Untitled

mizani:
viswavloT amocanebis
amoxsna
aTobiTi poziciuri
sistemis
gamoyenebiT
Tavi I. gayofadoba
§1.1. amocanebi naturaluri ricxvis Caweraze
Tvlis Sedegad miRebul ricxvebs naturaluri ricxvebi
ewodeba. naturaluri ricxvebia 1, 2, 3, 4, . . . .
ricxvebis Casawerad specialur simboloebs, cifrebs viyenebT.
yvelaze gavrcelebulia aTobiTi poziciuri sistema,
romelSic gamoiyeneba aTi cifri: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. am
sistemaSi Cawerili ricxvi - 5327 oTxniSna ricxvia (mis CanawerSi
oTxi cifria gamoyenebuli), romelic 5 aTaseulis, 3
aseulis, 2 aTeulis da 7 erTeulis jamis mokle Canawers warmoadgens.
Tu am ricxvs Tanrigobrivi Sesakrebebis jamis saxiT CavwerT, miviRebT:
5327=5·1000+3·100+2·10+7·1=5x10 3 +3x10 2 +2x10 1 +7
amocana 1. CavweroT umciresi aTniSna naturaluri ricxvi, romelSic yvela cifri
iqneba gamoyenebuli.
amoxsna: radgan sul aTi cifri gvaqvs, aTniSna ricxvis Casawerad TiToeuli cifris
mxolod erTxel gamoyeneba SegviZlia. umciresi ricxvis misaRebad maRal TanrigebSi
SesaZlo umciresi cifrebi unda CavweroT. amasTan, Canaweris 0-iT dawyeba
ar SeiZleba, amitom pirveli cifri iqneba 1, momdevno 0, Semdeg 2 da a.S. sabolood
miviRebT Canawers 1023456789.
pasuxi: saZiebeli ricxvia 1 023 456 789.
amocana 2. davadginoT luwi samniSna ricxvebis raodenoba.
amoxsna:pirvel rigSi davadginoT samniSna ricxvebis raodenoba. udidesi samniSna ricvia
999, e.i. 1-dan 999-is CaTvliT iqneba 999 ricxvi. magram maTgan pirveli 99 ricxvi araa samniSna.
amitom samniSna ricxvebis raodenoba 999-99 sxvaobis tolia. am 900 ricxvidan naxevari
luwi ricxvia, naxevari ki kenti. e.i. luwi samniSna ricxvebis raodenobaa 450.
pasuxi: luwi samniSna ricxvebis raodenobaa 450.
amocana 3. ramdenia iseTi orniSna naturaluri ricxvi, romlis CanawerSi mxolod
luwi cifrebia gamoyenebuli
amoxsna: amocana amovxsnaT ori gziT:
I gza. zrdis mixedviT CavweroT luwi cifrebiT Sedgenili orniSna ricxvebi da daviTvaloT:
20, 22, 24, 26, 28,
40, 42, 44, 46, 48,
60, 62, 64, 66, 68,
80, 82, 84, 86, 88.
sul gamovida 20 ricxvi.
II gza. sul gvaqvs 5 luwi cifri: 0, 2, 4, 6, 8. aqedan aTeulebis cifrad gamodgeba oTxi
cifri 2, 4, 6, 8. TiToeul maTgans erTeulebad SegviZlia mivuweroT xuTi cifridan
erT-erTi. magaliTad, Tu aTeu lebis TanrigSi 2-s davwerT, maSin saZiebeli saxis
ricxvebi iqneba: 20, 22, 24, 26, 28, xolo, Tu 6-s davwerT, maSin saZiebeli saxis ricxvebi
iqneba: 60, 62, 64, 66, 68.
2 6
20 22 24 26 28 60 62 64 66 68
ase, rom sul miviRebT 4 × 5 raodenobis ricxvs.
pasuxi: luwi cifrebiT sul 20 orniSna ricxvi iwereba.
