maTematika - mes.gov.ge 4 III.pdf1 gamravlebis Tvisebebi. gavixsenoT gamravlebis cxrili gakveTilebi...
Transcript of maTematika - mes.gov.ge 4 III.pdf1 gamravlebis Tvisebebi. gavixsenoT gamravlebis cxrili gakveTilebi...
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nawili
moswavlis wigni
maswavleblis wigni moswavlis wigni
dafinansebulia
`moswavleebis
saxelmZRvaneloebiT
uzrunvelyofis programis~
farglebSi
maTematika
��maswavleblis wigni
inteleqti
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rCevebi wigniT sargeblobisTvis .................................................................................... 4
1. gamravlebis Tvisebebi. gavixsenoT gamravlebis cxrili .............................. 5
2. gamravleba da gayofa. gayofis Tvisebebi ......................................................... 14
3. vamravlebT nulebiT daboloebul ricxvebs .................................................... 22
4. vamrgvalebT Tanamamravlebs da vpoulobT namravls miaxloebiT ......... 29
proeqti ............................................................................................................................. 34
5. erTniSna ricxvze gamravleba ................................................................................. 35
6. orniSna ricxvze gamravleba .................................................................................... 42
7. vamravlebT samniSna ricxvze .................................................................................. 47
8. moqmedebaTa Tanamimdevroba .................................................................................... 53
9. gayofa naSTiT ............................................................................................................... 58
10. erTniSna ricxvze gayofa .......................................................................................... 64
jgufuri proeqti ........................................................................................................ 68
11. Sesabamisoba ..................................................................................................................... 71
proeqti ............................................................................................................................. 75
12. gamravlebisa da gayofis ucnobi komponentis povna ................................... 78
13. amocanebis amoxsna (amocanebi zedmeti mocemulobiT) ................................ 81
SeamowmeT Tqveni codna ............................................................................................ 86
damatebiTi amocanebi .................................................................................................. 87
V Tavis Semajamebeli amocanebi............................................................................. 92
pasuxebi ............................................................................................................................. 95
maTematikuri simboloebi da maTi gamoyenebis magaliTebi ..................... 106
ariTmetikuli moqmedebebis Sesrulebis Tanamimdevroba ......................... 106
ariTmetikuli moqmedebebis Tvisebebi .............................................................. 106
zomis erTeulebi ........................................................................................................ 107
sivrculi figurebi ................................................................................................... 107
maTematikuri terminebis leqsikoni ................................................................... 108
sarCevi
naturaluri ricxvebis gamravleba da gayofa5
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r C e v e b i w i g n i T s a r g e b l o b i s T v i s
waikiTxeT es rCevebi, gaecaniT specialuri simboloebis daniSnulebas.
es simbolo klasSi Sesasrulebeli samuSaoebis dawyeba
ze migviTiTebs. am amocanebis nomrebi wreebSia Cas
muli, feradicaa, magaliTad, 4 .
es simbolo Sin muSaobisTvis gankuTvnil amocanebs
warmogvidgens. am amocanebis nomrebi samkuTxedebSia
Casmuli, magaliTad, 5 .
`sxvadasxva~ _ saintereso faqtebsa da istoriebs
warmogvidgens.
am simbolos mosdevs amocanebi, romelTa amosaxsnelad
sakmao gamWriaxobis gamovlenac mogiwevT. am amo canebis
nomrebi kvadratebSia Casmuli, magaliTad, 1 .
am simboloTi jgufuri muSaobis proeqtebia gamo
yofili _ aseTi davalebebi TanaklaselebTan erTo
blivad muSaobis gamocdilebas SegmatebT.
am simboloTi TamaSebia aRniSnuli – maTi saSuale
biT maTematikuri codnis gamoyenebis gamocdilebas
SeiZenT.
vin iqneba pirveli. am simboloTi warmodgenili amo
canebis amoxsnisas ecadeT, gamWriaxobasTan erTad
sxa rti azrovnebac gamoavlinoT.
teqstis ukeT gagebis mizniT, saWirod CavTvaleT
zogierTi sityvis warmomavlobis, misi msgavsi mniSvn
elobebis miTiTeba. aseTi Canawerebi teqstSi moniSnu
lia aq gamosaxuli simboloTi.
am simboloTi gamoyofili yvela amocana unda gadaita
noT rveulSi da DSemdeg SeasruloT.
