100

= 577

: 577 - 477 = 100.

: 577.

4.

103

592.

- 103 = 592

= 592 + 103

= 695

: 695 - 103 =592

? 685 714 ?

279 578

1.

352, 428.

:

- 352 = 428

= 428 + 352

= 780

: 780 - 352 = 428.

2. 721

196.

.

:

721- = 196

=721 - 196

= 525

: 721- = 196.

197, 346.

.

346 - = 197

= 346 - 197

= 149

: 346 - 149 = 197


42/11440

e. .

:

0, 1, 2, 3, 4, 5, 6, 7, 8 9.

0, 1, 2, 3, 4, 5, 6, 7, 8 9.

.

1, 3, 5, 7 9

, .

{1,3,5,7,9}

, : ,

.

, ,

.

.

1.

.

.

2.

.

4.

.

.

3.

.

E


43/11441

.

. ,

. , ,

D,

D = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.

11, 12, 13, 14, 15, 16, 17, 18, 19 20 D.

:

11

D, 12

D, 13

D, 14

D, 15

D, 16

D, 17

D, 18

D, 19

D, 20

D.

, 11 D : 11 D 11 D.

25 , D.

25 D

: 25 D 25 D.

.

{ }.

1.

,

, , , 74 .

2.

B . B = {, , , , },

B, * B, 122 B, B.

3.

C = {1, 22, 333}

1 C, 2 C, 22 C, 3 C, 33 C 333 C.

{11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.


44/11442

1. p + 6 13, .

p 0 1 2 3 4 5 6 7 8 9

p + 6 6 7 8 9 10 11 12 13 14 15

{0, 1, 2, 3, 4, 5, 6, 7},

p + 6 13, p {0, 1, 2, 3, 4, 5, 6, 7}.

. 17 .

8 , ?

x. 8 + x 17,

8 + x < 17.

, x = 0. 8 + 0 < 17. 8 < 17,

0 .

1 , x = 1. 8 + 1 < 17. 9 < 17,

1 .

2 , x = 2. 8 + 2 < 17. 10 < 17,

2 .

8 + x < 17

{0,1,2,3,4,5,6,7,8}.

- .

8 + x < 17 x {0, 1, 2, 3, 4, 5, 6, 7, 8}.

9 , 8 + 9 < 17, 17 < 17

.

:

0 x < 9.

: x , 9.

.

x 0 1 2 3 4 5 6 7 8 9

8 + x 8 9 10 11 12 13 14 15 16 17

.


45/114

01

23

45

67

89

1011

12

1500gr

200gr100gr 50gr

2

6

9

4

10


46/11444

(mm km)

.

, .

. :

.

1 1 m.

, :

, dm;

, cm.

:

1 m = 10 dm;

1 dm = 10 cm;

1 m = 10 dm = 100 cm.

, , AB MN.

AB.

11 cm. 11 cm, 11 , a cm .

.

, cm 11 AB.

11 cm :

11 cm = 1 dm 1 cm.

A

A

B

B

0 1 2 3 45 6 7 8 9

10 11 12

MN

01

23

45

67

89

10

11

12


47/11445

,

.

MN.

4 cm 5 cm. MN,

. , mm.

10 ,

1 cm = 10 mm.

:

1 cm = 10 mm;

1 dm = 10 cm = 100 mm;

1 m = 10 dm = 100 cm = 1 000 mm.

MN

MN = 43 mm.

, MN

MN = 4 cm 3 mm.

. 1 m = 1 000 mm,

.

, , ,

1 m. , km.

1 000 ,

1 km = 1 000 m.

81 km,

204 km.

0 1 2 3 4 5 6 7 8 9 10 11 12

0 1 2 3 4 5 6 7 8 9 10 11 12

MN

1cm 1cm 1cm 1cm 1cm 1cm 1cm 1cm 1cm 1cm

10mm

1dm


48/11446

(kg, g t)

,

. , .

.

.

1 1 kg.

.

, .

2 kg, 3 kg.

1 kg, ,

, g.

1 000 .

1 kg = 1 000 g

700 g, 5 kg 200 g.

11

11 1

500gr1 1 1 1 1

200gr 200gr

1500gr

200gr100gr 50gr


49/11447

1.

, :

1 kg 100 g = 1 000 g 100 g = 900 g;

1 kg 200 g = 1 000 g 200 g = 800 g;

1 kg 50 g = 1 000 g 50 g = 950 g

, t.

1 000 .1 t = 1 000 kg

2.

1 t 360 kg 2 t.

3.

30 kg,

2 kg.

?

30 kg 2 kg = 28 kg,

28 kg.

,

. .

,

. .

1

1

1

100 g

200 g

50 g


50/114

,

. ,

1 .

.

1 1 l.

1 l 1 dm.

1 l

:

, dl;

, cl;

, ml.

