Wazee wa Mathematics: Jibu lipi ni sahihi hapa?

Wazee wa Mathematics: Jibu lipi ni sahihi hapa?

Kweli Tanzania ukifa kwa stress ni uzembe

Aisee[emoji1787][emoji23][emoji1787][emoji23]
 
Chokoletitamusana said:
Sasa mkuu mbona umerudi tena kwenye magazijuto[emoji23][emoji23]
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Nimemuambia asahau kuhusu BODMAS na tuzingatie MAGAZIJUTO kwani kwenye MAGAZIJUTO na BODMAS kuna utofauti kidogo mbali na kwamba moja ni acronym ya kiswahili na hiyo nyingine ni kiingereza.
 
Gily said:
What you guys don't know is that this is ambiguous mathematics questions which can have multiple answer according to your interpretations. This means 1 and 9 can be both right answers, I will explain. .

If you calculate by smartphone calculator 6÷2(2+1)
Then due to basic programming it give result from left to right as
6÷2(3)= 9
3(3)=9
9 is a correct answer to this by applying the above formula. Those who got 9 got it right through explanation.

On other hand, scientific calculator calculate 6÷2(2+1) -
=6÷2(3)
=6÷6
=1
But 1 is correct answer by standard mathematics as this formula should be interpreted as “6 / (2 * (2 + 1))”, so the result is 1.

Hesabu huwa inatoa majibu mazuri kupitia mifano, got this somewhere:
I buy a snack for $2 and a drink $1, and I do this twice a week. How many weeks can I do this with $6?
$6 / 2($2+$1) = 1 (week)
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Tutapataje hili swali ama tuandike majibu yote kwenye pepa?
 
mtunzasiri said:
Tutapataje hili swali ama tuandike majibu yote kwenye pepa?
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Nilimjibu jamaa kiona 2(3) maana yake ni 2 x 3 = 6.
Ukifungua mabano unazidisha siku zote, Ukiona unafungua mabano inayofuata ni kuzidisha kilicho kwenye mabano.
6÷2(3)= 6 ÷ 2 x 3
sasa hapo anatakiwa atumie BOMDAS instead of BODMAS. Nikamjibu kuwa Division and Multiplication are interchangeable. Akauliza nimeandika kitu gani kwa sababu ya ubishi tu. Hili swali kutokana lilivyo unatumia MAZIGAJUTO na sio MAGAZIJUTO.
1661931413688.png

Kwenye paper majibu yote yatakuwa sawa kutokana na watu wanajibu kutokana na uelewa. Nikamwambia hesabu yeyote unatakiwa uje kwenye practical ujue which is the best answer.
Sasa ukiapapply swali:
Nimenunua andazi kwa Sh. 2 na Soda kwa Sh. 1, na nafanya hivyo mara mbili (2) kwa juma, Je naweza nunua soda na andazi kwa juma ngapi nikiwa na Sh 6?
Sh. 6 / 2 (Sh 2 + Sh. 1) = 1 (Juma)
Hao wanaosema 9 ni jibu sahihi zaidi wajue haliwezi kuwa kwenye practical, kama wanabisha watuwekeee kwenye practicality na mfano tuone waache ubishi. Scientific calculator iko vizuri zaidi as it it gives the answer according to the standard of mathematics. Ndo maana nikawajibu hayo majibu ni kutokana na ones own interpretetion which will make all the answers true. Ila the most correct answer is 1. .
 
Gily said:
Nilimjibu jamaa kiona 2(3) maana yake ni 2 x 3 = 6.
Ukifungua mabano unazidisha siku zote, Ukiona unafungua mabano inayofuata ni kuzidisha kilicho kwenye mabano.
6÷2(3)= 6 ÷ 2 x 3
sasa hapo anatakiwa atumie BOMDAS instead of BODMAS. Nikamjibu kuwa Division and Multiplication are interchangeable. Akauliza nimeandika kitu gani kwa sababu ya ubishi tu. Hili swali kutokana lilivyo unatumia MAZIGAJUTO na sio MAGAZIJUTO.
View attachment 2340664
Kwenye paper majibu yote yatakuwa sawa kutokana na watu wanajibu kutokana na uelewa. Nikamwambia hesabu yeyote unatakiwa uje kwenye practical ujue which is the best answer.
Sasa ukiapapply swali:
Nimenunua andazi kwa Sh. 2 na Soda kwa Sh. 1, na nafanya hivyo mara mbili (2) kwa juma, Je naweza nunua soda na andazi kwa juma ngapi nikiwa na Sh 6?
Sh. 6 / 2 (Sh 2 + Sh. 1) = 1 (Juma)
Hao wanaosema 9 ni jibu sahihi zaidi wajue haliwezi kuwa kwenye practical, kama wanabisha watuwekeee kwenye practicality na mfano tuone waache ubishi. Scientific calculator iko vizuri zaidi as it it gives the answer according to the standard of mathematics. Ndo maana nikawajibu hayo majibu ni kutokana na ones own interpretetion which will make all the answers true. Ila the most correct answer is 1. .
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Mkuu, wewe unapotosha watu.