Cveni
leqsikoni
jgufuri
saSinao
moisazre
sxvadasxva
TamaSi
klasSi
gaufrTxildiT wigns!
masSi Tqvenma Canawerebma (amoxsnebma, miTiTebebma) wigni SeiZleba sxvebisTvis
gamousadegari gaxados!
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• ramdeni wrea TiToeul striqonSi?
• sul ramdeni striqonia wreebiT Sedgenili?
• ipoveT wreebis odenoba gamravlebis gamoyenebiT da
Se a dareT Tqven mier miRebuli Sedegi aq warmo dgenils _
6⋅4=24.
axla amave wreebiT Sedgenil 4 svets davxedoT.
TiToeul svetSi 6 wrea.
• amjerad rogor vipovoT wreebis odenoba ricxvebis gamravlebiT?
am msjelobas mivyavarT gamravlebis I Tvisebamde:
gadanacvlebadobis Tviseba magaliTi
TanamamravlTa gadanacvle
biT namravli ar icvleba.
6 ⋅ 4 = 24
4 ⋅ 6 = 24
viTvliT kvadratebis odenobas, gvaqvs:
4 ⋅ 8 =32
axla kvadratebis es erToblioba swori xa
ziT gamoyofil or nawilad warmovadginoT:
4 ⋅ 3 =12 4 ⋅ 5 = 20
• sul oTxi striqoni gvaqvs, TiToeuli striqonSi kvadratebis
toli raodenobaa: 3 + 5. sul – 4 ⋅ (3 + 5). maSasadame,
4 ⋅ (3 + 5) = (4 ⋅3 ) + (4 ⋅ 5 ).
I Tanamamravli II Tanamamravli namravli
I Tanamamravli II Tanamamravli namravli
naturaluri ricxvebis gamravlebada gayofa
1 gamravlebis Tvisebebi. gavixsenoT gamravlebis cxrili
gakveTilebi 93-95
5ricxvebze moqmedebebis codnis gareSe SeuZlebelia swavlaSi war matebis imedi gqondeT. am TavSi Tqven mniSvnelovnad gaiRrma vebT cod nas am sakiTxebSi, SeiswavliT araerTi saintereso amo canis amox snis gzebs. gisurvebT warmatebas.
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am magaliTiT gamravlebis kidev erT Tvisebas warmovadgenT:
jamze gamravlebis Tviseba(ganrigebadobis Tviseba)
magaliTebi
ricxvis jamze gamravlebisas es ricxvi
unda gavamravloT TiToeul Sesakrebze,
Semdeg ki miRebuli namravlebi SevkriboT
5⋅(3+4)=5⋅3+5⋅45⋅7=15+20
35=35
4⋅(3+4+2)=4⋅3+4⋅4+4⋅24⋅9=12+16+8
36=36
axla gamravlebis kidev erTi Tvisebis _ jufTebadobis Tvisebis _ magaliTebi warmovadginoT: vamravlebT ricxvebs: 3⋅2⋅4. gamravleba SeiZleba sxvadasxva xerxiT SevasruloT: erTi da imave raodenobis
wreebi jer 4 jgufad davyoT, Semdeg – sam jgufad.
maSasadame, (3⋅2)⋅4=3⋅(2⋅4)
ricxvebis gamravlebisas Tanamamravlebi SeiZleba nebismieri
TanamimdevrobiT davajgufoT.
gavixsenoT gamravlebis kidev ori Tviseba:
• SeecadeT sityvierad CamoayaliboT 1isa da 0is es Tvisebebi.
axla gamravlebis cxrili gavixsenoT.
