High School Math 101

[skijunkie55]

Alright, so I have some acquaintances on FB who have been sharing and commenting on the following image. They are teachers in today's education system.

https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-xpf1/v/t1.0-9/11016097_10155218441160176_1672664357858086713_n.jpg?oh=2705b08d3fa25452c8cd326df661c820&oe=5580B83B&__gda__=1431123268_cdb706762314c020a6247ed711aad3c8

Here's my steps

6 / 2(1+2) = 1

6 / 2(3)

6 / 6 = 1

Everyone else is getting 9. I personally think these people are re-writing the formula.

6 / 2(1+2)

6 / 2 * (3)

3 * 3 = 9

I plug in the formula to my handy Casio fx-270W Plus calculator which has gotten me through grad school without fail, and it says 1.
Google says 6 ÷ 2(1 + 2) = 9

Am I getting old and just don't remember how to do math? Or is there no hope for American public school education?

[Ryno12]

Order of operations working from left to right. Calculations inside parentheses are calculated first, then exponents, then multiplying & dividing, then addition & subtraction. Since multiplication & division are the same hierarchy, you go from left to right.

6 divided by 2=3

3x3=9


You're calculating 2x3 before the first #6. That is out of order.

Here is another video explaining it.

http://youtu.be/TvfBYi83BwE

[SilverBullet432]

The answer should be 1.

[Airhasz]

My answer would be 1 also. Glad it's not a life or death question if wrong...:cool:

[Eurodriver]

Solve

6 / x(1+2) = 9

X = ?

[SilverBullet432]

In your case, you would need to first solve for x. In the example, it is already there. So did they put that there to purposely throw people off?

[cbx]

31881

[skijunkie55]

http://i594.photobucket.com/albums/tt28/skijunkie55/Mobile%20Uploads/IMG_4005.jpg

http://i594.photobucket.com/albums/tt28/skijunkie55/Mobile%20Uploads/IMG_4006.jpg

[Ryno12]

3190031901

https://www.youtube.com/watch?v=V022T7ZWHgw

[Alex V]

I get 9.

Multiplication and division are ranked equally and go left to right. So I divide 6 by 2 then multiply by 3.

[Onyx Z]

PEMDAS is the order of operations: Parentheses, exponent, multiply, divide, ad, subtract. I don't remember multiplying and dividing being on the same hierarchy. It was specifically in the PEMDAS order.

6 / 2(1+2) = x

6 / 2(3) = x

6 / 6 = x

x = 1

[nova3930]

Order of operations working from left to right. Calculations inside parentheses are calculated first, then exponents, then multiplying & dividing, then addition & subtraction.


Yep, never forget good ole PEMDAS.

[Lincoln7]

Ahhhh! I keep getting 1. I don't know how to determine if this is correct but I would never perform the equation to get 9.

[zombiescometh]

Apparently this went around in 2012 and probably before that. Here's a good explanation. http://youtu.be/pUctSzO4BnU

[Ryno12]

Yep, never forget good ole PEMDAS.

Yep. It's easy to remember:

Please Excuse My Dear Aunt Skijunkie

:p

[Alex V]

PEMDAS is the order of operations: Parentheses, exponent, multiply, divide, ad, subtract. I don't remember multiplying and dividing being on the same hierarchy. It was specifically in the PEMDAS order.

6 / 2(1+2) = x

6 / 2(3) = x

6 / 6 = x

x = 1

According to mathisfun there is a left to right hierarchy... http://www.mathsisfun.com/operation-order-pemdas.html

[zombiescometh]

PEMDAS is the order of operations: Parentheses, exponent, multiply, divide, ad, subtract. I don't remember multiplying and dividing being on the same hierarchy. It was specifically in the PEMDAS order.

6 / 2(1+2) = x

6 / 2(3) = x

6 / 6 = x

x = 1
Alex beat me to it.
P

Parentheses first

E

Exponents (ie Powers and Square Roots, etc.)

MD

Multiplication and*Division (left-to-right)

AS

Addition and*Subtraction (left-to-right)

So PEDMAS equals 9

[Lnxgeek]

Python console (a programming language) can be used as a calculator, it agrees with the 9 answer:

Python 2.7.9 (default, Dec 10 2014, 12:24:55) [MSC v.1500 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> 6/2*(1+2)
9

[Onyx Z]

According to mathisfun there is a left to right hierarchy... http://www.mathsisfun.com/operation-order-pemdas.html

That website is not credible because MATH IS NOT FUN. :p

[Alex V]

Python console (a programming language) can be used as a calculator, it agrees with the 9 answer:

Python 2.7.9 (default, Dec 10 2014, 12:24:55) [MSC v.1500 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> 6/2*(1+2)
9

Excel gave me the same answer but I'm thinking the difference may be that a computer can't understand the 2(X) part and has to see it as 2*(x). Maybe the syntax makes the difference?