: 1 l = 10 dl; 1 dl = 10 cl; 1 cl = 10 ml;

1 l = 10 dl = 100 cl = 1 000 ml;

1 dl = 10 cl = 100 ml.

1 l, 1 dl.

48

(l, dl, cl, ml hl)

1 dl

1 cl

1l1 dl

1 dl

1 dl

1 dl

1 dl

1 dl

1 dl

1 dl

1 dl

1 dl

1 dm

1dm

1dm 1l


51/11449

, hl.

100 .

1 hl = 100 l

3.

21 ml = 2 cl 1 ml

74 cl = 7 dl 4 ml

546 ml = 5 dl 4 cl 6 ml

352 cl = 3 l 5 dl 2 cl

104 ml = 1 dl 4 ml

4.

745 l = 7 hl 4 dl 5 l

513 l = 5 hl 1 dl 3 l

308 l = 3 hl 8 l

200 l = 2 hl

2.

2 cl = 20 ml

8 dl = 80 cl = 800 ml

7 l = 70 dl = 700 cl

1.

9 cl 1 ml = 91 ml

6 dl 3 cl 2 ml = 632 ml

3 dl 2 ml = 32 ml

1 hl . 4 l.

?

1 hl : 4 l = 100 l : 4 l = 25

1 hl 25 4 l.

10 l, 5 l 6 dl 7 cl . 3 dl 3 cl, a

400 cl . , , ?

5 l 6 dl 7 cl + 3 dl 3 cl + 400 cl =

567 cl + 33 cl + 400 cl =

600 cl + 400 cl =

1000 cl =

10 l .

5.

6.


52/11450

(, )

.

.

8 , , 20 .

8 .

60 , .

1 h,

1 h = 60 min

.

1 min = 60 s

24 , .

1 = 24 h

7 . :

, , , , , .

, .

.

30 31 , ,

28 29 .

12 , .

1 = 12

365 366 ,

. 29 ,

366 . ,

365 .

10 .

1 = 10

100 , .

1 = 100

.

31

28 29

31

30 31

30

31

31

30

31

30

31

12

6

9

8

7 5

4

3

2

111

10

12

6

9

8

7 5

4

3

2

111

10


53/114

1000

(360:6)+

(450:9)

=60+50=110;

(640

:8

)(2

70:9)=8

030=50

(+b).c=a. c+b. c


54/11452

.

28 : 7 = 4

4 . 7 = 28

1.

4 . 5 = 20,

20 : 5 = 4 20 : 4 = 5.

.

2. ,

5 . 7 = 7 + 7 + 7 + 7 + 7.

3. ,

6 + 6 + 6 + 6 = 4 . 6.

4. e 0 , 0,

4 . 0 = 0 0 . 2 = 0.

5. 1, ,

6 . 1 = 6 1 . 7 = 7.

6. .

8 . 3 = 3 . 8.

7. . .

5.

6.

2 = (5.

6).

2 = 5.

(6.

2)

8. 1 , ,

9 : 1 = 9.

9. , 1,

42 : 42 = 1.

10. 0 , 0,

0 : 12 = 0


55/11453

10 100

10 + 10 + 10 + 10, 4 . 10,

10 + 10 + 10 + 10 = 4 . 10.

1.

10.

16 . 10 = 160 20 . 10 = 200 31 . 10 = 310 10 . 63 = 630 10 . 97 = 970

10 .

2.

17 10.

17 . 10 = 170

170 17 10.

100 + 100 + 100 + 100 + 100 5 . 100,

100 + 100 + 100 + 100 + 100 = 5 . 100.

3.

100

2 . 100 = 200 8 . 100 = 800 3 . 100 = 300 100 . 6 = 600 100 . 9 = 900

100 .

4.

:

6 100; 600,

6 . 100 = 600.

10 100; 1 000,

10 . 100 = 1 000.

4 100; 400,

4 . 100 = 400.

5 100; 500,

5 . 100 = 500.


56/11454

, ,

10.

10.

320 : 10 = 32 500 : 10 = 50 420 : 10 = 42 610 : 10=61 100 : 10 = 10

10

.

1.

5.

.

500 : 10 = 50

100

600 : 100 = 6 200 : 100 = 2 900 : 100 = 9 800 : 100 = 8 300 : 100 = 3

100

.

2.

.

1000 : 100 = 10.

3.

100 700 , 400 ,100 500?

700 : 100 = 7 400 : 100 =4 100 : 100 = 1 500 : 100 = 5

: 7, 4, 1 5.

10 100

1 . 10 = 10

2 . 10 = 20

3 . 10 = 30

4 . 10 = 40

5 . 10 = 50

10 : 10 = 1

20 : 10 = 2

30 : 10 = 3

40 : 10 = 4

50 : 10 = 5

6 . 10 = 60

7 . 10 = 70

8 . 10 = 80

9 . 10 = 90

10 . 10 = 100

60 : 10 = 6

70 : 10 = 7

80 : 10 = 8

90 : 10 = 9

100 : 10 = 10


57/11455

1.