× 0 1 2 3 4 5 6 7 8 9
0 0
1 0 1
2 0 2 4
3 0 3 6 9
4 0 4 8 12 16
5 0 5 10 15 20 25
6 0 6 12 18 24 30 36
7 0 7 14 21 28 35 42 49
8 0 8 16 24 32 40 48 56 64
9 0 9 18 27 36 45 54 63 72 81
8⋅1=8, 1⋅8=8. 9⋅0=0, 0⋅9=0.
magaliTi 1 magaliTi 2
4 jgufidan TiToeulSi
3⋅2 wrea, sul 4⋅(3⋅2), anu
(3⋅2)⋅4 wre
aq sami jgufidan
TiToeulSi 2⋅4 wrea,
sul 3⋅(2⋅4) wre
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klasSi
Sevsebulia mxolod `diagonali~ (ricxvebi wiTladaa gaferadebu
li) da `diagonalis~ qveda ujrebi.
moifiqreT raime wesi (magaliTad, gamravlebis Tviseba an striqo
nebis Sevseba erTi da imave bijiT gadaTvlili ricxvebiT), romlis
gamoyenebiTac SeiZleba Seivsos danarCeni ujrebi.
• ra ricxvebia warmodgenili diagonalze?
• ra Tvisebaze migviTiTebs meore svetSi dawerili nulebi?
• ra Tvisebaze migviTiTebs pirveli da mesame svetebis Sedareba?
SearCieT swori pasuxi (imuSaveT rveulSi):
1 ricxvis nulze gamravlebiT aucileblad miiReba
a) erTi b) ori
g) igive ricxvi d) nuli.
2 ricxvis erTze gamravlebiT aucileblad miiReba
a) nuli b) ori
g) igive ricxvi d) sxva ricxvi.
3 ra ricxvs aRniSnavs , Tu ⋅ 7=7 ⋅ 8?
a) 7 b) 1 g) 8 d) 5.
4 ra ricxvia aRniSnuli n asoTi, Tu n⋅(6+7)=5⋅6+5⋅7?
a) 6 b) 7 g) 1 d) 5.
5 CawereT gamosaxuleba namravlis saxiT: 6+6+6+6+6.
a) 6⋅6 b) 4⋅6 g) 5⋅6 d) 3⋅6.
6 ramdeniTaa 3⋅9 meti 2⋅9ze?
a) 8iT b) 9iT g) 3iT d) 2iT.
7 (2⋅3)⋅8=
a) 36 b) 48 g) 24 d) 16.
8 CawereT jamis saxiT gamosaxuleba: 3⋅4.
a) 4+4+4 b) 3+3+4 g) 4+4 d) 4+3+4+3.
8
nimuSi
9 Tu ninos kargad axsovs, rom 7⋅7=49, maSin 8⋅7is sapovnelad
sakmarisia man 49s
a) gamoaklos 7 b) miumatos 8
g) miumatos 7 d) gamoaklos 8.
10 mocemulia gamosaxulebebi:
I. 2⋅9+5⋅9 II. 3⋅9+4⋅9 III. 4⋅9+3⋅9 IV. 7⋅9+4⋅9 V. 5⋅9+3⋅9.
romeli gamosaxulebis mniSvnelobis tolia 7⋅9?
a) I da IV b) II da V
g) mxolod II da III d) I, II da III.
11 romeli suraTi dagexmarebaT, rom ipovoT 3jer 4?
a) b) g) d)
12 TiToeul suraTze gamosaxuli sagnebis odenoba warmoadgineT
gamravlebisa da Sekrebis Semcveli gamosaxulebebiT:
a) b)
g) d)
ipoveT namravli:
13 3⋅2 14 3⋅7 15 4⋅6 16 4⋅5
17 6⋅6 18 8⋅7 19 9⋅7 20 9⋅9
21 4⋅4 22 6⋅9 23 (2⋅3)⋅8 24 7⋅(3⋅2)
25 2⋅(2⋅2)⋅2.
