Why you can't trust your calculator, or What is 48/2(9+3)?

Domo1
Anyway I got 288.

Knowyourmeme article on this actually breaks it down fairly well.

Yes that is a good source explaining the different calculation methods, but I think I addressed some things they didn't address.

bitsforbytes
If you need a calculator do that equation then you deserve to be mislead!

They just didn't make the terms multiply when there is no operator in between them. Read the manual!

No, that's not the problem. They did multiply in both cases, even when there's no operator. The discrepancy results from the sequence in which operations are performed.

This is one reason I have never gone back from using hp and the RPN input. It intuitively follows the order of operations and is pretty hard to make any other calculation than exactly what you intend. Well worth the hour or so to learn, and no more parens.

reply to post by Arbitrageur


Yeah you did, I should have said something about it becoming a thing on the internet (I wouldn't call it a meme personally). I was surprised when I started a Googlin' that it autocompleted the equation. Cool thread, I need to go take a math class or 10.

reply to post by Halfswede


Yeah RPN is awesome, and way faster because you don't have to type all those parentheses, if you take the time to learn it. However I don't know what answer the teacher was looking for, so we can't count on the RPN calculator to result in a good score on the homework assignment.

I think research showed people got fewer wrong answers when using RPN but it was mainly because of avoiding the mistakes people made when typing all the extra parentheses. It's funny if someone who doesn't know RPN borrows your RPN calculator, and they can't find the equals sign anywhere.

reply to post by Arbitrageur


It seems that once a divide sign is placed everything that comes after is part of the denominator.

I still hold my position though that calculators should be seldom used.

bitsforbytes
It seems that once a divide sign is placed everything that comes after is part of the denominator.

I'm very biased to think so because my textbooks followed this convention, and it's still the convention in some physics journals. I was actually quite shocked to find about half the population polled disagrees with this. This is a partially accepted convention, but not universal. I say it would benefit everyone if it was universal.

It's kind of funny - I remember all through grade school the following formula for the order.

Please Excuse My Dear Aunt Sally
-Parenthesis
-Exponents
-Multiplication
-Division
-Addition
-Subtraction

Anyone remember those solar-powered calculators that you were given in 5th grade? The non-scientific one's would analyze numbers based on the order that you entered the number in.

For example:
5 + 3 * 10 would come out to 80, instead of coming out to 35. That explains why they had us do it on paper - technology didn't work as expected.

Now, in my college textbooks, the rules have been shortened to the following:
-Parenthesis
-Exponents
-Multiplication and Division
-Addition and Subtraction

I guess this makes sense, as I could have five apples, and you take away three, but someone else gives me two back (5 - 3 + 2 = 4, and 5+2-3 = 4).

Now, if only they could accept that when you divide an object by 0, you still have that object (IE: One apple divided among 0 people is still one apple), but that's a whole different topic.

-fossilera

I'm not a math wiz or anything, but I was taught the parentheses are dealt with first: (9+3) = 12

Then you would calculate 48/2: 24

So you are left with 24(12) or 24x12. That equals 288.

I'm smarter than a calculator!

We were taught BODMAS

Brackets off
Division
Multiplication
Addition
Subtraction

Different calculators follow different orders of operations. Most non-scientific calculators without a stack work left to right without any priority given to different operators, for example giving

1 + 2 X 3 = 9

while more sophisticated calculators will use a more standard priority, for example giving

1 + 2 X 3 = 7

The Microsoft Calculator program uses the former in its standard view and the latter in its scientific and programmer views.

Link

Much of this seems to be the whim of who built it or it's capabilities. Looks like understanding how something is asked to be calculated is a must. No free lunches.

PhoenixOD
We were taught BODMAS

Brackets off
Division
Multiplication
Addition
Subtraction

As I explained in the OP, the O stands for "Order", which is a way of saying exponent or power. If you were taught O meant off then I would scold your teacher.

