🔒 Closed 8÷2×(2+2)

[Kaplok Kaplok]

PEMDAS - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
(US, France, Philippines)

8÷2×(2+2) = x
8÷2×4 = x
8÷8 = x
1 = x​

BEDMAS - Brackets, Exponents, Division/Multiplication, Addition/Subtraction
(UK, Canada, India)

8÷2×(2+2) = x
8÷2×4 = x
4×4 = x
16 = x​

Why is there a difference?

It boils down to wether multiplication and division should be done first.

The misconception in using either PEMDAS or BEDMAS is that the priority between the two operations (M & D) is to be followed as to the acronym. But they really have equal priority. So, in the E×ρréššion,

8÷2×4 = x​

it should be solved from left to right. Coincidentally, the BEDMAS order gets the correct answer, 16. (Sorry PEMDAS fans..)

HOWEVER, in reality, mathematical E×ρréššions will not be written this way by an instructor. The symbols × and ÷ will rarely, if ever used at all. The problem should be E×ρréššed like this to avoid confusion,

8/[2(2+2)] = 1

or

(8/2)(2+2) = 16
​

to make it correct either using PEMDAS or BEDMAS "the wrong way".

 

[Pen_J]

8÷2x(2+2) = (8÷2)x(2+2) = 4x4 = 16?
Nawala yung distributive property? >>> 2x(2+2) = (4+4) = 8

Kahit na ambiguous ang presentation ng equation, Ito pa rin ang tama:
8 ÷ 2(2 + 2) = 8 ÷ (4 +4) = 8 ÷ 8 = 1

 

[Kaplok Kaplok]

8÷2x(2+2) = (8÷2)x(2+2) = 4x4 = 16?
Nawala yung distributive property? >>> 2x(2+2) = (4+4) = 8

Kahit na ambiguous ang presentation ng equation, Ito pa rin ang tama:
8 ÷ 2(2 + 2) = 8 ÷ (4 +4) = 8 ÷ 8 = 1

Distributive property has nothing to do with order of operation.
Kung ung nasa loob ng parenthesis ay meron variable (letters in algebraic E×ρréššions), tpos simplified na ang E×ρréššion sa loob, doon mo sya gagamitin.
Pero generally, parenthesis/Brackets always first, if can be simplified further in the bracket.

 

[Pen_J]

Linawin natin yung E×ρréššion:
8÷2x(2+2) = 8/2(2+2) ≠ (8/2)(2+2)

 

[plhbg1]

PEMDAS iyan

 

[Kaplok Kaplok]

Linawin natin yung E×ρréššion:
8÷2x(2+2) = 8/2(2+2) ≠ (8/2)(2+2)

Mas malinaw sana kung alin ung ipapailalim sa slash na portion. Mahirap lng tlga isulat dito.

 

[Pen_J]

Kaya nga nasa presentation iyan, TS. Kung ano yung nakikita mo, iyon ang ipo-process mo. Tandaan din natin na ang PEMDAS at BODMAS (= BEDMAS) ay mga guides lang, hindi sila excuse para i-violate ang numbers law.

 

[Kaplok Kaplok]

Kaya nga nasa presentation iyan, TS. Kung ano yung nakikita mo, iyon ang ipo-process mo. Tandaan din natin na ang PEMDAS at BODMAS (= BEDMAS) ay mga guides lang, hindi sila excuse para i-violate ang numbers law.

They do not violate the distributive law, the E×ρréššion itself should say if the distributive law should be used or not. Like I explained kung bakit may difference sa sagot dito is because of the misconception about using the OOP regarding multiplication and division, saka ung deliberate ambiguity nung first equation.

The thing is, math is actually the most universal language. Guides like pemdas or bedmas should not have conflicts. There should be no room for subjectivity.

What is the use of parenthesis if we don't use them or we ignore them altogether.

This is the same as the use of comma(,) in any language.

 

[Pen_J]

Actually wala naman talagang conflict between PEMDAS at BODMAS, nagkaroon lang ng conflict sa paraan ng paggamit nila, ayon sa interpretation ng gumagamit.
Hindi naman ma-eliminate yung parenthesis kung hindi gagamitin yung distributive property, multiplication over addition iyan, distribute muna yung katabing number ng parenthesis bago multiplication at addition sa loob ng parenthesis, pag nakuha na yung total by addition dun pa lang pwedeng alisin yung parenthesis. irrespective iyan kung may variable ba sa loob ng parenthesis o wala, presented siya as polynomial, so i-treat mo siya as polynomial.