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upasuxe kiTxvebs:
1. rogor ricxvs ewodeba naturaluri ricxvi
2. ramdeni cifri gamoiyeneba aTobiT poziciur sistemaSi ricxvebis Casawerad
3. ramdenniSna ricxvia 1 023 456 789 rogor ikiTxeba es ricxvi
4. ra raodenobis luwi samniSna ricxvi arsebobs kenti samniSna
5. ramdeni orniSna ricxvis Caweraa SesaZlebeli luwi cifrebiT
6. amocana 3-is amoxsnis romeli gza ufro moxerxebulia ratom
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savarjiSoebi
waikiTxe ricxvebi: a) 123 456 b) 90 090 090 g) 101 102 103 104.
Cawere Tanrigobrivi Sesakrebebis jamis saxiT ricxvebi:
a)13 592 b) 3 507 890 g) 100 100 100
Cawere SesaZlo umciresi samniSna ricxvi cifrebiT 0, 3, 4.
Cawere SesaZlo udidesi oTxniSna ricxvi cifrebiT: 5, 7, 9, 0.
gamoiyene cifrebi 0, 2, 5, 7 TiTojer da Cawere SesaZlo udidesi luwi oTxniSna
ricxvi.
Cawere udidesi aTniSna naturaluri ricxvi, romelSic yvela cifri
TiTojer iqneba gamoyenebuli.
ras udris umciresi eqvsniSna da udidesi samniSna naturaluri ricxvebis sxvaoba
ras udris udidesi oTxniSna da umciresi samniSna naturaluri ricxvebis namravli
nikam ricxvSi 2597 cifri 5 Secvala 8-iT. ramdeniT meti ricxvi miiRo nikam
Secvlis Sedegad
Tedom ricxvSi 3481 cifrebi 4 da 1 gadaanacvla. gaizarda Tu Semcirda Tavdapirveli
ricxvi ramdeniT
Team samniSna ricxvs marcxnidan miuwera cifri 7. Tavdapirvelze ramdeniT
meti ricxvi miiRo Team
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laSam oTxniSna ricxvs marcxnidan miuwera cifri 5. Tavdapirvelze ramdeniT
meti ricxvi miiRo laSam
daadgine, ramdeni orniSna naturaluri ricxvi arsebobs da maT Soris ramdenia
luwi da ramdeni kenti.
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ramdenia iseTi orniSna ricxvi, romlis CanawerSi mxolod kenti cifrebia gamoyenebuli
ras udris udidesi da umciresi samniSna ricxvebis namravli
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lukam xuTive kenti cifris, xolo maTem xuTive luwi cifris gamoyenebiT Sesa-
Zlo udidesi xuTniSna ricxvebi Caweres. lukas Cawerili ricxvia meti, Tu maTes
Cawerili ricxvi ramdeniTaa meti
ramdenia iseTi samniSna ricxvi, romlis CanawerSi mxolod kenti cifrebia gamoyenebuli
ramdenia iseTi samniSna ricxvi, romlis CanawerSi mxolod gansxvavebuli kenti
cifrebia gamoyenebuli
salomem 48567-2573 sxvaobis gamoTvlisas maklebSi 5-s da 3-s adgilebi Seucvala.
am cvlilebis Sedegad gaizarda Tu Semcirda sxvaoba da ramdeniT
naturaluri ricxvis Canawers marjvnidan miuweres cifri 7. miRebuli ricxvi
9-iT metia Tavdapirvel ricxvze. ipove Tavdapirveli ricxvi.
