I Tavi

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I <strong>Tavi</strong> (7,24,25) 20 (35,12,37) (5, 12, 13) (65,72,97) 10 1 = 10 10 2 = 100 10 3 = 1 000 10 4 = 10 000 = 10 aTasi 10 5 = 100 000 = 100 aTasi 10 6 = 1 milioni 10 9 = 1000 milioni = = 1 miliardi 10 12 = 1000 miliardi = = 1 trilioni 10 15 = 1000 trilioni = = 1 kvadrilioni 10 18 = 1000 kvadrilioni = = 1 kvintilioni kvadratis farTobia: S = a2 a sm (kv. sm) kubis moculoba: V = 33 = 27 sm3 3 sm (33,54,65) a sm 3 sm (65,48,73) (15, 8, 7) (3, 4, 5) 3 sm (45,28,53) (39,30,89) 3 ricxvis (21, 20, 29) (91,60,109) (65,88,137) naturaluri xarisxi 1. mefes sami Svili hyavda. ramdeni memkvidrisgan Sedgeba mefis meoTxe Taoba, Tu CavTvliT, rom misi STamomavlebis yovel warmomadgenels sami Svili hyavda? erTi da imave Tanamamravlebis namravli SegviZlia CavweroT gamosaxulebis saxiT, romelsac xarisxi ewodeba. magaliTad, 7·7·7·7·7=7 5 . a ricxvis n naturaluri xarisxi – an , sadac n>1, ewodeba n cali ricxvis namravls, romelTagan TiToeuli as tolia. as xarisxis fuZe ewodeba, ns _ xarisxis maCvenebeli. miRebulia, rom a1 = a . moyvanili magaliTis SemTxvevaSi 7 xarisxis fuZea, 5 _ xarisxis maCvenebeli. xarisxi a fuZiTa da n maCvenebliT Semdegnairad iwereba _ a n , xolo ikiTxeba `a xarisxad n~, an `a-s n xarisxi~. xarisxis ganmartebidan, a 2 = a · a; a 3 = a · a · a; a 4 = a · a · a · a. n zogadad, a = a· a· ... · a 1 42 4 3 - . n jer ricxvis xarisxis povnas xarisxSi ayvanas an axarisxebas uwo deben. 34 = S 3· 3· 3· 3 4- jer . 03 = 0·0·0 = 0. 73 = S 7· 7· 7. 81 = 8. 3- jer daasaxeleT xarisxis fuZe, xarisxis maCvenebeli da gamoTvaleT: a) 3 5 ; b) 2 4 ; g) 5 3 . SeasruleT moqmedeba: 3·5 2 ·2 2 – 2·4 3 + 7. SevTanxmdeT, rom me-2 xarisxs `kvadrati~ vuwodoT, me-3 xarisxs _ `kubi~.
cxadia, paragrafis dasawyisSi dasmuli problema ase gadawydeba: mefe I Taoba xarisxis ganmartebis Semdeg SegviZlia mravalniSna ricxvi saTanrigo Sesakrebebad Semdegnairad CavweroT: 27865=2·10000+7·1000+8·100+6·10+5=2·10 4 +7·10 3 +8·10 2 +6·10+5. magaliTi 1. ipoveT gamosaxulebis mniSvneloba: a) 2·10 3 ; b) 2 6 +3 4 . amoxsna: a) 103 = 10·10·10 = 1000; 2·10 3 = 2·1000 = 2000. b) 2 6 = 2·2·2·2·2·2 = 64; 2 6 = 64; 3 4 = 3·3·3·3 = 81 2 6 + 3 4 = 64 + 81 = 145. 1 2 3 II Taoba 1 2 3 4 5 . . . . . . 6 7 8 9 me-4 Taoba Sedgeba 3 4 =81 memkvidrisgan magaliTi 2. ipoveT 144-isa da 80-is udidesi saerTo gamyofi da umciresi saerTo jeradi. amoxsna: 144 12 · 12 2 · 2 · 3 · 2 · 2 · 3 e.i. 144 = 2 4 · 3 2 240 = 2 4 · 3 · 5 240 24 · 10 3 · 2 · 2 · 2 · 2 · 5 u.s.g. (144;240) = 2 4 · 3 = 48 144 = 2·2·3·2·2·3 = 2 4 ·3 2 . 240 = 3·2·2·2·2·5 = 2 4 ·3·5. 144 = 24 · 32 240 = 24 · 3 · 5 u.s.j. (144;240) = 2 4 · 3 2 · 5 = 720 ganxiluli sqemis mixedviT aRwereT mocemuli ricxvebis udidesi saerTo gamyofisa da umciresi saerTo jeradis moZebnis xerxebi. aTiaTaseulebi gavixsenoT: 2 7 8 6 5 aTaseulebi aseulebi aTeulebi ufrCxilo gamosa xulebaSi pirvelad Sesruldeba axarisxeba. wiTeli cifrebiT miTi- Tebulia moqmedebis rigi. 144 72 36 18 9 3 1 2 2 2 2 3 3 21 erTeulebi
Page 3: nana jafariZe � maia wilosani �
Page 6 and 7: III Tavi . . . . . . . . . . . . .
Page 8 and 9: 6 rogor visargebloT wigniT wignze m
Page 10 and 11: I Tavi 8 1 VI klasSi Seswavlili mas
Page 12 and 13: I Tavi 10 savarjiSoebi: gamoiangari
Page 14 and 15: I Tavi msgavsi wevrebi rom Sevkribo
Page 16 and 17: I Tavi 14 Tvlis sistemebi Tema Tvli
Page 18 and 19: I Tavi 16 Tbilisi 180 km 2 gamosaxu
Page 20 and 21: I Tavi 18 SeavseT gamotovebuli adgi
Page 24 and 25: I Tavi 22 imetyvele sworad! a 5 1.
Page 26 and 27: I Tavi 2,51 = = 5 1 2 + + 2 10 10 2
Page 28 and 29: I Tavi 26 Seamowme Seni codna: 1 mT
Page 30 and 31: I Tavi „ar iyofa“ aRiniSneba
Page 32 and 33: I Tavi 30 3 mwkrivSi dgas 137 jaris
Page 34 and 35: I Tavi 32 jgufuri mecadineoba TamaS
Page 36 and 37: I Tavi naSTi yovelTvis nak lebia ga
Page 38 and 39: I Tavi 353 = 3·100 + 10·5 + 3 478
Page 40 and 41: I Tavi 38 22 ramdeni samniSna ricxv
Page 42 and 43: I Tavi 40 1 ∇ 2 3 ∇ 2 2 ∇ 1 s
Page 44 and 45: I Tavi 42 naxiri rema arve fara xal
Page 46 and 47: I Tavi 44 amoxsna: gamoviyenoT 3-ze
Page 48 and 49: I Tavi 46 7 simravleTa toloba . qve
Page 50 and 51: I Tavi 48 B A C 4. K qarTvel xelova
Page 52 and 53: I Tavi 50 8 simravleTa 1, 2, 3, 4,
Page 54 and 55: I Tavi 52 magaliTi 1. vTqvaT A={3;5
Page 56 and 57: I Tavi 54 I Tavis damatebiTi savarj
Page 58 and 59: I Tavi 56 26 udidesi orniSna ricxvi
Page 60 and 61: I Tavi 58 Seamowme Seni codna: 1. m
Page 62: 60 I TavSi Seswavlili masalis mokle

I Tavi

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