3⋅4=4+4+4
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gamoiyeneT sqema:
am sqemis mixedviT SeadgenT tolobas: 9 ⋅ 4 = 6 ⋅
miTiTeba
ipoveT namravli ori sxvadasxva xerxiT:
26 3⋅(2+5) 27 4⋅(2+3) 28 5⋅(2+6)
ipoveT ucnobi ricxvi
29 8 ⋅ =8 30 ⋅ 5=0 31 6 ⋅ (4+3)= ⋅ 4+ ⋅ 3
32 2 ⋅ (4 ⋅ 3)=( ⋅ 4) ⋅ 3 33 8 ⋅ =0 34 6 ⋅ =9 ⋅ 6
35 ⋅ 1=13 36 ⋅ (4+2+1)=3 ⋅ 4+3 ⋅ 2+ ⋅ 1.
ipoveT ucnobi ricxvebi:
37 4 ⋅ ( ⋅ 9)=( ⋅ 6) ⋅
38 4 ⋅ (5 ⋅ )=( ⋅ 5) ⋅ 7
39 ⋅ (4+ +1)=5 ⋅ 4+ ⋅ 3+ ⋅ 1.
amoxseniT amocanebi:
40 levanma akaki wereTlis, vaJafSavelasa da galaktion tabiZis oTx
oTxi leqsi iswavla. ramdeni leqsi iswavla levanma?
41 baTumis portSi Semosul satvirTo ge
mebs 4 kviris ganmavlobaSi clidnen. yo
vel kviraSi icleboda 9 gemi. ramdeni
kvi ra dasWirde boda amave gemebis daclas,
Tu yo vel kviraSi daicleboda 6 gemi?
42 ra kanonzomierebiT SeiZleba iyos warmodgenili ricxvebi?
1, 4, 9, 16.
dawereT Semdegi 5 ricxvi imave kanonzomierebis mixedviT.
4 kvira
9 gemi
? kvira
6 gemi
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moisazre
ecadeT warmoadginoT amocana
sqemis saxiT, magaliTad, ase:
miTiTeba
43 kalaTburTelTa matCis saukeTeso moTamaSe
4 periodidan TiToeulSi TamaSidan 6 qulas
agrovebda, jarimebidan _ 3 qulas. sul ramdeni
qula daagrova am moTamaSem? ipoveT qulebis
odenoba ori xerxiT.
amocanis pirobis mixedviT SeadgineT ricxviTi gamosa-
xuleba, romelic Seicavs gamravlebisa da Sekrebis moqme-
debebs. upasuxeT amocanis kiTxvas:
44 qarTvelma kalaTburTelma zaza faCuliam erTerT SexvedraSi 6
samquliani da amdenive orquliani burTi Caagdo. manve 7 erTquliani
jarima gamoiyena. sul ramdeni qula daagrova am SexvedraSi zaza
faCuliam?
45 ori soflidan erTmaneTis
Se saxvedrad ori turisti gae
marTa. pirveli yovel saaTSi 5
kms gadioda. meore _ 3 kms. 3
saaTis Semdeg maT Soris manZili 2 kmia. ra manZilia soflebs So ris?
ucnobi ricxvi x-iTaa aRniSnuli. ipoveT x:
1 6 ⋅ 8 = (6⋅x) – (6 ⋅ 1) 2 (6 ⋅ 3) – (6⋅2) = (6 ⋅ x)
3 6 ⋅ 0 = (6 ⋅ 8) – (6 ⋅ x) 4 (7 ⋅ 4) = (7 ⋅ 2) + 7 ⋅ x
amoxseniT amocanebi (isargebleT gamravlebis cxriliT):
5 nikam Cafiqrebuli ricxvi jer 2ze gaamravla, Semdeg 9ze.
waSala bolo (erTeulebis) cifri da miiRo 7. ipoveT Cafiqrebuli
ricxvi.
4 periodi
TamaSidan
sajarimoebidan
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SearCieT swori pasuxi (imuSaveT rveulSi):
1 7 ⋅ 1=
a) 1 b) 8 g) 9 d) 7.
2 8 ⋅ 0=
a) 0 b) 8 g) 1 d) 9.
3 ra ricxvia aRniSnuli niT, Tu n ⋅ 8=8 ⋅ 9?
a) 8 b) 9 g) 10 d) 17.
4 ra ricxvia aRniSnuliT xiT, Tu 7 ⋅ (5+x)=7 ⋅ 5+7 ⋅ 3?
a) 5 b) 7 g) 3 d) 4.
5 ramdeniT aris 5 ⋅ 9 meti 2 ⋅ 9ze?
a) 27iT b) 18iT g) 9iT d) 36iT.
6 4 ⋅ 2 ⋅ 8=
a) 36 b) 32 g) 64 d) 20.
