magaliTad, Tu sawyisi fasia : a: lari da moxda
magaliTad, Tu sawyisi fasia : a: lari da moxda magaliTad, Tu sawyisi fasia : a: lari da moxda
– 1, 2b -s. miRebuli marTkuTxedis farTobi iqneba 1,1a × 1, 2b = 1, 32ab = 1, 32S . e. i. farTobi gaizrdeba 32%-iT. #18. vTqvaT, Tambaqos nawarmi Rirda a lari. 20 da 40 procentiT orjeradi gaZvirebis Semdeg misi Rirebuleba iqneba a× 1, 2 × 1, 4 = 1, 68a(l). e. i. Tambaqo gaZvirda 68%-iT. #19. sasurvelia, amoixsnas jgufur mecadineobaze. moswavleebs avuxsnaT, rom mTeli wre Seesabameba saqarTvelos mTel mosaxleobas. gamoTvlebis dros sasurvelia kalkulatoris gamoyeneba. # 20. nawilebze es savarjiSo aucileblad gavakeTebinoT, raTa moswavleebi Semdegi paragrafisaTvis SevamzadoT. 3.4 ori sididis fardobis procentuli warmodgena mizani: moswavleebs vaswavloT, ras gviCvenebs ori sididis fardobis procentuli Canaweri. gamovumuSaoT maT procentebis saxiT warmodgenili monacemebis Sedgenisa da gamoyenebis unari. codna da unari: moswavlem unda icodes: 1) ra SemTxvevaSi SeiZleba ori sididis Sefardebis procentis saxiT warmodgena; 2) ras gviCvenebs ori sididis procentuli fardoba. moswavles unda SeeZlos: 1) erTi sididis gamosaxva meore sididis procentiT; 2) ori sididis fardobis procentis gamoyeneba praqtikuli amocanebis amosaxsnelad; 3) procentis saxiT warmodgenili monacemebis Sedgena da gamoyeneba. meToduri komentarebi: moswavleebma ician, rogor ipovon, erTi ricxvi (sidide) meoris ra nawilia. Tu nawilis maCvenebel wilads CavwerT procentis saxiT, anu gavamravlebT 100-ze, miviRebT fardobis procents, romelic gviCvenebs, erTi ricxvi (sidide) meoris ramdeni procentia. amitom am paragrafis amocanebi SegviZlia nawilebze amocanebis analogiurad amovxsnaT. sasurvelia, davubrundeT wina paragrafis me-20 savarjiSos da amovxsnaT procentebSi. sabolood moswavleebma unda aiTvison `formula~: procenti = nawili ×100. paragrafis amocanebTan dakavSirebiT unda aRvniSnoT, rom rZeSi (amocana1) cximis procentuli Semadgenloba gviCvenebs, 100g rZeSi ramdeni grami cximia (4,5 g), xolo burTis tyorcnis sizuste gviCvenebs, imave sizustiT as-asjer rom etyorcnaT, ramden burTs Caagdebdnen ( pirveli kalaTburTeli 75-s, meore 70-s). gansakuTrebuli yuradReba mivaqcioT xsnarebsa da naerTebSi amaTuim nivTierebis koncentarciis cnebas, romelic procentuli fardobiT ganimarteba. 16 200 komentarebi savarjiSoebis Sesaxeb da pasuxebi. #3.b) × 100% = % ; d) 72 9 7 × 100% = 35% .#4. TiToeuli monacemi unda gavyoT moswavleTa mTlian 20 raodenobaze (miviRebT, ra nawilia) da gavamravloT 100-ze. # 5. sasurvelia, mivceT Sebrunebuli amocanebic. magaliTad, ra nawilia 25%, 50%, 1%, 100%. #15. amocana SeiZleba amoixsnas ori gziT: I gza. jer gavigoT namatis raodenoba: 18– 12 = 6 (TeTri). gamovTvaloT 6-isa da 18-is fardobis procenti: 6 100% 50%. 12 × = II gza. gamovTvaloT 18 -isa da 12-is fardobis procenti: 18 ( 100)% 150%. 12 × = iyo 100% da gaxda 150%, anu gazrdila 50%-iT. 47