10 . 43 . o ?

:

I : II :

10 . 43 = 43 . 10

.

. b = b . a

2.

10 5 , 6 .

.

:

I : ,

:

(10 . 5) . 6 = 50 . 6 = 300.

II : :

10 . (5 . 6) = 10 . 30 = 300.

?

o

.

(a . b) . c = a . (b . c) = (a . c) . b

3.

2 5 . 7 . ?

2 . 5 . 7 = ( 2 . 5 ) . 7 = 10 . 7 = 70

70 .

4.

6 . 5 kg . ?

2 . 6 . 5 = ( 2 . 5 ) . 6 = 10 . 6 = 70

60 kg .


58/11456

(4. 30)

4 . 30 .

?

:

I :

: 30 + 30 + 30 + 30 = 120

II :

4 30: 4 . 30 = 120

30 3 . 10 :

(4 . 3) . 10 = 12 . 10 = 120.

.

1.

:

5 . 60 = (5 . 6) . 10 = 30 . 10 = 300

20 . 7 = (2 . 10) . 7 = (2 . 7) . 10 = 14 . 10 = 140

2.

7 40 30 8?

( 7 . 40 ) ( 30 . 8) = 280 240 = 40

7 40 40 30 8.

3.

(9 . 60 ) + (70 . 4 ) = 540 + 280 = 820

(7 . 70 ) (4 . 40 ) + 50 = 490 160 + 50 = 380


59/11457

(120 : 4)

120 , .

?

.

120 : 4 = 30

120 : 4 = 30, 30 . 4 = 120.

:

180 : 3 = 60 60 . 3 = 180 320 : 4 = 80 80 . 4 = 320

420 : 7 = 60 60 . 7 = 420 180 : 9 = 20 20 . 9 = 180

1.

120 6

312.

(120 : 6 ) + 312 = 20 + 312 =332

2.

:

490 7 .

?

490 + ( 490 : 7 ) = 490 + 70 = 560 560 .

3.

72 0 + (420 : 7 ) = 720 + 60 = 780 ; 960 (810 : 9 ) = 960 90 = 870


60/11458

. 30 6 ,

50 . ?

:

: 30 . 6 = 180;

: 50 . 6 = 300,

: 180 + 300 = 480 .

: .

(30 + 50) . 6 = 80 . 6 = 480,

(30 + 50) . 6 = 30 . 6 + 50 . 6.

( + b) . c = a . c + b . c a . (b + c) = a . b + a . c

1.

, , :

54 . 3 = ( 50 + 4 ) . 3 = 50 . 3 + 4 . 3 =150 + 12 = 162.

2.

:

(420 + x) . 6 = 420 . 6 + 5 . 6 ; x = 5

(c + 38) . 9 = 62 . 9 + 38 . 9; c = 62.

:

6 . 67+ 6 . 33 = 6 . (67 + 33) = 6 . 100 = 600.

3.

:

24 . 5 + 5 . 76 = (24 + 76) . 5 = 100 . 5 = 500 36 . 2 + 64 . 2 =(36 + 64) . 2 = 100 . 2 = 200

72 . 6 + 6 . 28 = (72 + 28) . 6 = 100 . 6 = 600 47 . 3 + 53 . 3 =(47 + 53) . 3 = 100 . 3 = 300


61/11459

:

49 . 6 = (40 + 9) . 6 = 40 . 6 + 9 . 6 = 240 + 54 = 294.

,

.

:

49 . 6 = (50 - 1) . 6 = 50 . 6 - 1 . 6 = 300 6 = 294.

,

. .

(a - b) . c = a . c - b . c a . (b - c) = a . b - a . c

1.

:

37 . 3 = (40 - 3) . 3 = 40 . 3 3 . 3 = 120 9 = 111.

:

88 . 7 = ( 90 2 ) . 7 = 90 . 7 2 . 7 = 630 14 = 616.

:

2.

100 3 ,

.

( 100 3 ) . 9 = 100 . 9 3 . 9 = 900 27 =873

3.

6 9. ?

9. 89.

89 . 6 = ( 90 1 ) . 6 = 90 . 6 1 . 6 = 540 6 = 534

4.

98 . 9 = (100 - 2 ) . 9 = 100 . 9 2 . 9 = 900 18 = 882

69 . 7 = ( 70 1 ) . 7 = 70 . 7 1 . 7 = 490 7 =483


62/11460

. .

:

34 . 2 = (30 + 4) . 2 = 30 . 2 + 4 . 2 = 60 + 8 = 68

.

79 . 3 = (80 - 1) . 3 = 80 . 3 - 1 . 3 = 240 - 3 = 237

.

:

23 . 3 = 69

1.

:

32 . 2 = 64 43 . 2 = 86 12 . 4 = 48 11 . 8 = 88

:

23 . 4 = 92

:

36 . 4 =144

:

2.