Mfano ulioutoa na jinsi ulivyouandika kimahesabu (mathematical expression) sio sawa, huo.mfano wako ilitakiwa uandikwe hivi:-

6÷[2(sh2+sh1)] au 6/[2(sh2+sh1)] hapo ndipo unapata jibu la 1 juma na sio iandikwe 6÷2(sh2+sh1) halafu jibu liwe 1 juma !!!!, hapo sio sawa na haikubaliani na universally accepted mnemonic BODMAS.

Ni kweli kwamba katika case fulani za mathematics unaweza ku interchange operation za division na multiplication hasa zikiwepo operations hizo hizo mbili pekee na hii hali ipo katika operantions za kujumlisha na kutoa pia na mtu ukapata jibu sawa yaani unaweza kuanza na operation yoyote na ukapata jibu lilelile lakini sio kwa case ZOTE hasa zile zenye mchanyiko wa operations mfano ni hiyo expression 6÷2(2+1), na ni kutokana na hali hiyo ya mkanganyiko ndio wanamahesabu wakabuni huo mnemonic wa BODMAS (PEMDMAS) ili kuwepo na lugha na tafsiri moja ya kimahesabu kimataifa.

Kwa mantiki hiyo expression 6÷2(2+1)=9 ni jibu sahihi kimataifa na 6÷[2(2+1)]=1 nalo ni jibu sahihi kimataifa hivyo swali lako la andazi na soda kimahesabu na kimataifa linatakiwa liandikwe hivi:-

6/[2(2+1)]=1 na sio vinginevyo.

Screenshot_20220831-183146.png
 
Mokaze said:
Mkuu, wewe unapotosha watu.

Mfano ulioutoa na jinsi ulivyouandika kimahesabu (mathematical expression) sio sawa, huo.mfano wako ilitakiwa uandikwe hivi:-

6÷[2(sh2+sh1)] au 6/[2(sh2+sh1)] hapo ndipo unapata jibu la 1 juma na sio iandikwe 6÷2(sh2+sh1) halafu jibu liwe 1 juma !!!!, hapo sio sawa na haikubaliani na universally accepted mnemonic BODMAS.

Ni kweli kwamba katika case fulani za mathematics unaweza ku interchange operation za division na multiplication hasa zikiwepo operations hizo hizo mbili pekee na hii hali ipo katika operantions za kujumlisha na kutoa pia na mtu ukapata jibu sawa yaani unaweza kuanza na operation yoyote na ukapata jibu lilelile lakini sio kwa case ZOTE hasa zile zenye mchanyiko wa operations mfano ni hiyo expression 6÷2(2+1), na ni kutokana na hali hiyo ya mkanganyiko ndio wanamahesabu wakabuni huo mnemonic wa BODMAS (PEMDMAS) ili kuwepo na lugha na tafsiri moja ya kimahesabu kimataifa.

Kwa mantiki hiyo expression 6÷2(2+1)=9 ni jibu sahihi kimataifa na 6÷[2(2+1)]=1 nalo ni jibu sahihi kimataifa hivyo swali lako la andazi na soda kimahesabu na kimataifa linatakiwa liandikwe hivi:-

6/[2(2+1)]=1 na sio vinginevyo.

View attachment 2341085
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Umeona hapo alipokuandikia solve from left to right and from right to left, (kwenye mfano wako). Ile swali linatakiwa liwe solved from left to right. Nilitaka kukukumbusha tu. .

Alafu we Mokaze shida yako unakariri hesabu. Hesabu nyingine zinaweza kuwa solved in more ways unakaririr njia moja, sina maswali mengi kwa sababu kama huwezi weka jibu lako kwenye practicality kama nilivyoweka mimi basi unakuwa mbishi
Sijampoteza mtu yeyote 🙂
 
Mokaze people are arguing all over the world about the same question. Ila nilijaribu kuangalia online Harvad wameandika haya:

It is an interesting angle. But note that the recommendation to ``simplify"
is where the problem of the ambiguity is located:


Yes, one can simplify 6/2(1+2) by introducing x=2(1+2) = 6, then get 6/6=1
But one can also simplify by defining x=6/2, then get x(1+2) = 9.

Actually, this is also historically interesting. You mention Euclid.
Euclid did not use any algebra as we know it. Symbolic algebra came only with
Viete in the 16th century. As far as we know, one only has realized in the 20th century
that there is really an ambiguity. It is clearly stated in Cajori's book on
mathematical notation, which is the authority on the matter.