100 # 11. 100% 25%. 100 + 300 ⋅ = 6 # 12. 200⋅ 0,03 = 6; ⋅ 100% = 1%. 600 # 13. marilwylis wona 120 g iqneba. aqedan 30g marilia, xolo 90 g wyali. pasuxi: 90 g wyali unda davumatoT. # 16. pasuxi: 40%. #17. gamoTvalon da Sedegi Seamowmon kalkulatoriT. #19-20 amocanebSi moswavleebi gaixseneben wriul da svetovan diagramebs. #21. arsebobs ori aseTi wertili. monakveTis SigniT da mis gagrZelebaze unda gadavzomoT B-dan 3,2sm. #22. Tavidan mocemuli ricxvi 100%-ia. 3-jer gazrdiT iqneba 300%, e. i. gaizarda 200%-iT. #23. Tavidan mocemuli ricxvi 100%-ia. aTjer Semcirebis Semdeg darCeba 10%, e.i. Semcirda 90%-iT. #24. aseT amocanebSi unda gavutoloT im nivTierbis masebi (am SemTxvevaSi marilis), romelic ucvleli rCeba. vTqvaT unda davamatoT x g wyali. wylis damatebamde marilis masa iyo 200⋅ 0,3=60g, xolo Semdeg( x+200)⋅ 0,2. miviReT gantoleba: ( x+200)⋅ 0,2 = 60. pasuxi: 100g. #25. amocanis Sesabamisi gantolebaa 500⋅ 0,8+300⋅ 0,7=800⋅ x. pasuxi: 76,25%. 500⋅ 0,8 + 300⋅0,7 305 1 gamosaxulebiT ki ase amoxsnian: = = 76 . 800 4 4 #26. vTqvaT iyo x g, maSin 0,3x+ 50 = ( x+ 50) ⋅ 0,8 , saidanac x = 20. pasuxi: 20g. #28. 1-ze patara wiladebi, romelTa mniSvneli 12-ia, aris: 1 2 3 4 5 6 7 8 9 10 11 , , , , , , , , , , . 12 12 12 12 12 12 12 12 12 12 12 maTgan 4 1 = , xolo 10 = 5 . 4 10 -sa da 12 3 12 6 12 12 -s Soris moqceuli wiladebis mricxvelebis jamia: 5+6+7+8+9=35. Semajamebeli samuSao #5 I varianti 1) gamoTvale: a)15-is 20%; b)180-is 0,6 nawili. 2) ipove ricxvi, romlis: a) 3 5 nawili tolia 1,8-is; b) 25% tolia 16-is. 3) mariams saSinao davalebis Sesrulebaze 3sT da 20 wT dasWirda, anas ki – am drois 75%. ramdeni wuTiT swrafad Seasrula anam davaleba? 4) marwyvis gamyidvelma gadawyvita, gaekeTebina yoveldRiuri Canaweri myidvelebisa da maT mier nayidi marwyvis raodenobis Sesaxeb. xuTi dRis Semdeg mis mier Segrovili informacia aseTi saxis iyo: I dR.: 7 myidv. gaiyida 7kg marwyvi II dR.: 10 myidv. gaiyida 12kg marwyvi III dR.: 13 myidv. gaiyida 20kg marwyvi IV dR.: 16 myidv. gaiyida 33kg marwyvi V dR.: 21 myidv. gaiyida 40 kg marwyvi am monacemebis mixedviT Seadgine cxrili da upasuxe SekiTxvebs: a) sul ramdeni kg marwyvi gaiyida? b) marwyvze moTxovnileba izrdeboda Tu mcirdeboda? 48
- Page 2 and 3: sarCevi 1. Sesavali ---------------
- Page 4 and 5: mricxveli, mniSvneli. Tvisebrivi: w
- Page 6 and 7: santimetrad, amitom 0,52m=52sm da s
- Page 10 and 11: g) ramdeni procentiT meti marwyvi g
- Page 12: Semajamebeli samuSao #6 I varianti
– 1, 2b -s. miRebuli marTkuTxedis farTobi iqneba 1,1a × 1, 2b = 1, 32ab = 1, 32S<br />
. e. i.<br />
farTobi gaizrdeba 32%-iT.<br />
#18. vTqvaT, Tambaqos nawarmi Rir<strong>da</strong> a <strong>lari</strong>. 20 <strong>da</strong> 40 procentiT orjeradi<br />
gaZvirebis Semdeg misi Rirebuleba iqneba a× 1, 2 × 1, 4 = 1, 68a(l). e. i. Tambaqo<br />
gaZvir<strong>da</strong> 68%-iT.<br />
#19. sasurvelia, amoixsnas jgufur mecadineobaze. moswavleebs avuxsnaT, rom<br />
mTeli wre Seesabameba saqarTvelos mTel mosaxleobas. gamoTvlebis dros<br />
sasurvelia kalkulatoris gamoyeneba.<br />
