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Comparing Fractions 2

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    Tafuta Kigawe kidogo cha Shirika (KDS) cha hizi namba zifuatazo
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    15, 6, na 10?
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    kigawe kidogo cha shirika ni
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    kama neno lenyewe linavyosema.
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    Ni kigawe kidogo cha shirika ya namba hizi.
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    Na ninafahamu kwamba hiyo haijakusaidia sana kuelewa.
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    Hebu tufanye baadhi ya mifano.
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    Ili tuweze kufanya hebu tufikirie vigawe tofauti vya
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    15, 6, na 10 na kisha kutafuta kigawe chao kidogo kuliko vyote
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    cha shirika.
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    Hebu tutafute vigawe vya 15.
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    Kwa hiyo tuna 1 mara 15 ni 15.
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    2 mara 15 ni 30.
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    Kisha kama ukiongeza 15 tena, utapata 45.
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    Unaongeza 15 tena, unapata 60.
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    Unaongeza 15 tena, unapata 75
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    Unaongeza 15 tena, unapata 90.
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    Unaongeza 15 tena, unapata 105.
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    Lakini bado hakuna vigawe ambavyo ni vya shirika
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    kwa mfumo huu tunaweza kuendelea zaidi.
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    Lakini nitaishia kwenye hii namba hapa.
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    kwa hiyo hivyo ndivyo vigawe vya 15 mpaka 105.
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    Vinginevyo tunaweza kuendelea tu.
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    Sasa hebu tutafute vigawe vya 6.
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    1 mara 6 ni 6.
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    2 mara 6 ni 12.
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    3 mara 6 ni 18.
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    4 mara 6 ni 24.
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    5 mara 6 ni 30.
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    6 mara 6 ni 36.
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    7 mara 6 ni 42.
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    8 mara 6 ni 48.
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    9 mara 6 ni 54.
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    10 mara 6 ni 60.
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    60 tuishie hapa kwa sababu
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    tayari ni kigawe cha shirika cha 15 na 60,
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    ingawa tuna vigawe viwili hapa.
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    Tuna 30 na 30 yenyewe.
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    Tuna 60 na 60 yenyewe.
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    kwa hiyo kigawe kidogo kuliko vyote na kama
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    tungekuwa tunataka vigawe vya 15 na 6,
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    tungesema 30.
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    Ngoja niandike hapa kama namba ya katikati.
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    kwa hiyo KDS cha 15 na 6,
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    yaani kigawe kidogo kabisa ambacho ni cha shirika,
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    tunaviona hapa.
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    15 mara 2 ni 30.
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    Na 6 mara 5 ni 30.
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    Kwa hiyo hiki ni kigawe kidogo cha shirika.
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    Na ndiyo kigawe kidogo cha shirika kuliko vyote.
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    60 ni pia kigawe cha shirika.
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    Lakini ni kikubwa.
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    Hiki ni kigawe kidogo cha shirika.
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    Nacho ni 30.
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    Lakini bado hatujafikiria kuhusu 10 .
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    Hebu tuiandike 10 hapa.
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    Nadhani umeshaona inapoelekea.
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    Hebu tutafute vigawe vya 10.
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    Ni 10, 20, 30, 40.
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    Tumeshaandika vya kutosha,
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    kwa sababu tumeshafika 30.
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    Na 30 ni kigawe cha shirika cha 15 na 6.
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    Na ndicho kigawe cha shirika kidogo kuliko vyote.
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    Ni kweli kwamba KDS cha 15, 6, na 10
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    ni 30.
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    Hii ni njia ya kwanza kutafuta kigawe cha shirika.
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    Hebu angalia vigawe vya kila namba
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    na kisha angalia zina kigawe gani kidogo kuliko vyote
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    ambacho ni cha shirika.
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    Namna nyingine ya kufanya ni kuangalia
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    vigawo tasa vya hizi namba.
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    Na kigawe kidogo cha shirika ni ile namba ambayo
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    ina sifa ya vigawo tasa
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    vya hizi namba na si vinginevyo.
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    Kwa hiyo ngoja nikuoneshe ninamaanisha nini.
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    Ungeweza kufanya hivi.
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    Au ungeweza kusema 15 ni sawa na 3 mara 5.
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    ndiyo hivyo tu.
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    Ndiyo kigawo tasa chake.
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    15 ni 3 mara 5.
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    Zote 3 na 5 ni tasa
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    Tunaweza kusema 6 ni sawa na 2 mara 3.
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    Hiki ni.
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    Kigawo tasa chake.
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    Zote 2 na 3 ni tasa.
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    Kisha tunaweza kusema kwamba 10 ni sawa na 2 mara 5.
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    Zote 2 na 5 ni tasa.
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    Kwa hiyo tunatafuta vigawo.
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    Kwa hiyo kigawe kidogo cha shirika cha 15, 6 na 10
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    tunatakiwa kuwa na vigawo tasa hivi vyote.
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    Ninachomaanisha, inatakiwa iwe inagawanyika kwa 15,
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    inatakiwa kuwa na angalau 3 moja na 5 moja
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    katika kutafuta vigawo tasa vyake.
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    Kwa hiyo inatakiwa angalau 3 moja na 5 moja.
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    Kwa kuwa na 3 mara 5 katika kutafuta vigawo tasa vyake ,
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    inatuhakikishia hii namba inagawanyika kwa 15.
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    Ili kugawanyika kwa 6, inatakiwa kuwa na angalau 2 moja na 3 moja.
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    Kwa hiyo inatakiwa kuwa na angalau 2 moja.
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    Na tayari tuna 3 hapa.
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    Hicho ndicho tulichokuwa tunataka.
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    Tunahitaji 3 moja.
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    kwa hiyo 2 na 3, ni 2 mara 3,
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    hakikisha zinagawanyika kwa 6.
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    Ngoja niweke bayana.
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    Hii hapa ni 15
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    Na ili kuhakikisha kwamba inagawanyika kwa 10,
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    inabidi tuwe na angalau 2 moja na 5 moja.
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    Hizi mbili hapa hakikisha zinagawanyika kwa 10.
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    Tayari tumeshapata vyote.
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    Hii ni 2 mara 3 mara 5 ina vigawo tasa vyote
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    vya 10, 6, au 15.
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    Kwa hiyo ni kigawe kidogo cha shirika.
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    Na kama ukiizidisha hii, utapata 2 mara 3 ni 6.
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    6 mara 5 ni 30.
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    Kwa hiyo kwa kutumia njia yoyote, zote hizi mbili zinafaa.
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    Na umeona kwa nini zinaleta maana.
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    Hii njia ya pili ni nzuri zaidi
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    kama utakuwa na namba kubwa
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    ambazo utahitaji kuzizidisha kwa muda mrefu.
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    Njia yoyote, kati ya hizi zinafaa
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    kutafuta kigawe kidogo cha shirika.
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Title:
Comparing Fractions 2
Description:

Need help comparing fractions? Try simplifying them first then finding a common denominator. The result are two fractions you can really compare.

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/e/comparing_fractions_2?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/v/ordering-fractions?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Missed the previous lesson?
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/comparing-fractions-pre-alg/v/comparing-fractions?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we will introduce to you here: negative numbers, absolute value, factors, multiples, decimals, and fractions to name a few. So buckle up and move your seat into the upright position. We're about to take off!

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Video Language:
English
Team:
Khan Academy
Duration:
05:24

Swahili subtitles

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