Cawere yvela orniSna ricxvi, romlis cifrTa namravli 24-is tolia.
gamoTvale gamosaxulebis mniSvneloba:
a) 1432 : 24 + 32575 : 25
b) 233 :184 - 10240 : 128
g) 16500 : (1100 : 11 - 5:17)
d) (3357 : 36 - 317 : 18) : 11 : 99
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Cawere wiladis saxiT: naxevari, meoTxedi, ori mesamedi, TerTmeti meSvidedi.
vaSli daWrilia 4 tol naWrad. vaSlis ra nawilia 1 naWeri ori naWeri sami naWeri
TaTiam torti 8 tol naWrad daWra da maTgan sam-sami naWeri beqas da Tinikos
gaunawila. tortis ra nawili darCa TaTias
aba, gamoicani!
1. romeli ori ricxvis namravlia erT maTganze 10 - jer, meoreze ki 100_jer
meti
2. romeli ori ricxvis jamia erT maTganze 7-iT, meoreze ki 17-iT meti
3. ra cifriT dabolovdeba yvela erTniSna naturaluri ricxvis namravlis
Canaweri
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mizani:
amovxsnaT amocanebi
naturaluri
ricxvis
gamyofebsa da
jeradebze.
§1.2. martivi da Sedgenili ricxvebi
amocana 1. ramdennairad SeiZleba 14 kurdRlis galiebSi
Tanabrad ganawileba
amoxsna: 14 kurdRlis galiebSi Tanabrad ganawileba sxvadasxvanairad
SeiZleba. SesaZlebeli variantebis raodenoba im
ricxvebis raodenobis tolia, romelzec 14 unaSTod iyofa.
ricxvi 14 unaSTod iyofa Semdeg ricxvebze: 1, 2, 7, da 14. maSasadame,
14 kurdRlis galiebSi Tanabrad ganawileba oTxnairadaa
SesaZlebeli:
I.erT galiaSi movaTavsoT yvela kurdReli;
II.kurdRlebi 2 galiaSi movaTavsoT, TiToSi 7 kurdReli;
III.kurdRlebi 7 galiaSi movaTavsoT, TiToSi 2 kurdReli;
IV.kurdRlebi 14 galiaSi movaTavsoT, TiToSi TiTo kurdReli
1, 2, 7 da 14 warmoadgenen 14-is gamyofebs. maSasadame, 14-s oTxi gamyofi aqvs.
vTqvaT mocemulia ori naturaluri ricxvi M m da M nN. Tu M M m unaSTod iyofa M n N-ze,
maSin N M n-s M M m-is gamyofi, xolo M M m-s N M n-is jeradi ewodeba.
magaliTad, 7 gamyofia 14-is, xolo 14 jeradi 7-is. yovel naturalur ricxvs uamravi
jeradi aqvs. magaliTad, 7-is jeradebia TviTon 7, 14, 21, 28 da a.S.
ganxilul amocanaSi 14-is nacvlad 13 kurdReli rom yofiliyo gasanawilebeli,
galiebSi maTi Tanabrad ganawileba mxolod ornairad iqneboda SesaZlebeli. ker-
Zod, an cametives erT galiaSi, an TiTo kurdRels TiTo galiaSi movaTavsebdiT.
am SemTxvevaSi galiebSi kurdRlebis Tanabari ganawilebis mxolod ori SesaZlebloba
imitomaa, rom 13-s mxolod ori gamyofi gaaCnia, 1 da 13.
naturalur ricxvs, romelsac mxolod ori gamyofi aqvs, martivi ricxvi ewodeba.
magaliTad, 13 martivi ricxvia. umciresi martivi ricxvia 2. martivi ricxvebia 2, 3,
5, 7, 11, 13, 17, 19, 23 da a. S.
orze meti gamyofis mqone naturalur ricxvs Sedgenili ricxvi ewodeba.
Sedgenili ricxvebia: 4, 6, 8, 9, 10, 12, 14, 15 da a. S.
