Emigendanyo(Proportions)

Gakuweebwa Muwanga !!Emigendanyo oba emigendaganyo (Proportions)

Omugendanyo (proportion) ly’erinnya lye tuwa ekigambululo ekigamba nti emigerageranyo ebiri gyenkanankana.Emigerageranyo ebiri bwe giba gyenkanankana mu ngeri emu oba endala giba  gigendana ( proportional).Kino kino kye kivaamu omulamwa gw’omugendanyo (proportion) era kiyinza okuwandiikibwa mu ngeri bbiri:

•	Nga  emikutule  ebiri , 

oba, 
•	Okukozesa ,    a:b = c:d

Emigerageranyo ebiri bwe giba gyenkanankana , ebitondeko byagyo ebisalagana biba nabyo byenkanankana.Kino kitegeeza, omugendanyo, a:b = c:d  gwenkana
a x d = b x c       

Ebikunizo bino bijja kukuyamba okunokoolayo emigendaganyo nga obadde oweereddwa emigerageranyo ebiri:

3/5 ne  6/7 

Gikola omugendaganyo? 

Osobola okulaga oba nga emigerageranyo ebiri gyenkanankana nga okubisaamu osalaganya ebitondeko byagyo,Singa ebitondeko by;ekisalaganya(cross products) biba byenkanankana, awo giba gikola omugendaganyo. 

Jjukira nti ekitondeko eky’ekisalaganyo(a cross product) okifuna nga okubisa kinnawaggulu eky’omukutule ogunu ne kinnawansi wky’omukutule omulala.

Ebitondeko eky’ekisalaganyo  ekya 3/5 ne  6/7 biri

3 emirundi 7 = 21 ne 

5 emirundi  6 = 30 

21 teyenkana  30. N’olwekyo, 3/5 ne 6/7 tegikola mugendaganyo.
Eky’okulabirako ekirala: Emigerageranyo  10/16 ne  5/8 gikola emigendaganyo? 

10 emirundi  8 = 80  ne

16 emirundi  5 = 

80 yenkana ne  80, n’olwekyo, zikola omugendaganyo

Kirabe era nti  10/16 ne  5/8 mikutule egyenkanankana. 

Okutwalira awamu , singa emikutule ebiri gyenkanankana , giba gikola omugendanyo
Ekigambululo kyonna oba nakyenkanyanjuyi egamba nti emigerageranyo ebiri gyenkanankana kiyitibwa mugendanyo (proportion).  Ekintu ekikulu okujjukira nga obalanguza emigerageranyo egyenkanankana(emigendanyo) kiragibwa wano bwe kiti: 

x      m                  ekitondeko kya x ne n   kye ekisooko
- =   --    
y       n		 ekitondeko kya  m ne y kye kifundikiro 

N’olwekyo omugendanyo guba mwenkanyo gwa migerageranyo ebiri nga “okubisaamu ekisalaganya”(cross multiplication). Mu mugendanyo, ekitondeko(product) ky’ekisooko kyenkanankana n’ekitondeko ky’ekifundikiro mu “kukubisamu okw’ekisalaganya”( cross multiplication). 

Kitegeeza:

x.n = m.y  .   Eky’okulabirako , wano wansi mu

2      6                   			
- =   --   okubisa nga osalaganya bwoti:      2 x 9   =   6 x 3
3     9              
					18= 18   

Ebikunizo by’Emigendanyo egigendana obutereevu (Directly Proportional Problems)
Ekikunizo tekitera kukutegeeza nti ebirimu “bigendana butereevu”(are directly proportional)  wabula kikuwa emiwendo gy’ebintu bibiri  ebikwatagana ne kikusaba olowooze ku muwendo gw’ekintu ekimu singa omuwendo gw’ekirala guba gukyuse.

Ebikunizo by’emigendanyo bitera okufaanana bwe biti:


Singa a  olwo  b  oba  singa x olwo y.Singa singa  x efuulibwa a , olwo omuwendo gwa y gunaaba ki ? 

Ekyokulabirako:

Singa ebitabo bibiri biri ku siringi 1,500, osobola kugula ebitabo bimeka ne siringi 12,000?
Ky’osookerako kwe kukyusa ekikunizo okukijja mu bigambo okukiraga nga:
Singa  x olwo x. Singa  xefuulibwa a  olwo omuwendo gwa  y gunaaba ki ? 



Ekyokulabirako.Lowooza ku kigambululo:

Singa ebitabo bibiri bigula siringi 1,500, bitabo bimeka by’ogula ne siringi 12,000 ? Singa siringi 1,500 olwo ebitabo bibiri. Singa siringi 12,000 olwo ebitabo?
Wandiika akakwate ak’omugendaganyo: