Finding Common Denominators

Finding Common Denominators

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/equivalent-fractions-pre-alg/e/equivalent_fractions?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/comparing-fractions-with-greater-than-and-less-than-symbols?utm_source=YT&utm_medium=Desc&utm_campaign=PreAlgebra

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https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/equivalent-fractions-pre-alg/v/equivalent-fractions-example?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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Tunatakiwa kuziandika tena

sehemu zifuatazo kama zenye asili ndogo ya shirika.

Hivyo asili ndogo ya shirika ya sehemu hizi mbili

itakuwa ni kigawe kidogo cha shirika cha

hizi asili.

Na thamani ya kufanya hivyo itakuwa

kama unaweza kuzifanya hizi kuwa na asili zinazofanana,

basi unaweza kuzijumlisha hizi sehemu mbili.

Na tutaiona hii kwenye video nyingine.

Lakini kwanza, tutafute kigawe kidogo cha shirika.

Nitaiandika kwa sababu wakati mwingine KDS

inaweza maanisha kitu kingine.

Hivyo asili ndogo ya shirika ya sehemu hizi

itakuwa kitu kile kile kama kigawe kidogo cha shirika

cha hizi asili mbili hapa.

Kigawe cha kidogo cha shirika cha 8 na 6.

Kuna njia nyingi za kutafuta kigawe cha shirika--

unaweza kuchukua vigawe vya 8 na 6

na kuangalia kigawe kidogo kabisa ni kipi.

Tuanze na njia hii sasa.

Hivyo vigawe vya 6 ni, 12, 18, 24, 30.

Na tungeendelea kama bado tusingepata kigawo kidogo

katika kundi hili . Hivi ni vigawe vya 8.

Navyo ni 8, 16, 24,

na inaonekana tumeshamaliza.

Na tungeendelea mpaka 32,

na kuendelea.

Ila nimekwishapata kigawe ambacho

ndio kigodo kabisa.

Kuna vigawe vingine vya shirika kama --48 na 72,

na tunaweza endelea kuongeza zaidi na zaidi.

Ila hiki ndicho kigawe kidogo kabisa cha shirika,

kigawe kidogo kabisa.

Ni 24.

Njia nyingine ya kutafuta kigawe kidogo cha shirika

kama ukichukua vigawo tasa vya 6

na ukasema hivi ni 2 na 3.

Hivyo kigawe kidogo kabisa kitakuwa 1, 2, na 1, 3

kwenye vigawo tasa ili

viweze kugawanyika kwa 6.

Na ungejiuliza, vigawe tasa vya 8 ni vipi?

ni 2 mara 4, na vya 4 ni 2 mara 2.

Hivyo ili viweze kugawanyika kwa 8,

angalau uwe na 2 mbili kwenye vigawo tasa.

Ili vigawanyike kwa 6, inabidi uwe na 2 mara 3.

Halafu ili vigawanyike kwa 8, inabidi uwe na

2 mbili.

Unatakliwa uwe na mbili uizidishe kwa yenyewe mara 3

naweza kusema hivyo.

Haya tuna mbili ya kwanza hapa.

Kisha tuna 2 nyingine na 2 nyingine.

Hivyo sehemu hii hapa inagawanyika kwa 8.

Na hii sehemu hapa inaifanya igawanyike kwa 6.

Nikichukua 2 mara 2 mara 2 mara 3, itanipa jibu 24.

Hivyo kigawe kidogo cha shirika cha 8 na 6,

ambacho pia kina asili sawa cha hizi

sehemu mbili kitakuwa 24.

Tunachotaka kufanya ni kuziandika upya sehemu zifuatazo

na 24 kama asili.

Nitaanza na 2 juu ya 8.

Na ninataka kuiandika kama kitu juu ya 24.

Kupata asili iwe 24,

inabidi kuizidisha kwa 3.

8 mara 3 ni 24.

Na kama hatutaki kubadili

thamani ya sehemu, tunazidisha

asili na kiasi kwa namba ile ile.

Sasa tuzidishe kiasi kwa 3 pia.

2 mara 3 ni 6.

Hivyo 2/8 ni sawa na 6/24.

Ili kuielewa vizuri,

unaweza kusema, kama nina 2/8 na nikiizidisha mara 3

juu ya 3, itanipa 6/24.

Na hizi ni sehemu sawa kwa sababu 3 juu ya 3

maana yake ni 1.

Moja nzima..

Hivyo 2/8 ni 6/24, hebu tufanye hivi kwa 5/6.

Hivyo 5 juu ya 6 ni sawa na kitu juu ya 24.

Nitaifanya kwa kutumia rangi nyingine.

Rangi ya bluu.

Kitu fulani juu ya 24.

Kupata asili toka kwenye 6 mpaka 24,

tunazidisha kwa 4.

Hivyo kama hatutaki kubadili thamani ya 5/6,

tunazidisha kiasi na asili

kuwa namba ile ile..

Hebu tuzidishe kiasi mara 4.

5 mara 4 ni 20.

5/6 ni sawa na 20/24.

Tumemaliza.

Tumeandika 2/8 kama 6/24 na tumeandika 5/6 kama 20/24.

Kama tukitaka kuzijumlisha, tunajumlisha

6/24 na 20/24.

Nitaishia hapa kwa sababu hatujaambiwa

kufanya hivyo.