It has also become a pedagogical issue:
students today get mostly taught the PEMDAS rule which formally puts
multiplication before division and would recommend the result
6/2(1+2) =1. If you give the expression to a computer algebra system they all
give 6/2(1+2) = 9. It was examples like that which produced all these discussions.

The first rule of algebra is still a nice rule. It is good advise. Unfortunately
it does not resolve the ambiguity. But I agree that it helps a writer to avoid
the ambiguity. But you know, the issue came up mostly in educational settings.
If a teacher asks a student what is 6/2(1+2) , the teacher does not want to
simplify that, as it would already solve the problem. If today, a teacher asks
students what is 6/2(1+2), then this is just asking for trouble. The right thing to
do is to clarify and either write either (6/2)(1+2) or 6/(2(1+2)).
It was clear already to Cajori that avoiding the parenthesis does not produce
well defined mathematical expressions.

Source: https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html
 
March 4, 2021: the social media discussions still seem to go on: I got the following email:
I was wondering about this equation.
6/2(1+2)=? My answer is 1. It's because I believe that 2(1+2) is a
whole number. Another example is 9/3(1+2)=1 also Where 9/3(3) which can
also be written as 9/3^2. If so PEMDAS RULE SAYS Exponents is 2nd. So my
question really is Exponents are also form of Multiplication so why is it
now M is same as D on the equation where it is now changed to PE (M or D
left to right) (A or S left to right)? In my math years Multiplication is
third because Exponential and Multiplication is the same. Also when we
simplify 6/9 simplifies as 2(3)/3(3) we can't simplify this as answer of
6 when it should be 2/3. Here is a new one on social media: 24/4(8/4)
and my answer is= 3. Some says it's 12. After what I have explained
above. What is your answer? Thanks in advance.

My Answer:
The case 6/2(1+2) is now a classic. Most people get 1. It is not because
it is a whole number but because 2(1+2) is seen as a unit. Most
computers get 9 because (M and D) are evaluated on the same level.

I have not seen the new 24/4(8/4). You have got 3, what most people get.
Millions of them because it is entrenched in PEMDAS rules (M before D)
and because it is often written in books as such. Most computers get 12.

There is no right or wrong answer here. The question is just posed
in an ambiguous way. This has now been known for 100 years. It is
interesting that the social media still hum about it. But that makes it
interesting and aware.

Source: https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html
 
Mokaze said:
Hapa hatupimani nani anajua zaidi bali ni suala la kuelimishana tu kwani hakuna anayejua kika kitu isipokuwa Mungu tu.

Haya hebu tuanze darasa:-

6÷2(2+1), hii ni sawa na kuandika, 6÷2×(2+1), kwa sheria ya MAGAZIJUTO (forget about BODMAS), lazima tuanze na expression iliyomo ndani ya mabano "MA" yaani (2+1) ambapo unapata 3, hivyo expression nzima inakuwa hivi; 6÷2×3; katika expression hiyo kuna matendo mawili; tendo la kugawanya na kuzidisha, kwa sherai ya MAGAZIJUTO ni LAZIMA uanze na kugawanya ndipo umalizie na kuzidisha kwani MA= Mabano, GA=Gawanya, ZI=Zidisha, JU=Jumlisha, TO=Toa, kwahiyo 6÷2×3 ni sawa na (6÷2)×3,

Yaani, 6÷2×3=(6÷2)×3= 3×3=9.

Kama unayohoja hapo karibu tujadiliane kwani kujadilana ni moja ya njia ya kujifunza, ni kitu ambacho wenzetu Wazungu hufanya na hivyo kujiongezea elimu, tofauti kwa sisi Waafrika ni mashindano ya nani anajua zaidi hatimaye siku zote tupo nyuma ya Wazungu.
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We jamaa wewe. ndio nini sasa?
Mokaze said:
Hebu na sisi tujaribu:

6÷2(2+1)= 6÷2×3, kulingana na sheria ya BODMAS, yaani MAGAZIJUTO lazima uanze na 6÷2 na ndipo jibu lake uzidishe kwa 3; yaani (6÷2)×3=3×3=9.
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Umefungua vipi mabano mkuu?
 
man dunga said:
Kweli vilaza ni wengi Sana. Hesabu rahisi hivyo halafu kuna mtu. anakuambia jibu ni 1. Jibu ni 9 nyinyi vilaza.
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sisi wazee wa pure mathematics tumesema jibu ni 9 watu wa hkl tena div 0 wanakuja na majibu yao ya kiwaki tungeleta hesabu za kuassigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data ingekuwaje ?..Yan wanatutangazia indirectly kwamba yalitaga hesabu 🤣 🤣 🤣 🤣 🤣 🤣 🤣 🤣 🤣
 
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