# 20. nawilebze es savarjiSo aucileblad gavakeTebinoT, raTa moswavleebi<br />
Semdegi paragrafisaTvis SevamzadoT.<br />
3.4 ori sididis fardobis procentuli warmodgena<br />
mizani: moswavleebs vaswavloT, ras gviCvenebs ori sididis fardobis<br />
procentuli Canaweri. gamovumuSaoT maT procentebis saxiT warmodgenili<br />
monacemebis Sedgenisa <strong>da</strong> gamoyenebis unari.<br />
codna <strong>da</strong> unari: moswavlem un<strong>da</strong> icodes:<br />
1) ra SemTxvevaSi SeiZleba ori sididis Sefardebis procentis saxiT<br />
warmodgena;<br />
2) ras gviCvenebs ori sididis procentuli fardoba.<br />
moswavles un<strong>da</strong> SeeZlos:<br />
1) erTi sididis gamosaxva meore sididis procentiT;<br />
2) ori sididis fardobis procentis gamoyeneba praqtikuli amocanebis<br />
amosaxsnelad;<br />
3) procentis saxiT warmodgenili monacemebis Sedgena <strong>da</strong> gamoyeneba.<br />
meToduri komentarebi: moswavleebma ician, rogor ipovon, erTi ricxvi (sidide)<br />
meoris ra nawilia. <strong>Tu</strong> nawilis maCvenebel wilads CavwerT procentis saxiT, anu<br />
gavamravlebT 100-ze, miviRebT fardobis procents, romelic gviCvenebs, erTi<br />
ricxvi (sidide) meoris ramdeni procentia. amitom am paragrafis amocanebi<br />
SegviZlia nawilebze amocanebis analogiurad amovxsnaT. sasurvelia,<br />
<strong>da</strong>vubrundeT wina paragrafis me-20 savarjiSos <strong>da</strong> amovxsnaT procentebSi.<br />
sabolood moswavleebma un<strong>da</strong> aiTvison `formula~:<br />
procenti = nawili ×100.<br />
paragrafis amocanebTan <strong>da</strong>kavSirebiT un<strong>da</strong> aRvniSnoT, rom rZeSi (amocana1)<br />
cximis procentuli Semadgenloba gviCvenebs, 100g rZeSi ramdeni grami cximia (4,5<br />
g), xolo burTis tyorcnis sizuste gviCvenebs, imave sizustiT as-asjer rom<br />
etyorcnaT, ramden burTs Caagdebdnen<br />
( pirveli kalaTburTeli 75-s, meore 70-s). gansakuTrebuli yuradReba mivaqcioT<br />
xsnarebsa <strong>da</strong> naerTebSi ama<strong>Tu</strong>im nivTierebis koncentarciis cnebas, romelic<br />
procentuli fardobiT ganimarteba.<br />
16 200<br />
komentarebi savarjiSoebis Sesaxeb <strong>da</strong> pasuxebi. #3.b) × 100% = % ; d)<br />
72 9<br />
7<br />
× 100% = 35% .#4. TiToeuli monacemi un<strong>da</strong> gavyoT moswavleTa mTlian<br />
20<br />
raodenobaze (miviRebT, ra nawilia) <strong>da</strong> gavamravloT 100-ze.<br />
# 5. sasurvelia, mivceT Sebrunebuli amocanebic. <strong>magaliTad</strong>, ra nawilia 25%,<br />
50%, 1%, 100%. #15. amocana SeiZleba amoixsnas ori gziT:<br />
I gza. jer gavigoT namatis raodenoba: 18– 12 = 6 (TeTri). gamovTvaloT 6-isa <strong>da</strong><br />
18-is fardobis procenti: 6 100% 50%.<br />
12 × =<br />
II gza. gamovTvaloT 18 -isa <strong>da</strong> 12-is fardobis procenti: 18 ( 100)% 150%.<br />
12 × = iyo<br />
100% <strong>da</strong> gax<strong>da</strong> 150%, anu gazrdila 50%-iT.<br />
47
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