, :

46 . 3 53 . 5 73 . 4 63 . 7

138 265 292 441

4 . 6 = 24 4 , .

4 . 3 = 12 12 2 .

14 . 144.

4 . 3 = 12

4 . 2 = 8

8 + 1 = 9

29 . 8 77 . 9 64 . 8 37 . 5

232 693 512 185

12 1 2. 2. ,

2 4, 8 1,

9. 9 2. 92.


63/11461

9 12 ,

.

:

9 : 3 = 3 .

, : 12 : 3 = 4 .

, 3 4 . ,

9 : 3 + 12 : 3 = 3 + 4 = 7 .

:

(9 + 12) : 3 = 21 : 3 = 7

: (a + b) : c = ( a : c ) + ( b : c )

1.

Ao , :

77 : 7 = ( 70 + 7 ) : 7 = 70 : 7 + 7 : 7 = 10 + 1 = 11.

.

, :

87 : 3 = (90 3) : 3 = 90 : 3 3 : 3 = 30 1 = 29

: ( - b) : c = a : c b : c.

2.

96 : 4 ,

.

( 80+ 16 ) : 4 = 80 : 4 + 16 : 4 = 20 + 4 = 24

( 100 4 ) : 4 = 100 : 4 4 : 4 = 25 1 = 24


64/11462

___

81 : 3 = 27

- 6

21-21

0___

68 : 2 = 34

- 6

8___

- 8

0___

91 : 7 = 13

- 7

21___

- 21

0___

76 : 5 = 15

- 5

26___

- 25

1___

59 : 4 = 14

- 4

19___

- 16

3___

82 : 7 = 11

- 7

12___

-7

5___

6 : 2 = 3 : 3 . 2 = 6 6 - 6 = 0

8 : 2 = 3 : 4 . 2 = 6 8 - 8 = 0

8 : 3 = 2 : 2 . 3 = 6 6 - 6 = 0

21 : 3 = 7 : 7 . 3 = 21 21 - 21 = 0

46 : 3 = 15

- 3

16

___

- 15

1___

36

. ?

:

36 : 3 = (30 + 6) : 3 = 30 : 3 + 6 : 3 = 10 + 2 = 12

12 .

1. 46: 2.

46 : 2 = ( 40 + 6 ) : 2 = 40 : 2 + 6 : 2 = 20 + 3 = 23

:

2. 91 , 7, :

3. , .

4. : 76 : 5, 59 : 4 82 : 7.


65/11463

123 . 3 ?

:

123 . 3 = (100 + 23) . 3 = 100 . 3 + 23 . 3 = 300 + 69 = 369.

1.

212 . 4 = (200 + 12 ) . 4 = 200 . 4 + 12 . 4 = 800 + 48 = 848

.

2.

123 . 3

1) 3 3: 3 . 3 = 9

2) 2 3: 3 . 2 = 6

3) 1 3: 3 . 1 = 3

123 . 3 = 369

3.

, 223 . 4;

223 . 4 = (200 + 23 ) . 4 = 200 . 4 + 23 . 4 = 800 + 92 = 892.

:

223 . 4 = 892 1) 4 . 3 = 12 2 , ;

223.4 2) 4 . 2 = 8 8 + 1 = 9 , 9

892 3) 4 . 1 = 4

4.

327 2.

1000 ( 327 . 2 ) = 1000 654 = 346

5.

(227 . 2) + ( 136 . 3 ) = 454 + 408 = 862

(342 . 2) - (137 . 3) = 684 - 411 =273

917 - (235 . 3) = 917 - 705 = 212


66/11464

3 6 2 , 2

: 2 . 3 = 6, 6 - 6 = 0

3 9 3 , 3: 2 . 3 = 6, 6 - 6 = 0

3 3 1 , 1

: 1 . 3 = 3, 3 - 3 = 0

693 : 3 = 231

- 6

9____

- 9

3____

- 3

0____

5 5 1 , 1: 1 . 5 = 5, 5 - 5 = 0

5 8 1 , 1

: 1 . 5 = 5, 8 - 5 = 3 ()

5

5 35 7 , 7

: 7 . 5 = 35, 35 - 35 = 0

585 : 5 = 117- 5

8____

- 5

35____

- 35

0____

693 ,

. ?

:

693 : 3 = (600 + 93) : 3 = 600 : 3 + 93 : 3 = 200 + 31 = 231

1. 848 4.

848 : 4 = (800 + 48 ) : 4 = 800 : 4 + 48 : 4 = 200 + 12 = 212

, 693 : 3, .

2.

I : 585 : 5 = (500 + 85) : 5 = 500 : 5 + 85 : 5 = 100 + 17 = 117.

II :

3. 324 121 5.

(324 + 121) : 5 = 445 : 5 = 89

4. 1000 276 4.

(1000 276 ) : 4 = 724 : 4 = 181

5. .