7 vTqvaT, kalkulatoris gamoyenebiT vpoulobT namravls: 4*2*5.
amave pasuxs miviRebT, Tu vipoviT namravls:
a) 2*6*3 b) 2*8*4 g) 2*5*4 d) 3*2*5.
8 (3 ⋅ 0) ⋅ 9=
a) 9 b) 3 g) 4 d) 0.
saSinao
6 mSoblebma daviTs gauorkeces Tanxa, romelic mas hqonda.
daviTma daxarja 8 lari da darCa 10 lari. ra Tanxa
hqonda daviTs Tavdapirvelad?
7 rusikos yulabaSi 55 lari aqvs. es Tanxa Sedgenilia
20lariani, 10lariani da 5lariani kupiurebiT. maTi
ricxvia 5. ramdeni 5lariania rusikos yulabaSi?
8 oTxi erTnairi burTis SesaZenad paatam molares 100lariani
miawoda. molarem mas 8 cali 5lariani da 8 cali 2lariani
daubruna. ipoveT burTis fasi.
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9 (2 ⋅ 4) ⋅ 1=
a) 4 b) 2 g) 8 d) 1.
10 CawereT jamis saxiT: 4 ⋅ 5.
a) 5+5 b) 5+5+5+5 g) 4+4+4 d) 4+4+4+4.
11 8 ⋅ 9 ar aris toli
a) (7 ⋅ 9+9)is b) (6 ⋅ 9+2 ⋅ 9)is
g) (5 ⋅ 9+3 ⋅ 9)is d) (6 ⋅ 9+3 ⋅ 9)is.
ipoveT namravli:
12 8 ⋅ 1 13 4 ⋅ 4 14 9 ⋅ 3 15 4 ⋅ 8
16 7 ⋅ 7 17 8 ⋅ 0 18 4 ⋅ 5 19 5 ⋅ 5
20 4 ⋅ 6 21 9 ⋅ 8 22 7 ⋅ 0 23 6 ⋅ 6
24 1 ⋅ 9 25 9 ⋅ 0 26 6 ⋅ 2 27 8 ⋅ 8
28 7 ⋅ 9 29 2 ⋅ 7 30 7 ⋅ 6 31 6 ⋅ 9
32 9 ⋅ 4 33 8 ⋅ 5 34 3 ⋅ 8 35 9 ⋅ 7
36 1 ⋅ 4 37 9 ⋅ 5 38 8 ⋅ 6 39 7 ⋅ 5.
ipoveT rac SeiZleba meti wyvili im ricxvebisa, romelTa namravlia:
40 24 41 12 42 25
43 1 44 38 45 81.
amoxseniT amocanebi
46 kalaTburTelTa matCSi TiToeuli gundidan 9 kalaT
burTelma miiRo monawileoba. sul ramdeni kalaTburTe
li monawileobda SexvedraSi?
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47 qarTuli simRerebis konkursSi erTerTi skolis gundi scenaze
6 mwkrivad ganlagda. TiToeul mwkrivSi 8 moswavle iyo. meo
re skolis momReralTa gundi ki 5 mwkrivad iyo ganlagebuli,
TiToeul mwkrivSi _ 9 moswavliT. romeli skolis gundSi iyo
meti monawile?
amocanebis amoxsnisas SeadgineT ricxviTi gamosaxuleba, romelic Seicavs gamravlebisa da Sekrebis moqmedebebs da upasuxeT kiTxvebs:
48 mSoblebi vatos 5 dRis ganmavlobaSi samsam lars aZlevdnen
skolaSi sauzmisTvis. vato mxolod 1 lars xarjavda. kviris bo
los mSoblebma mas damatebiT 8 lari aCuqes. sul ramdeni lari
daugrovda vatos?
49 kote kviraSi samjer orori saaTi var
jiSobs fexburTis wreSi. SabaTobiT ki misi
varjiSi 4 saaTs grZeldeba. sul ram deni
saaTi varjiSobs kote kviris ganmavlobaSi?
50 mariamma kuburebi oTxoTxad daalaga. sul 8 aseTi oTxeuli mi
iRo da kidev 3 kubura darCa. sul ramdeni kubura hqonia mariams?
