Emigendano egya Kifuulannenge(Inverse proprotions)

Gakuweebwa Charles Muwanga ! Emigendano Egigendana Kifuulannenge (Inversely Proportional Problems) 

Ebikunizo eby’emigendanyo egya kifuulannnege bifaanagana n’ebikunizo eby’emigendanyo egigendana obutereevu ( directly proportional problems) naye enjawulo eri mu kuba nti  x bw’erinnya ate yo  y nga ekka  ate y bw’erinnya ate yo x nga ekka – guno gwe mukwanaganyo ogw ’omugendanyo okugendana  ekifuulannenge  (inverse proportion relationship). 

Eky’okulabirako ekisinga okweyoreka mu bulamu obwa bulijjo eky’omugendanyo ogugendana kifuulannenge  kyandibadde  “ abakozi gye bakoma okuba abanji  gye kikoma okutwala ekiseera ekitono okumaliriza omulimu”.

Wano era akakodyo kali mu kukyusa kikunizo kya mugendanyo okulabika nga: 
Singa   x olwo  y. Singa  x efuulibwa  a,  y eba muwendo ki ? 
N’olyoka omukwanaganyo ogw’omugendanyo ogugendaga kifuulannenge (wegendereze embeera ya “kifuulannenge”): 
 
Ekyokulabirako :  Kyetaagisa abasajja 8 n’essaawa 12 okulima ekkubo lya bulungi bwansi .Kimala essaawa meka abasajja  14 okukola omulimu gwe gumu mu kigerageranyo(rate) kye kimu ?
Ekisooka : Lowooza ku bigambo ebiri mu kikunizo kino nga: 

Singa abasajja baba 8 bamala essaawa 12.Bwe baba 14 bamala essaawa meka ? 

Ekiddako: Wandiika omukwanaganyogw’omugendanyo  ogwa kifuulannenge (write out the inverse relationship): 

Ansa : batwaala essaawa eziwera: 
8                          12

14                  8/14 x 12  =  essaawa 6.9

Omulamwa gwa omugendanyo ogwa kifuulannenge (inverse proportionality) guyinza okugerageranyizibwa n’ogw’omugendanyo  omutereevu (direct proportionality). 

Emiwendo ebiri(two quantities)ebiri giba gigendana kifuulannenge singa ogumu  gwekubisibwamu oba okugabizibwamu namba yonna endala egabizibwamu oba ekubisibwamu namba y’emu. 
 
Okukwataganyizibwa kuno era kulagibwa nga:
y ∝ x−1
Ggulaafu y’enkiise bbiri ezigendana ekifuulannenge eyitibwa kayipabola(hyperbola).
Emisinde n’ebiseera bigendana kifuulannnege  kubanga buli emisinde lwe gyeyongera, ebiseera ebyetaagisa okutuuka  nga bikendeera.

Twala enkyuso(enkiise) bbiri ezigambibwa okuba nga zigendana kifuulannenge . Singa enkyuuso(enkiise) endala zonna ziba mu ntakyuka, omuwendo ogw’enkomeredde(magnitude / absolute value) ogw’enkyuuso emu egendana ekifuulannenge  guba gukka wansi buli enkyuso endala lwe yeyongera ,kyokka  ekitondeko kyazo  kiba kijja kukka wansi singa enkeyuso endala edda waggulu  kyokka  ekitondeko kya gyo, eno nga y’entakyuka ey’omugendanyo (constant of proportionality)  kyo kiba ky kimu.

Okutwalira awamu enkiise  bbiri ziba za mugendaganyo gwa kifuulannenge(are inversely proportional ) , oba okwawukana kifuulannenge (varying inversely) oba guba mukugendana kifuulannenge n’enkyuso x, singa wabaawo entakyuka k etali ya ziro(non-zero constant k ), okuba nti 
 
Entakyuka etuukibwako nga okubisaamu enkyuso eya x eya nansangwawo  n’enkyuso eya y.
Eky’okulabirako, ebiseera ebyetaagisa okumalako olugendo biba kigendana kifuulannenge n’emisinde  okutambulirwa ate era ebiseera   ebyetaagisa  okutikka ttipa y’omusenyu  biba bigendana kifuulannenge ne namaba y’abantu abagutikka. 

Ggulaafu y’ebintu bibiri ebyawukana kifuulannenge ku mutendera gw’Ekikwataganyo kya Kateesiya (Cartesian coordinate plane) ekola “kayipabola (hyperbola). Omutondeko gw’emiwendo gya   x ne  y  egya buli punkuti(katonnyeze) ku ekkuvve  guba gwenkana entakyuka ey’omugendanyo (k), ntegeeza omungereza ky’ayita “constant of proportionality” (k). Olw’okuba ku x ne y tekuli yenkana ziro, ggulaafu tegenda kuyita ku ekisiisi zino. 

Ebyokulabirako:

Abazimbi basatu bazimba ekisenge mu ssaawa 12 . Kitwala ssaawa meka  abazimbi 6okukola omulimu gwe gumu?

Mu ky’okulabirako kino , omuwendo gw’abakozi n’ebiseera bigendana kifuulannenge kubanga namba y’abazimbi bw’ekka wansi ebiseera nga byeyongera  ate namba y’abantu bw’erinnya,ebiseera nga bikka. 

Goberera emitendera  gino okumaliriza ekigambululo ky’omugendaganyo gwa kifuulannenge (inverse proportionality word problem):

	Wandiika omugerageranyo nga weekuusiza ku kintu kimu, namba y’abakozi oba ekiseera .
 
	Wandiika wansi omugerageranyo n’ekintu eky’okubiri, namba y’abakozi oba ekiseera.