1 araa martivi,
radgan mas
mxolod erTi
gamyofi aqvs
magaliTi 1. martivia, Tu Sedgenili ricxvi 12075
amocana: gavixsenoT, rom 5-ze daboloebuli ricxvi unaSTod iyofa
5-ze. amitom 12075-s sul mcire, sami gamyofi mainc aqvs 1, 5 da 12075.
pasuxi: 12075 Sedgenili ricxvia.
magaliTi 2. ramdeni gamyofi aqvs: a) 9-s b) 23-s g) 30-s
amoxsna: a) 9-is gamyofebia: 1, 3 da 9. e.i. 9-s sami gamyofi aqvs.
b) 23-is gamyofebia: 1 da 23. e.i. 23-s ori gamyofi aqvs.
g) 30-is gamyofebia: 1, 2, 3, 5, 6, 10, 15, 30. e.i. 30-s rva gamyofi aqvs.
magaliTi 3. ramdeni martivi gamyofi aqvs 18-s
amoxsna: 18-is gamyofebia: 1, 2, 3, 6, 9, 18. maTgan martivi ricxvebia 2 da 3.
pasuxi:. 18-s ori martivi gamyofi aqvs.
upasuxe kiTxvebs
1. ras ewodeba ricxvis gamyofi jeradi
2. ra ricxvi iqneba mocemuli ricxvis udidesi gamyofi umciresi gamyofi
3. rogor ricxvebs hqvia martivi Sedgenili
4. arsebobs Tu ara luwi martivi ricxvi kerZod romeli
5. SeiZleba Tu ara iTqvas, rom yvela kenti ricxvi martivia
6. ramdeni gamyofi aqvs 1-s
7. ramdeni gamyofi aqvs martivi ricxvis kvadrats

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dawere a) 12-is b) 20-is g) 19-is d) 63-is yvela gamyofi.
ramdeni gamyofi aqvs 4-s 36-s 23-s 46-s
daasaxele 45-is udidesi gamyofi.
savarjiSoebi
ramdennairad SeiZleba 16 wignis Taroebze Tanabrad ganawileba
ramden bavSvs SeiZleba Tanabrad gavunawiloT 25 vaSli ise, rom vaSlebi ar
gavWraT
CamoTvale orniSna ricxvebi, romelic jeradia a) 10-is b) 15-is g) 17-is d) 33-is.
orniSna ricxvebidan ramdeni ricxvia a) 5-is b) 7-is g) 13-is jeradi
Semdegi gamonaTqvamebidan romelia WeSmariti:
a) 27 gamyofia 9-is;
g) 51 jeradia 17-is;
b) 6-s aqvs ori gamyofi;
d) 10 jeradia 100-is.
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martivia Tu Sedgenili ricxvi 1 2 613 27
Semdegi ricxvebidan amowere martivi ricxvebi:1, 11, 21, 31, 41, 51, 61, 71, 81, 91.
Semdegi ricxvebidan amowere Sedgenili ricxvebi:3, 13, 23, 33, 43, 53, 63, 73, 83, 93.
ra ricxvia 17-is jeradi martivi ricxvi
martivia Tu Sedgenili a) 135 b) 102576 g) 98530
ramdeni martivi gamyofi aqvs a) 7-s b) 25-s 12-s 70-s
Cawere 0-iT daboloebuli 3-is jeradi orniSna ricxvebi.
Cawere 19-is jeradi luwi orniSna ricvebi.
daasaxele ricxvi, romelsac mxolod sami gamyofi gaaCnia.
daasaxele 5-is jeradi a) martivi ricxvi;
b) umciresi Sedgenili ricxvi;
g)udidesi samniSna ricxvi;
d) umciresi SvidniSna ricxvi.
daasaxele ricxvi, romlis ori momdevno ricxvi martivia. ramdeni aseTi ricx
vis dasaxelebaa SesaZlebeli
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konkretul magaliTebze Seamowme Semdegi gamonaTqvamebis marTebuloba:
a) Tu Sesakrebebi erTi da imave naturaluri ricxvis jeradia,
maSin jamic am ricxvis jeradi iqneba.
b) Tu ori Sesakrebidan erT-erTi raime naturaluri ricxvis
jeradia, xolo meore ara, maSin jami ar iqneba am ricxvis jeradi.
g) Tu erT-erTi Tanamamravli raime naturaluri ricxvis jeradia,
maSin namravlic am ricxvis jeradi iqneba.