51 darbazSi 7 magida dgas. TiToeul magidasTan 4 skamia. aqve, ke
delTan kidev sami skamia. sul ramdeni skamia darbazSi?
52 ninikos 3 akvariumi aqvs. TiToeul akvariumSi 5 Tevzia. mariams
3 akvariumi aqvs. TiToeul akvariumSi 4 Tevzia. ramdeni Tevzia
orive gogonas akvariumebSi?
53 qeTis saxli 9 sarTuliania. am saxls ori sadarbazo aqvs. I
sadar bazoSi yovel sarTulze 8 binaa, II sadarbazoSi yovel sar
Tulze 7 binaa. ramdenbiniania qeTis saxli?
14
a) vatom 20 suraTi albomis ramdenime cariel gverdze ase ga
naTavsa _ TiTo gverdze 4 suraTi. maSasadame, 20 suraTi 4 tol
jgufad gaiyo.
• ra moqmedebiT ipoviT am suraTebiT Sevsebuli gverdebis ode
nobas?
vmsjelobT _ Tu yovel gverdze 4 suraTia, maSin am suraTebiT
Sevsebuli gverdebis odenobis 4ze namravli toli unda iyos 20
is. Tu saZiebeli gverdebis odenobas aRvniSnavT niT, maSin n ⋅ 4=20.
aseTi n ricxvi 20is 4ze ganayofia _ n=20:4.
cxadia, 5 ⋅ 4=20. amrigad, 20:4=5, n=5.
b) 15 wigns 3 Taroze Tanabrad vanawilebT. ramdeni
wigni iqneba TiToeul Taroze?
• ra moqmedebiT vpoulobT wignebis odenobas TiToeul
Taroze?
wina amocanis amoxsnis analogiurad vmsjelobT:
n ⋅ 3=15
5 ⋅ 3=15 maSasadame, 15:3=5.
• SeadareT a) da b) magaliTebi: erTobliobas (wignebis, suraTe
bis) jgufebad vyofdiT. ras veZebdiT pirvel SemTxvevaSi? ras ve
ZebdiT meore SemTxvevaSi?
am suraTs ukavSirdeba gamravlebisa da gayofis
moqmedebebi:
3 ⋅ 6=18 18:6=3
6 ⋅ 3=18 18:3=6 (1)
gayofa SeiZleba sxvadasxvanairad CavweroT:
18 : 3 = 6 18 3
6
gasayofi, gamyofi, ganayofi gayofis komponentebia,
Tanamamravlebi da namravli _ gamravlebis komponentebi.
gasayofi gasayofigamyofi
gamyofi
ganayofi ganayofi
2 gamravleba da gayofa. gayofis Tvisebebi
gakveTilebi 96-99
15
klasSi
• dawereT ricxvebis gayofisa da gamravlebis ma
galiTebi, romlebic am suraTs ukavSirdeba.
dawerili tolobebiT gamravlebisa da gayofis
komponentebs Soris kavSirebia warmodgenili.
• am tolobebis mixedviT ipoveT ucnobi komponenti, romelic n aso
Tia aRniSnuli:
1) n ⋅ 6=24 2) n : 6=4
4 ⋅ n=24, 24 : n=6.
g) axla gayofis sxva Tvisebebi warmovadginoT;
magaliTebi: 9 : 1=9, 9 : 9=1, 0 : 5=0.
8 : 0 _ ara aqvs azri.
• SeecadeT am magaliTebiT aRwerili Tvisebebi sityvierad Camoaya
liboT.
SearCieT swori pasuxi (imuSaveT rveulSi):
1 Tu raime ricxvs gavyofT 1ze, miviRebT
a) amave ricxvs b) 1s g) 0s d) 2s.
2 Tu nulisgan gansxvavebul ricxvs gavyofT amave
ricxvze, maSin miviRebT
a) nuls b) 1s g) 2s d) amave ricxvs.
3 Tu nuls gavyofT nulisgan gansxvavebul ricxvze, miviRebT
a) 0s b) 1s g) 2s d) amave ricxvs.
