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28-05-2021 17:33
gfm7175Profile picture★★★★★
(2189)
Some schools must mistakenly teach the PEMDAS acronym in a manner where "multiplication must be done before division" and "addition must be done before subtraction"... That's not how I was taught. I was taught that M&D were on an equivalent level and performed from left to right, and that A&S were on an equivalent level and likewise performed from left to right.
28-05-2021 19:21
IBdaMannProfile picture★★★★★
(9345)


gfm7175 wrote:IOW, they do everything on the right of the divide symbol before addressing the 8 on the left side of it. They are not following proper order of operations.

I think the intended trick to this question is the "self-imposed limitation" whereby the reader mistakenly imposes an additional set of parentheses.

i.e. the problem reads 8/2(2+2) but the reader mentally sees 8/(2(2+2))

... which is more or less what you wrote. It might not be anything more complicated than the reader not looking at it correctly.

At this point I'm tempted to note that if I were someone who was susceptible to making mistakes that I might have gotten it wrong as well ... but I'd rather just keep my explanation grounded in reality.


28-05-2021 19:38
gfm7175Profile picture★★★★★
(2189)
IBdaMann wrote:
gfm7175 wrote:IOW, they do everything on the right of the divide symbol before addressing the 8 on the left side of it. They are not following proper order of operations.

I think the intended trick to this question is the "self-imposed limitation" whereby the reader mistakenly imposes an additional set of parentheses.

i.e. the problem reads 8/2(2+2) but the reader mentally sees 8/(2(2+2))

... which is more or less what you wrote. It might not be anything more complicated than the reader not looking at it correctly.

At this point I'm tempted to note that if I were someone who was susceptible to making mistakes that I might have gotten it wrong as well ... but I'd rather just keep my explanation grounded in reality.

That's quite possible. In that case, even people who know better could mistakenly come up with a "1" answer instead of a "16" answer. Good point.


28-05-2021 21:48
Xadoman
★★★☆☆
(514)
I was taught to make the multiplication before the division. My initial answer was 1. And I am not alone. Some even get 6 for answer.
28-05-2021 23:00
IBdaMannProfile picture★★★★★
(9345)


Xadoman wrote:I was taught to make the multiplication before the division.

You were taught incorrectly. Multiplication and division are performed left to right, as you would read words on a page. You don't shift words around due to any sort of precedent, nor do you shift the order of multiplication and division.

Left -> Right

Xadoman wrote: My initial answer was 1.

Now try it again. I bet you get different results this time.

Xadoman wrote:And I am not alone.

The reason we have the term "common misunderstanding" is that some misunderstandings are common.

Xadoman wrote:Some even get 6 for answer.

The reason we have unemployment offices is because there are people who somehow get "6" when computing 8/2(2+2) (although this might just be a typo when trying to type "16" which would be correct).

28-05-2021 23:15
Into the NightProfile picture★★★★★
(15685)
Xadoman wrote:
I was taught to make the multiplication before the division. My initial answer was 1. And I am not alone. Some even get 6 for answer.


It's done left to right. You can find the priority in the specifications for several programming languages (especially procedural languages).

Priority is negations, exponents, division/modulation/multiplication (all the same priority), then addition/subtraction. Parenthesis are used to override.

In some systems, such as postfix notation, there are no parenthesis and order is strictly left to right. In prefix notation, the order follows strict nesting and is otherwise left to right.

Most folks might remember postfix notation on the HP (Reverse Polish Notation) calculators.

Most math these days is written in infix notation, using the left/right and priorities discussed.


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28-05-2021 23:20
Into the NightProfile picture★★★★★
(15685)
IBdaMann wrote:

Xadoman wrote:I was taught to make the multiplication before the division.

You were taught incorrectly. Multiplication and division are performed left to right, as you would read words on a page. You don't shift words around due to any sort of precedent, nor do you shift the order of multiplication and division.

Left -> Right

Xadoman wrote: My initial answer was 1.

Now try it again. I bet you get different results this time.

Xadoman wrote:And I am not alone.

The reason we have the term "common misunderstanding" is that some misunderstandings are common.

Xadoman wrote:Some even get 6 for answer.

The reason we have unemployment offices is because there are people who somehow get "6" when computing 8/2(2+2) (although this might just be a typo when trying to type "16" which would be correct).


Quite right. Infix notation in mathematics is common because most languages are infix in their construction, including those in Europe and the States.

In Asia, it's been an interesting trip for them, since Chinese and Japanese are postfix languages. The math notation they now use is inherited from Europe and the States, which is usually in infix notation. Thus, the math notation they use is 'unnatural' for them. They cope with it pretty well, though.


The Parrot Killer

Debunked in my sig. - tmiddles

Google keeps track of paranoid talk and i'm not on their list. I've been evaluated and certified. - keepit

nuclear powered ships do not require nuclear fuel. - Swan
28-05-2021 23:44
gfm7175Profile picture★★★★★
(2189)
Xadoman wrote:
I was taught to make the multiplication before the division. My initial answer was 1.

Then you were taught incorrectly.

Xadoman wrote:
And I am not alone.

Indeed you aren't.

Xadoman wrote:
Some even get 6 for answer.

I have no idea how anyone would manage to come up with that. According to the order of operations, the answer is 16.


29-05-2021 00:42
Xadoman
★★★☆☆
(514)
have no idea how anyone would manage to come up with that. According to the order of operations, the answer is 16.


Maybe this way:

8/2x2+2x2=8/4+4=6
29-05-2021 00:59
IBdaMannProfile picture★★★★★
(9345)


Into the Night wrote:In Asia, it's been an interesting trip for them, since Chinese and Japanese are postfix languages. The math notation they now use is inherited from Europe and the States, which is usually in infix notation.

I remember back when I was learning Farsi (just out of curiosity/interest). I thought it was very strange indeed that they read/write from right to left but numbers are written from left to right as we write them in English. When I asked why they did it that way I got the shoulder-shrug.

29-05-2021 01:15
Into the NightProfile picture★★★★★
(15685)
IBdaMann wrote:


Into the Night wrote:In Asia, it's been an interesting trip for them, since Chinese and Japanese are postfix languages. The math notation they now use is inherited from Europe and the States, which is usually in infix notation.

I remember back when I was learning Farsi (just out of curiosity/interest). I thought it was very strange indeed that they read/write from right to left but numbers are written from left to right as we write them in English. When I asked why they did it that way I got the shoulder-shrug.


Sounds about right!
I get the same thing with Japanese.


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Debunked in my sig. - tmiddles

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