Semdegi gamonaTqvamebidan romelia WeSmariti:
a) yoveli martivi ricxvi kentia;
b) yoveli kenti ricxvi martivia;
g) yoveli naturaluri ricvi an martivia an Sedgenili;
d) 2-ze meti yoveli luwi ricxvi Sedgenilia.
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daasaxele ori martivi ricxvi, romelTa sxvaoba a) 1-is tolia; b) 2- is tolia;
g) 4-is tolia.
Seamowme WeSmaritia Tu ara Semdegi gamonaTqvami: Tu samniSna ricxvs misi
Canaweris cifrTa jams gamovaklebT, miviRebT 9-is jerad ricxvs.
ekam xuTive kenti cifris, xolo anam xuTive luwi cifris gamoyenebiT SesaZlo
umciresi xuTniSna ricxvebi Caweres. ekas Cawerili ricxvia meti, Tu makas Cawerili
ricxvi ramdeniTaa meti
ramdenia iseTi samniSna ricxvi, romlis CanawerSi mxolod gansxvavebuli luwi
cifrebia gamoyenebuli
gamosaxe wiladiT figuris gaferadebuli nawili:
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moifiqre wiladi, Aromlis
a) mricxveli 3-iT metia mniSvnelze;
b) mniSvneli 4-jer metia mricxvelze
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mocemul orive naxatze saswori gawonasworebulia.naxatis mixedviT Seadare:
a) kubis masa cilindris masas;
b) cilindris masa birTvis masas;
g) kubis masa cilindris masas;
gaiTvaliswine Sen mier Catarebuli gamoTvlebis Sedegebi da imis mixedviT
gansazRvre, rogor gavawonasworoT saswori qvemoT mocemul TiToeul Sem-
TxvevaSi.
#1
#2
#3
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mizani
1. viswavloT 3-ze
da 9-ze gayofadobis
niSnebi;
2. gamovi yenoT
gayofadobis
niSnebi wiladis
Sesakvecad.
1.3 gayofadobis niSnebi
gayofadobis niSnebi gvexmareba gayofis moqmedebis Sesrulebis
gareSe davadginoT, iyofa Tu ara esa Tu is naturaluri
ricxvi mocemul naturalur ricxvze una-STod.
rogorc mexuTe klasidan iciT imis dasadgenad, iyofa Tu
ara unaSTod ricxvi 2-ze, 5-ze da 10-ze, sakmarisia vicodeT
am ricxvis Canaweris bolo cifri. kerZod:
2-ze iyofa is da mxolod is ricxvebi, romelTa Canaweris
bolo cifri luwia.
5 –ze iyofa is da mxolod is ricxvebi, romelTa Canaweris
bolo cifria 0 an 5.
10 –ze iyofa is da mxolod is ricxvebi, romelTa Canaweris
bolo cifria 0.
magaliTad, ricxvebidan 2570, 35007 pirveli iyofa 2-zec, 5-zec da 10-zec, radgan
misi Canaweri akamayofilebs gayofadobis zemoTmocemul samive pirobas, xolo
meore ar iyofa arc 2-ze, arc 5-ze da arc 10-ze, radgan misi Canaweris bolo cifri
arc luwia, arc 0 da arc 5.
sakmarisia Tu ara bolo cifris codna imis dasadgenad, iyofa Tu ara mocemuli
ricxvi 9-ze. am kiTxvaze pasuxi uaryofiTia. magaliTad ric-xvebs 18-s da 28-s erTi
da igive bolo cifri aqvT, magram 18 iyofa 9-ze, 28 ki ara.