644 , 4 . ?

644 + (644 : 4 ) = 644 + 161 = 805

805 .


67/11465

20 . 3 = 60

?

2 : (20

.

2)

.

3 = 40

.

3 = 120 2 . 2 : 20 . (3 . 2) = 20 . 6 = 120 2 .

.

4 : (20 : 4) . 3 = 5 . 3 = 15 4 .

.

, .

1.

2.

1.

a . b = 120, :

(2 . ) . b = 120 . 2 = 240; (a : 2) . b = 120 : 2 = 60; a . ( b : 3 ) = 120 : 3 = 40.

2.

8 . 15 = 120,

16 . 15 = 120 . 2 = 240 ;

8 . 45 = 120 . 3 = 360 ;

4 . 15 = 120 : 2 = 60 .

3.

,

, .

9 . 12 = 108

( 9 . 3 ) . ( 12 : 3 ) = 27 . 4 = 108

.

4.

9.

12 = 108 , , :

27 . 12 = 324 , .

9 . 24 = 216 ,

18 . 6 = 108 , , .

.

3 . 36 = 108 , .


68/11466

1.

2.

54 . 5 = 270

?

(54 : 2) . (5 . 2) = 27 . 10 = 270(54 . 5) . (5 : 5) = 270 . 1 = 270

, .

.

1.

:

138 . 5 = ( 138 : 2 ) . ( 5 . 2 ) = 69 . 10 = 690

162 . 5 = ( 162 : 2 ) . ( 5 . 2 ) = 81 . 10 = 810

:

2.

a . b = 60 :

( a . 2 ) . b = 60 . 2 = 120

, .

( a : 2 ) . b = 60 : 2 = 30

, .

( a . 2 ) . ( b : 2 ) = 60

, , .

3.

, :

16 . 25 = (16 : 4 ) . ( 25 . 4 ) = 4 . 100 = 400( )

4.

, , :

18 . 50 = ( 18 : 2 ) . (50 . 2 ) = 9 . 100 = 900

25 . 32 = ( 25 . 4 ) . (32 : 4 ) = 100 . 8 = 800

36 . 25 = ( 36 : 4 ) . (25 . 4 ) = 9 . 100 = 90


69/11467

1.

.

a : b = 100 :

(a . 5 ) : b = 100 . 5 = 500 , .

(a : 5 ) : b = 100 : 5 =20 , .

a : ( b . 4 ) = 100 : 4 = 25 , .

a : ( b : 4 ) = 100 . 4 = 400 .

( : 3 ) : ( b : 3) = 100 .

2.

.

b je 180. :

( 5 . a ) : b = 900, je je 180 . 5 =900.

a : ( 2 . b ) = 90, 180 : 2 = 90.

( a : 4 ) : b = 45, 180 : 4 = 45.

( a : 3 ) : ( b . 3 ) = 20, je 180 : 9 = 20 .

.

( 7 . a ) : ( 7 . b ) = 180.

.

24 : 4 = 6

?

2 : (24 . 2) : 4 = 48 : 4 = 12 2 .

2 : (24 : 2) : 4 = 12 : 4 = 3 2 .

?

2 : 24 : (4 . 2) = 24 : 8 = 3 2

2 : 24 : (4 : 2) = 24 : 2 = 12 2

, .

.

, .

.


70/11468

,

. .

1.

:

450 : 5 = (450 . 2) : ( 5 . 2) = 900 : 10 = 90

335 : 5 = (335 . 2) : ( 5 . 2) = 670 : 10 = 67

215 : 5 = (215 . 2) : ( 5 . 2) = 430 : 10 = 43

125 : 5 = (125 . 2) : ( 5 . 2) = 250 : 10 = 25

, 10 .

2.

2, :

224 : 4 = (224 : 2) : (4 : 2) = 112 : 2 = 56

560 : 4 = (560 : 2) : (4 : 2) = 280 : 2 = 140

432 : 4 = (432 : 2) : (4 : 2) = 216 : 2 = 108

512 : 4 = (512 : 2) : (4 : 2) = 256 : 2 = 128

3.

. : b = 204, :

( : 2) : (b . 2 ) = 204 ; ( a . 2 ) : ( b . 2 ) = 204

( . 2) : (b : 2 ) = 204 ; ( a : 2 ) : ( b : 2 ) = 204

( . 3) : (b . 3) = 204 ; ( a : 3 ) : ( b . 3 ) = 204

( : 6) : (b : 6 ) = 204 ; ( a . 6 ) : ( b . 6 ) = 204

130 : 5 = 26

?

(130 . 2) : (5 . 2) = 260 : 10 = 26

(130 : 5) : (5 : 5) = 26 : 1 = 26


71/11469

1.

: 24 , 25 , 26 , 27 28 4. :

24 : 4 = 6; 25 : 4 = 6 (1); 26 : 4 = 6 (2); 27 : 4 = 6 (3); 28 : 4 = 7

, .