4 raime ricxvis gayofa nulze
a) mogvcems nuls b) ar SeiZleba
g) mogvcems 1s d) SeiZleba, Tu es gasayofi nulia.
5 72 : 8=9; am tolobaSi 72 aris
a) gamyofi b) ganayofi g) Sedegi d) gasayofi.
6 63 : 7=9; am tolobaSi 7 aris
a) gamyofi b) ganayofi g) Sedegi d) gasayofi.
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7 Tu 63 sagans toli odenobis 7 jgufad davyofT, maSin TiToeul
jgufSi sagnebis odenoba iqneba
a) 8 b) 9 g) 7 d) 11.
8 Tu 56 wigns davanawilebT 8 yuTSi ise,
rom yuTebSi toli odenobis wignebi iyos,
maSin TiToeul yuTSi iqneba
a) 8 wigni b) 6 wigni
g) 5 wigni d) 7 wigni.
9 Tu 48 wigns Taroebze ise davawyobT, rom TiTo Taroze 8 wigni
iyos, maSin dagvWirdeba
a) 8 Taro b) 6 Taro g) 7 Taro d) 5 Taro.
SeasruleT gayofa:
10 16 : 4. 11 7 : 7. 12 6 : 3. 13 3 : 1.
14 0 : 3. 15 28 : 4. 16 0 : 5. 17 15 : 3.
18 12 : 4. 19 48 : 6. 20 27 : 9. 21 64 : 8.
22 81 : 9. 23 54 : 6. 24 54 : 9.
dawereT ricxvebis gayofisa da gamravlebis yvela magali-
Ti, romelic SeiZleba mocemul suraTze striqonebisa da
svetebis odenobebs aRwerdes:
25 26 27
28 29
17
gamosaxeT raime sqemiT (suraTiT) ricxvebis gayofa, ipo-
veT ganayofi da miuwereT yvela sxva toloba, romlebiT-
ac gayofis komponentebi erTmaneTs gamravlebiT an gay-
ofiT ukavSirdeba:
30 18 : 9. 31 64 : 8. 32 14 : 7.
33 48 : 8. 34 42 : 6.
ipoveT ucnobi komponenti:
35 5 ⋅ n=45. 36 n : 6=7. 37 28 : n=4. 38 n : 3=8.
amoxseniT amocanebi:
39 ramdeni orTvliani velosipedis dasamzade
blad aris saWiro 12 Tva li?
40 ramdeni samTvliani velosipedis dasamzade
blad aris saWiro 27 Tvali?
41 Tedom 24 larad iyida 4 erTnairi bloknoti.
ra Rirs 1 bloknoti?
42 rusudanma Tavisi moswavleebisTvis 12 larad 3 erTnairi wigni
iyida. ramden lars gadaixdida igi imave fasian 5 wignSi?
43 12 enZelas, 18 gvirilis da 30 yoCivardasgan Sekres 3 erTnairi
Taiguli. ramdeni enZela, ramdeni gvirila da ramdeni yoCivardaa
TiToeul TaigulSi?
18
saSinao
SearCieT swori pasuxi (imuSaveT rveulSi):
1 5 : 5=
a) 5 b) 1 g) 0 d) 2.
2 5 : 1=
a) 5 b) 1 g) 2 d) 0.
3 8 : 8=
a) 0 b) 1 g) 2 d) 8.
4 0 : 8=
a) 0 b) 1 g) 8 d) 4.
5 ramdeni xuTeulisgan Sedgeba 30?
a) 6 b) 5 g) 4 d) 7.
6 ramdeni oTxeuli SeiZleba SevadginoT 20isgan?
a) 4 b) 5 g) 3 d) 20.
ipoveT ganayofi:
7 24 : 6. 8 63 : 9. 9 48 : 6. 10 32 : 8.
11 32 : 4. 12 42 : 7. 13 36 : 6. 14 49 : 7.
15 64 : 8. 16 54 9 17 45 9 18 72 9
19 9 9 20 16 8 21 56 7 22 72 8
23 9 1 24 48 8 25 24 3 26 40 5
27 36 9 28 32 8 29 64 8 30 7 7
31 35 7 32 0 4 33 56 8 34 28 7
35 27 3 36 54 6 37 24 8