9-ze gayofadobis niSnis dasadgenad ganvixiloT magaliTi:
magaliTi 1. gavarkvioT iyofa Tu ara 9-ze ricxvi a) 756; b) 321.
a) warmovadginoT 756 ori Sesakrebis jamad:
756=7:100+5:10+6=(7:99+7)+(5:9+5)+6=(7:99+5:9)+(7+5+6)
miRebuli jamis pirveli Sesakrebi 9-is jeradi ricxvia. 9-is jeradia meore Sesakrebic,
radgan 7+5+6 = 18. amitom maTi jamic iqneba 9-is jeradi, anu 756 iyofa
9-ze.
b) Tu 321-s warmovadgenT jamis saxiT miviRebT:
321=3:100+2:10+1=(3:99+3)+(2:9+2)+6=(3:99+2:9)+(3+2+1)
am SemTxvevaSic, miRebuli jamis pirveli Sesakrebi 9-is jeradia, xolo meore
Sesakrebi 3+2+1=6 - ara. amitom maTi jami ar gaiyofa 9-ze.
ganxilul orive magaliTSi mocemuli ricxvebi davSaleT ori Sesakrebis jamad,
romelTagan pirveli Sesakrebi iyofoda 9-ze, xolo meore Sesakrebi am ricxvebis
cifrTa jams warmoadgenda. amitom, am ricxvebis 9-ze gayofadoba mxolod maT cifrTa
jamze aRmoCnda damokidebuli.
sazogadod, nebismieri naturaluri ricxvi SegviZlia 9-is jeradi ricxvisa da
am ricxvis cifrTa jamis saxiT warmovadginoT. magaliTad, oTxniSna naturaluri
ricxvi, romlis aTaseulebis cifria a, aseulebis cifri b, aTeulebis cifri b da
erTeulebis cifri d, Semdegi saxiT warmodgeba:
1000a +100b +10c +d =(999a + 99b + 9c)+(a +b +c+c )
aqedan vaskvniT:
9-ze iyofa is da mxolod is naturaluri ricxvebi, romelTa Canaweris cifrTa
jami iyofa 9-ze.
imis gamo, rom zemoaRniSn ul warmodgenaSi 9-is jeradi Sesakrebi 3-is jeradicaa,
ricxvis 3-ze gayofadobac am ricxvis cifrTa jamze iqneba damokidebuli.
3-ze iyofa is da mxolod is naturaluri ricxvebi, romelTa Canaweris cifrTa
jami iyofa 3-ze.

magaliTi 2. davadginoT Semdegi ricxvebidan romlebia 3-is jeradi: 3512, 8.10 9 +10,
18.10 7 +4, 9.13+12
amoxsna: 35012-is cifrTa jamia 3+5+0+1+2=11. 11 araa 3-is jeradi, amitom 35012 araa
3-is jeradi.
8:10 9 +10 = 8 000 000 010. am ricxvis cifrTa jami 9-is tolia, amitom es ricxvi samis
jeradia.
18.10 7 +4 jamis pirveli Sesakrebi 18:10 7 3-is jeradia, radgan 18 jeradia 3-is,
meore Sesakrebi 4 ki araa 3-is jeradi. amitom jami araa 3-is jeradi.
9.13+12 jamis TiToeuli Sesakrebi 3-is jeradia, amitom jamic 3-is jeradi iqneba.
pasuxi: 8:10 9 +10 da 9:13+12 3-is jeradi ricxvebia, xolo 35012 da 18:10 7 +4 araa
3-jeradi.
gayofadobis niSnebi SegviZlia gamoviyenoT wiladebis Sesakvecad. amisaTvis
gavixsenoT wiladis ZiriTadi Tviseba:
wiladis mricxvelisa da mniSvnelis nulis aratol ricxvze gamravleba-gayofiT
wiladis mniSvneloba ar icvleba.
magaliTi 3. SevkvecoT wiladi: a) 55 b) 51
65; 834
.
a) 55 wiladis mricxveli da mniSvneli bolovdeba 5-iT, amitom orive maTgani
65
unaSTod iyofa 5-ze.