2.

:

) 12 : 6 = 2; 13 : 6 = 2 (1); 14 : 6 = 2 (2); 15 : 6 = 2 (3); 16 : 6 = 2 (4); 17 : 6 = 2 (5);

) 18 : 6 = 3; 19 : 6 = 3(1); 20 : 6 =3 (2); 21 : 6 = 3 (3); 22 : 6 = 3 (4); 23 : 6 = 3 (5);

) 15 : 5 = 3; 16 : 5 = 3(1); 17 : 5 = 3(2); 18 : 5 =3 (3); 19 : 5 = 3 (4);

) 20: 5 = 4; 21: 5 = 4(1); 22 : 5 = 4(2); 23 : 5 = 4(3); 24 : 5 =4 (4);

.

3.

8 : 0, 1, 2, 3, 4, 5, 6 7.

4.

, :

3, 8, 2 8 . 3 + 2 = 24 +2 =26

5, 6, 4 6 . 5 + 4 = 30 +4 =34

7, 4, 5 4 . 7 + 5 = 28 +5 =33

9, 3, 6 3 . 9 + 6 = 27 +6 =33

8, 7, 4 7

. 8 + 4 = 56 +4 =60

19

3 ,

.

?

19 : 3 = 6, 1,

.


72/11470

8 576?

. x. :

8 . x = 576

.

576 : x = 8

576 : 8 = x

.

.

:

8 . x = 576

x = 576 : 8

x = 72

: 8 . 72 = 576 1.

5, 915?

, :

x . 5 = 915;

x = 915 : 5;

x = 183;

: 183 . 5 = 915

2.

y . 4 = 798 : 6 798 : 6,

. :

y . 4 = 798 : 6

y . 4 = 136

y = 136 : 4

y = 34

: 34 . 4 = 798 : 6

34 . 4 = 136

3.

. 6 372.

m. :

m . 6 = 372.

m = 372 : 6

m = 62

: 62 . 6 = 372

372.


73/11471

5 74?

. x.

:

x : 5 = 74.

.

74 . 5 = x.

.

.

:

x : 5 = 74

x = 74 . 5

x = 370

: 370 : 5 =74

144 36?

. y. :

144 : y = 36.

.

144 : 36 = x.

.

:

144 : x = 4

x = 144 : 4

x = 136

: 144 : 36 =4

1.

7 59? ,

:

: 7 = 59; = 59 . 7; = 413; : 413 : 7 = 59.

2.

168 : = 24, , :

= 168 : 24; = 7; : 168 : 7 = 24.


74/11472

1000

.

1.

12 10 2. , 12 . 10 = 120.

7 100 7. , 7 . 100 = 700.

2.

8. 8,

800 : 100 = 8.

3.

758 90 8 38,

758 (90 . 8 ) = 758 720 = 38.

4.

80 8 210 7 610,

80

.

8 210 : 7 = 640 30 = 610.

5. 624 6 , 624

600 + 24, 6. :

624 : 6 = (600 + 24 ) : 6 = 600 : 6 + 24 : 6 = 100 + 4 = 104.

6. 995 5 , 995

1 000 - 5. :

995 : 5 = (1000 - 5 ) : 5 = 1000 : 5 - 5 : 5 = 200 - 1 = 199.

7.

x : 6 +4 = 22 , x : 6 :

x : 6 = 22 4

x : 6 = 18,

.

x = 18 . 6; x = 108; : 108 : 6 = 18.

1000


75/114

O

p

r

a O

b


76/11474

.

.

.

.

.

. .

p A B.

p, B .

p, B p.

p.

.

N, .

, N .

.

.

.

N N : N.

B

XYA

p

a

b

p

B

A

N

M

N

M


77/11475

.

.

.

. ,

.

. .

.

.

, Sx, GH C, D, E F.

C Sx, D . C Sx,

D Sx. C Sx.

.

E GH, F . E GH, F

GH. E GH.

.

p .

p . o .

x

x

pA

A

S

G

C E

F

D

H

B M

N

M

p A

A

A


78/11476

, , .

, .

.

.

, , .

.

.

.

, ,

t, Bb MN.

, t, Bb MN

. ,

.

,

, , ,

.

.

.

A

B

M

t

b

N


79/11477

, a b A, B O.

A a, B b, O a b.

a b. a b .

m n .

m n , .

.

m n

mn,

: m n.

m n .

.

, , +.

c d. : c d.

, ,

cd.

: c d.

c d .

B

A O

ba

n

m

d

c


80/11478

n

m

M

n n

M

n

M

n

M

M

,

,

.

m.

,

m n .

m n.

n.

m, n .

.

,

.

. .


81/11479

b

a

B

a

a

a a

B

B

B B

b

b, B.

b B

a.

B, .

B.

a, b.

b, a B.

,

.

. .


82/11480

.

k

.

. K.

K.

.