Also it should be written like this:

Brackets
Order
Division and Multiplication
Addition and Subtraction

Which reflects there is no priority between division and multiplication, though the D and M are often interchanged, so BEMDAS is about the same. Did they give you a mnemonic for BODMAS like the PEMDAS menmonic? ("Please Excuse My Dear Aunt Sally").

what is 48/2(x+y)? i typically assume that 48 is being divided by 2(x+y). I guess it should be written like this 48/[2(x+y)].

From my college days in the 70s the standard order of operator precedence is
Exponentiation
multiplication and division (equal weight so evaluate left to right)
addition and subtraction (equal weight so evaluate left to right)

Evaluate terms within parentheses first (innermost first in the case of nested parentheses)

Simple calculators don't follow the rules - they simply evaluate in order of entry so you need to modify the expression to get the correct result.

eg 2x3^2 is really 18 but the older calculator would try to tell you it's 36 unless you enter it as 3^2x2
Parentheses allow the order to be changed eg 2x(3^2) = 18

There might have been some overestimations if mc^2 or 1/2mv^2 had been worked out on an ancient calculator with no regard to precedence

288.

Just use the same order of operations, i.e. BODMAS, for all operations whether explicit or not. No silly rules which apply some of the time depending on how the equation was written.

Try a double parenthesis: 48/(2x(9+3)) = 2

reply to post by Arbitrageur


The way the equation is presented is ambiguous. It can be interpreted as having (9+3) multiplied by the numerator or (9+3) multiplied by the denominator; hence the two different possible results . It should be written as 48/((2x(9+3)) or (48x(9+3))/2.

sheepslayer247
I'm not a math wiz or anything, but I was taught the parentheses are dealt with first: (9+3) = 12

Then you would calculate 48/2: 24

So you are left with 24(12) or 24x12. That equals 288.

I'm smarter than a calculator!

I got 2.

I dont know about BODMAS or whatever, but it is a must to simplify the equation first, so...

48/2(9+3)
after (9+3) = 12, you are left with 48/ 2(12), simplify!, so 48/24, simplify! so.... 2
trying algebra approach,
a/b(x+y)
a/(bx+by)

substituting a=48,b = 2, x = 9 and y = 3...
a/b(x+y) = a/(bx+by)
a/(bx+by) = 48/2(9+3)
a/(bx+by) = 48/(2(9)+2(3))
a/(bx+by) = 48/(18+6)
a/(bx+by) = 48/(24)
a/(bx+by) = 2

notice, you still have to solve the bx+by part first ? if you solve 48/2 part first, that would break the algebra
to properly arrive at 288, a new bracket/paren should be introduce
(48/2)(9+3)
moving to algebra
(a/b)(x+y)
((a/b)x) + ((a/b)y)
substitute
((a/b)x) + ((a/b)y) = ((48/2)x) + ((48/2)y)
((a/b)x) + ((a/b)y) = (24x) + (24y)
((a/b)x) + ((a/b)y) = (24(9)) + (24(3))
((a/b)x) + ((a/b)y) = (216) + (72)
((a/b)x) + ((a/b)y) = 288

so, in short,
48/2(9+3) = 2
(48/2)(9+3) = 288
or am I missing something ?

48÷2(9+3) in a Linux calculator I get 288

when I do this I get
48÷2÷(9+3) = 2?? points out the said calculator has a coding error.

now

48÷2x(9+3) = 288 gives out the correct answer.

Was always taught PEMDAS: Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction.

MD and AS are '/' because there's (as i understand it) no necessary order to them, other than left to right, as they appear in the problem. Therefore:

48/2(9+3) - What's inside the Parens comes first
48/2(12) - Now that the problem inside the Parens is done, it is understood that, that is just 2 x 12
48/2 x 12 - Left to right
24 x 12
288

As I was taught, the only way to express that everything after a / in a problem is part of the denominator, is to place it all in parens, as such
48/(2(9+3))

But then I suppose I was taught to write problems explicitly