55 65
= 55:5 11
65:5
= 13
;
b) 51 -is rigorc mricxvelis, ise mniSvnelis cifrTa jami 3-is jeradia. amitom
834
orive maTgani unaSTod iyofa 3-ze.
51
834
51:3
= 834:3
17
= 278
upasuxe kiTxvebs
1. rogor Seamowmeb mocemuli naturaluri ricxvi iyofa Tu ara 2-ze 5-ze 10-ze
2. sakmarisia Tu ara Canaweris bolo cifris codna imis dasadgenad, iyofa Tu ara
mocemuli ricxvi 9-ze 3-ze
3. rogor Seamowmeb mocemuli naturaluri ricxvi iyofa Tu ara 9-ze
4. arsebobs Tu ara 9-is jeradi ricxvi, romlis Canaweris cifrTa jami ar iyofa
9-ze
5. rogor Seamowmeb mocemuli naturaluri ricxvi iyofa Tu ara 3-ze
6. arsebobs Tu ara 3-is jeradi ricxvi, romlis Canaweris cifrTa jami ar iyofa
3-ze
7. gaiyofa Tu ara 9-ze jami, Tu a) yvela Sesakrebi iyofa 9-ze b) ori Sesakrebidan
erTi iyofa 9-ze, meore ki ara
8. SeiZleba Tu ara jami iyofodes 3-ze da arcerTi Sesakrebi ar iyofodes 3-ze
9. wiladis ra Tvisebas viyenebT Sekvecis dros
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savarjiSoebi
Semdegi ricxvebidan amowere 5-is jeradi ricxvebi:
23354, 30795, 17001, 16940.
Semdegi ricxvebidan amowere 5-is jeradi luwi ricxvebi:
73158, 3195, 230010, 2949, 13570.
ricxvebidan: 302, 45890, 1030, 5005, 5559, 557, 5023, 950 ramdeni ricxvia
5-is jeradi
SeiZleba Tu ara 75 kanfeti Tanabrad gaunawiloT 5 bavSvs 10 bavSvs
mxolod luwi cifrebis gamoyenebiT dawere 5-is jeradi ricxvi.
daTvale 5-is jeradi orniSna ricxvebis raodenoba.
Semdegi ricxvebidan amowere 9-is jeradi ricxvebi:
23354, 30795, 17001, 16940.
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ricxvebidan: 3024, 236, 102, 1729, 9021, 9531, 19395
ramdenia 9-is jeradi
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Semdegi ricxvebidan amowere 9-is jeradi kenti ricxvebi:
252, 3195, 530010, 2949, 330093.
Semdegi ricxvebidan amowere 3-is jeradi ricxvebi:
111, 350, 10796, 1701, 16942.
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mamam n TeTri sam Svils Tanabrad gaunawila. Semdegi tolobebidan romelia
SesaZlebeli: a) n = 35 b) n = 75 g) n = 130.
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SeiZleba Tu ara, rom klasSi iyos 28 moswavle, Tu moswavleTa mesamedi gogonaa
gaarkvie Semdegi gamonaTqvamebidan romelia mcdari:
a)5-is jeradi yvela luwi ricxvi 10-is jeradia;
b)3-is jeradi yvela luwi ricxvi 6-is jeradia;
g) 3-isa da 9-is jeradi yvela ricxvi 27-is jeradia;
d) 3-isa da 5-is jeradi yvela ricxvi 15-is jeradia.
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15
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Semdegi ricxvebidan amowere 6-is jeradi ricxvebi:
114, 231, 796, 1062, 10042.
ricxvebidan: 3020, 1235, 1025, 5490, 2580, 9574, 23346 ramdenia 15-is
jeradi
fifqis nacvlad ra cifrebis CasmiT miiReba 9-is jeradi ricxvi
a) 513*; b) 34*3; g) 1*370.
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