P T k. k.

M, N, P T K. K.

M N K.

B K.

K k.

, B, M, N, P, T, k K

.

.

.

, k.

A

PM

NT

B


83/11481

.

, ,

,

.

,

.

.

, .

.

, , :

O

.

,

.

.

.

, ,

,

.

.

:

.

, r.

.

,

.

O

rO


84/114

, ,

, .

, B, O k .

B k B O.

B ,

R d.

.

,

.

.

.

, , .

.

.

, .

O L.

L.

82

O

O

O

O

L

k

R

K

K

k

r

O

k

O

L

O

Bk

R

O

K

Rr


85/11483

.

.

, .

.

.

, , , .

O

O

,

.

.

OO

O

O


86/11484

A B,

: OB, AOb, aOB.

, aOb A, B, M, N, P S.

A, B, M, N, P O aOb, S . A, B, M, N, P O

aOb, S aOb.

A, B, N O aOb, M P aOb.

, Oa Ob.

aOb, : aOb. , ,

. O.

O

O

a

a

b

b

B

O

a

b

BP

M

NS


87/114

b.

.

.

.

,

.

85

O

O

O

b

a O

b

a

.


88/11486

aOb. m

, : aOm mOb.

. .

.

aOb. n

, : aOn bOn.

bOn , , aOn ,

. .

.

.

, .

O O

O

O

O

b b

bnb

a a

a

p

r

a

O

y

x

O

O p

r

m


89/114

N, KL, OP TS.

.

MN = 8 cm, KL = 50 mm, OP = 7 cm TS = 60 mm.

, , MN = 8 cm : MN 8 cm.

< > :

KL < TS < OP < N.

, KL, N.

AB, GH CD.

GH AB CD. :

1) G, H.2) ,

AB CD.

GH CD.

87

N

K L

T S

O

P

A GCB HD

G H C DA B


90/114

AB = 5 cm, CD = 3 cm.

EF AB CD? 3 + 5 = 8, 3 cm + 5 cm = 8 cm, F8 cm.

EF=AB + CD.

EF , ,

AB CD. .

a.

a , .

AB. ,

B.

CD. B

, D.

AD , AB CD.

EF AD.

, , .

88

A

a

a

a

a

CB D

A

A

B

B

D

D


91/11489

, B, C D ABCD.

:AB, BC, CD DA

. ABCD .

.

, B, C, D:

, B, C D.

, ,

.

C C

C

D D

D

A A

A

B B

B

C

D

A

B

:AB, BC, CD DA.

.

ABCD.

.

.

.


92/11490

, B, C D

ABCD. :AB, BC,

CD DA

.

.

.

.

AB = BC= CD = DA =

.

.

.

.

D

D

D D

D

D

D

C

C

C C

C

C

C

B

B

B B

B

B

B

A

A

A A

A

A

b

b

a

a

a

a

A

.

ABCD ,

:AB CD.

. ABCD

, :AB BC.

:

AB = CD =

BC= DA = b

:

AB = CD BC= DA.


93/114

.

.

.

.

91


94/114

,

.

, AB = 6 cm BC= 2 cm,

.

. AB = 6 cm.

.

. 4 cm.

. B .

C BC= 2 cm.

. C .

D CD =AB = 6 cm.

. D.

C

92

A B

A A

A A

B B

B B

A

A

D D

D D

A

B

C

C

C

C

C

B B


95/114

.

, 4 cm 2 cm, .

, ,

4 cm 2 cm.

. ,

4 cm, 2 cm.

. b

.

.

. ,

, 4 cm.

B.

.

2 cm.

b D.

.

AB. D .

.

AD. B ,

.

.

C.

. B C,

D C.

93

A

D

D

A A

A

b

a

a

a

a

b b

b

B B

B

D

D D

A

A A

a

a a

b

b b

B

B B

C C


96/114

, .

.

, o , .

, ,

b .

.

.

a b

.

.

.

.

.

.

94

a a a

aaa

DDDD

O O O

OOO

D

AAAA

AAAA

aaaa

aaa

bb

b b b

bbb

bb

bbb

BBBB

BBBB

CC


97/114

ABCD , .

AB = , BC= b, CD = DA = b.

p.

AB + BC+ CD + DA,

+ b + a + b.

. ,

= + b + a + b.

.

+ b + a + b = + a + b + b = 2 a + 2 b = 2 (a + b),

= 2 (a + b).

1. = 5 cm b = 2 cm,

= 2 (a + b)

= 2 (5 cm + 2 cm)

= 2 10 cm

= 20 cm.

2.

80 cm. 15 cm,

?

,

b. = 15 cm, = 80 cm,

= 2 (a + b)

80 cm = 2 (15 cm + b)

80 cm : 2 = 15 cm + b

40 cm = 15 cm + b

b = 40 cm - 15 cm

b = 25 cm.

25 cm.