 

[Kaplok Kaplok]

Hindi naman ma-eliminate yung parenthesis kung hindi gagamitin yung distributive property, multiplication over addition iyan,

So you have the impression na dapat mauna ung Multiplication sa labas ng parenthesis than anything inside the parenthesis? Kasi ung (2+2) is simplifiable by itself. Pakilinaw kung anong logic nagpipigil sayo mag simplify nyan first?

Although distributive property is a law saying a(b+c) = ab + ac, that is all it states. It has nothing to do with the order of operation. I really dont see why you would perform that rather than simplifying (2+2) to eliminate the parenthesis.

 

[Pen_J]

By your logic, hindi talaga mag-a-agree yung PEMDAS AT BEDMAS, dalawa yung tamang sagot?
Ano ang tingin mo dito? 8/(2+2)
At kung maglagay ka ng 2 sa tabi ng parenthesis? 8/2(2+2), magiging (8/2)(2+2)?
Hindi mo basta-basta na lang tatanggalin yung parenthesis kung may katabing number, kailangan mo munang i-multiply, kahit na sinimplify mo pa muna siya.

Suppose, i-apply natin yung commutative property:
8/2(2+2) = 8/(2+2)2, Ganito ba ang magiging resulta: [8/(2+2)]2? Pangatlong correct answer na iyan =4?

 

[sinner231_100]

PEMDAS or BEDMAS 16 padin sagot diyan...

 

[Kaplok Kaplok]

By your logic, hindi talaga mag-a-agree yung PEMDAS AT BEDMAS, dalawa yung tamang sagot?

Multiplication and division has the same priority. So, in the E×ρréššion,

8÷2×4 = x​

it should be solved from left to right. Yan ung next logic na dapat sundin. Technically pemdas and bedmas is actually, the same.

Hindi mo basta-basta na lang tatanggalin yung parenthesis kung may katabing number, kailangan mo munang i-multiply, kahit na sinimplify mo pa muna siya.

Nakikita ko yung sinasabi mo. But you are omitting the × symbol.
You assume kasi na parehas ang implied problem pag sinulat ng ganito

8÷2×(4) or 8÷2(4)​

Magkaiba yan. Kasi jan sa kanan, we really treat this like this:
8÷[2(4)]
pero ung sa kaliwa, there is still a possiblity na Ang intention nung given problem is:
8/2×(4) --> 8/2 treated as a fraction

If aalisin mo ung Multiplication symbol, alisin mo na din ung division symbol.

(⁸/₂)4 = 16 or ⁸/₂(4)=16
​

 

[Pen_J]

Walang ipinagkaiba diyan, convention na iyan sa engineering, inu-omit yung symbols ng multiplication at division para hindi magkaroon ng confusion sa pag-solve ng problems.
Di ba nga inalis na yung mga symbols, at eto yung E×ρréššion, 8/2(2+2), at hindi iyan kapareho ng
(8/2)(2+2) dahil hindi pa na-eliminate yung unang parenthesis, nag-introduce ka ng isa pang bago.
Ma-eliminate lang yung parenthesis kung susundin yung distributive property nung E×ρréššion.

⁸/₂(4)=16? >>> see. nag-proceed ka na sa next operation eh hindi pa na-eliminate yung parenthesis.

 

[Kaplok Kaplok]

Di ba nga inalis na yung mga symbols, at eto yung E×ρréššion, 8/2(2+2), at hindi iyan kapareho ng
(8/2)(2+2) dahil hindi pa na-eliminate yung unang parenthesis, nag-introduce ka ng isa pang bago.

Hindi ko magets. Ano ba ung simula na E×ρréššion na basis bago ka umabot jan? Un bang nasa title nung thread? And what is stopping you from simplifying 2+2?