95

D

p

A a

a a

b

b b

b

a

B

C


98/114

ABCD , .

:

AB = BC= CD = DA =

= + b + a + b :

= + + a +

.

+ + a + = 4 a,

= 4 a.

1.

= 3 cm

= 4 a

= 4 3 cm

= 12 cm

2.

32 cm. ?

. = 32 cm,

= 4 a

32 cm = 4 a

= 32 cm : 4

= 8 cm

8 cm.

96

D

A a

a

a

a

B

C


99/114

.

.

.

ABC.

:

AB, BC CA.

.

, B C ABC.

:AB, BC CA

. ABC .

. , B C:

, B C.

, ,

.

, ,

:

AB = c

BC= a

CA = b

a

97

A

A

A

A

A

cb

a

B

B

B

B

B

C

C

C

C

C


100/114

: BC, KLM PRS.

:

BC ;

KLM ;

PRS .

98

A

A

K

K

P

P

B

B

L

L

R

R

C

C

M

M

S

S

, .

.

AB = BC= CA

,

,

.

.

.

KL = KM

.


101/114

: DEF, GHI UVT.

:

DEF;

GHI ;

UVT.

.

.

.

99

D

D

G

G

U

U

E

E

H

H

V

V

F

F

I

I

T

T


102/114

B = 3 cm, BC= 5 cm CA = 4 cm, ,

.

.

:B, BC CA.

.

p , , B.

.

BC.

B p

p C.

.

AB.

B p

.

.

.

.

CA. C

p,

,

.

.

A B, A C.

100

.

.

, .

A

pB

C

B

BC

D

p p

pp

p

B BC C

CC

C

B

B

B


103/114

ABC, .

BC= , CA = b AB = c.

, p.

BC+ CA +AB,

+ b + c

. ,

= + b + c

.

, .

:

AB = BC= CA =

= + b + c :

= + + a

+ + = 3 a,

= 3 a

101

A

B C

c

c

b

a

A

B C

a a

a

p a b


104/114

.

:

AB =C= b BC= a

= + b + c :

= + b + b

+ b + b = a + 2 b,

= a + 2 b

2.

8 cm. 5 dm. ?

, b. = 8 cm, = 5 dm = 50 cm,

= + 2 b

50 cm = 8 cm + 2 b

2 b = 50 cm 8 cm

2 b = 42 cm

b = 42 cm : 2

b = 21 cm

21 cm.

1.

15 cm. ?

a. = 15 cm

= 3

15 cm = 3

= 15 cm : 3

= 5 cm

5 cm.

102

A

B C

b b

a


105/114


106/114104

, ,

. .

. .

.

: , , .

.

.

. .

: , , .

.

.

.

: , , .

1_2

1_2

1_4

1_8

1_4

1_

8


107/114

, ,

. .

, .

.

, .

, , ,

. . 1.

. ,

, , , ,

1. 32, :

32 16, 32 : 2 = 16

32 8, 32 : 4 = 8

32 4, 32 : 8 = 4

,

.

. , .

2. 15 cm, ?

, 15 cm,

8 15 cm = 120 cm

105

.

:

1_2

1_

2

1_2

1_4

1_

4

1_8

1_8

1_8

1_8

1_8

1_8

1_8

1_8

1_8

1_8

1_8

1_8

1_4

1_4

1_4

15 cm


108/114106

.

.

. .

: , , .

.

. .

: , , .

.

, ,1_3

1_6

1_9

1_

3

1_

6


109/114107

.

.

: , , .

.

1.

20 , 1 h : 3 = 60 min : 3 = 20 min

4 , 1 : 6 = 24 h : 6 = 4 h

189 21, 189 : 9 = 21

2.

75 , ?

, 75 ,

75

6 = 450

1_

3

1_6

1_9

1_9

1_9

1_

9

1_9

1_9

1_9

1_9

1_9

1_9

1_6

1_6

1_

6

1_

61_

6

1_6

1_6

1_6

1_3

1_3

1_3

:

111

10

9

12

2

3

4

5

8

76

1_9


110/114108

.

. .

: , , .

. .

: , , .

.

, ,1_5

1_7

1_10

1_5

1_7

.

. .


111/114109

,

1. 350 280,

350 : 5 + 280 : 7.

110,

350 : 5 + 280 : 7 = 70 + 40 = 110.

2. 150 . ,

. , ?

?

, 150 ,

150 : 10 = 15 .

, 150 ,

150 : 5 = 30 .

150 15 30 = 135 30 = 105

1_5

1_5

1_10

1_10

1_10

1_5

1_

5

1_7

: , , .

.

:

1_10

1_5

1_7

1_10

1_10

1_10

1_10

1_10

1_10

1_10

1_10

1_10

1_10

1_5

1_7

1_5

1_7

1_5

1_7

1_7

1_7

1_5

1_7


112/114110


113/11451


114/114

Documents

7. Matematika Plus 3 Uzbenik