Ung parenthesis kasi sa dito:

(⁸/₂)4 = 16 or ⁸/₂(4)=16

is not technically parentheses anymore. It is meant to separate the 4 from the other numbers and denote multiplication. It is not "adding" parenthesis.
The way you solve this:
8/2(4) = x
Assumes that it means:

_8 _

2(4)

When it could also mean:
⁸/₂(4)

Logic of reading 8÷2×4 left to right gets the answer 16. Kaya yan ang makukuha sa mga basic na calculator if you type it exactly as is.

Meaning, interpreting it 8/2 as a fraction is the more correct route.

The original question was meant to "hijack" the inclination of pemdas users' bias to do multiplication first before division, disregarding other interpretations.

 

[Pen_J]

The original question was meant to "hijack" the inclination of pemdas users' bias to do multiplication first before division, disregarding other interpretations.

by ignoring the mathematical rule: distributive property! Nagkaroon ng controversy dahil hindi kinumpleto yung procedure sa pag-eliminate ng parenthesis.
I-apply mo pa sa E×ρréššion yung commutative property ng multiplication, hindi dapat mababago yung answer, Isa lang dapat ang sagot kung walang variable na involve, kapareho nung unang sagot.
8/2(2+2) = 8/(2+2)2

Tanggapin na lang natin na hindi tayo mag-a-agree. Doon ako sa may sinusunod na rules.

 

[Kaplok Kaplok]

by ignoring the mathematical rule: distributive property! Nagkaroon ng controversy dahil hindi kinumpleto yung procedure sa pag-eliminate ng parenthesis.
I-apply mo pa sa E×ρréššion yung commutative property ng multiplication, hindi dapat mababago yung answer, Isa lang dapat ang sagot kung walang variable na involve, kapareho nung unang sagot.
8/2(2+2) = 8/(2+2)2

Dahil nga sa use of distributive property na yan kaya pinipilit unahin ung multiplication. At saka you rearrange the E×ρréššion already assuming the multiplication must be done first.

Distributive property is not a rule that encompasses order of operation. And so does commutative property. It only defines a certain equation is equivalent to another. It is not even required here.
Bago ka makapagdecide kung gagamitin mo yan or hindi, how did you arrive to the conclusion na dapat mo yan gamitin? Paki sulat nga step by step.

 

[Pen_J]

Hindi pinipilit unahin yung multiplication kundi pinipilit ma-eliminate yung parenthesis, hindi mo ma-eliminate yung parenthesis kung addition ng loob lang ang gagawin mo, iyon ang dahilan kung bakit kailangan i-multiply muna bago yung susunod na operation.

Distributive property is not a rule that encompasses order of operation. And so does commutative property.

So, exempted sa rules ang order of operation? Hindi katanggap-tanggap yung commutative property dahil mababago yung result?

 

[Kaplok Kaplok]

So, exempted sa rules ang order of operation? Hindi katanggap-tanggap yung commutative property dahil mababago yung result?

No that is not the point. Eto ung original question ha.
8÷2×(2+2) = x
So gusto mo gamitin ung distributive sa portion na 2×(2+2). You can only do that when you are sure this portion has to be done first than the 8÷2 portion.

This is an inherent bias ng misundertunding ng pemdas.

Kahit gamitin natin ang distributive, since 8÷2 appeared first on the equation, it must be done first.
4×(2+2) = 16

---

If the problem appeared like this:
8÷2(2+2) = x

No argument tama ka. Kasi may implication na ibig sabihin nyan ganito

8÷[2(2+2)] = 1

Again, if written using × and ÷ , this two operation has the same priority.
Left to right lang yan.

---

This is really a case of conventions ending up wrong due to lack of nuance.

 

[Pen_J]

Kahit gamitin natin ang distributive, since 8÷2 appeared first on the equation, it must be done first.
4×(2+2) = 16

So, ang may bias ay yung procedure na sinusunod mo, enclosed na siya sa imaginary parenthesis kaya hindi pwedeng i-apply yung mga rules.
Paano ba i-apply yung distributive property, 2(2+2) para ma-eliminate yung parenthesis? hindi ba multiplication over addition, 2(2+2) = (4+4) = 8. Hindi yung shortcut 2(2+2) = 2(4). Sabi ko nga, walang conflict ang PEMDAS at BODMAS (BEDMAS), kundi nasa individual na gumagamit ng procedure. Doon ako sa may rules.

Tapusin na natin ito, paps. Alam naman natin na hindi tayo mag-a-agree sa procedure.