[moonshot]

6/2(1+2)=X

X=1

this can be written as

6
_______

2(1+2)

which can be simplified as

6
_______
6


which = 1




If it were written as

(6/2)(1+2) =x

then x = 9

[WickedWillis]

Math was always and still is easily my worst subject.

[Lnxgeek]

I'm thinking the difference may be that a computer can't understand the 2(X) part and has to see it as 2*(x).

Yes, in programming languages 2x would not work, you have to specify 2*x.

Unless you mean 2(X) should mean something other than "2 times X"?

[skijunkie55]

so Multiply and Divide are equal and go left to right... Guess I missed that point -_-


Now let's do this same problem with Common Core Math!!

6 / 2(1+2) = 100 - 6 x 6 / 4 + 1 x 2 - 100 + 16 = 9

[223to45]

Well my phone says 9, since it is smart phone it must be right [emoji15] .

When ever I put the ( ) in the phone automatically adds a x between the 2 and ( ).

Sent from my SM-G900V using Tapatalk

[Alex V]

Yes, in programming languages 2x would not work, you have to specify 2*x.

Unless you mean 2(X) should mean something other than "2 times X"?

No, 2(X) meaning, "X" multiplied by "2". You got it right. I think this is why people using digital devices to solve the problem get 9, and those using the paper/brain get 1. When I first looked at it, I got 1. But if, in fact, multiplication and division are equal and are prioritized left to right, then the answer has to be 9.

[zombiescometh]

6/2(1+2)=X

X=1

this can be written as

6
_______

2(1+2)

which can be simplified as

6
_______
6


which = 1




If it were written as

(6/2)(1+2) =x

then x = 9
6/2(1+2)=x

X=9

This can be written as

6
_____
2
X
1+2

Which can be simplified as

3 x 3

Which = 9

If it were written as

6/(2(1+2)=x

Then x=1

[4DAIVI PAI2K5]

I got 1. Lol

[polydeuces]

If you're the Fed you don't give a f#@ck, raise taxes on the middle class, increase tax-shelters & loopholes (welfare) for the rich and large corporations and just print more $$$$$$$
Which is why we don't need math anymore
(FWIW I got one as well)

[Lnxgeek]

Any programming book will instruct you to type it in this format:

(6/2)*(1+2)

[6933]

Please My Dear Aunt Sally...The answer as it is written is one. Period.

[skijunkie55]

So it seems we're 50/50 on which answer is correct...

I still think it's 1.

[Sam]

https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-xpf1/v/t1.0-9/11016097_10155218441160176_1672664357858086713_n.jpg?oh=2705b08d3fa25452c8cd326df661c820&oe=5580B83B&__gda__=1431123268_cdb706762314c020a6247ed711aad3c8

Here's my steps

6 / 2(1+2) = 1

6 / 2(3)

6 / 6 = 1

Everyone else is getting 9. I personally think these people are re-writing the formula.

6 / 2(1+2)

6 / 2 * (3)

3 * 3 = 9

I plug in the formula to my handy Casio fx-270W Plus calculator which has gotten me through grad school without fail, and it says 1.
Google says 6 ÷ 2(1 + 2) = 9

Am I getting old and just don't remember how to do math? Or is there no hope for American public school education?

I can understand how some got 9 and some got 1. I am with the one crowd and agree with the explanation that you've given. Here is another way to work that equation:

Using the "distributive property" of arithmetic, the 2(1+2) part becomes (2x1) + (2x2) = 2 + 4 = 6 There simply is no other correct way to manipulate that part of the equation, the way it is written. Dividing 6 by 2 first just doesn't make sense.

So now we have left: 6 divided 6 = 1

Unless junior high school (or middle school) arithmetic/algebra changed since the 1980s, I'm going to stick with 1.

I've had 6 college level calculus and differential equation courses, so I've used math a few times.

[Lnxgeek]

Please My Dear Aunt Sally...The answer as it is written is one. Period.

Aunt Sally does not remind you of the left to right precedence :)

6/2(1+2)

becomes

6/2(3)

since Parenthesis go first, the Mnemonic helps you remember multiplication and division go before adding and substraction.
But at this point all you have left is multiplication and division.

[TehLlama]

I learned LaTeX specifically to avoid dealing with stupid problems like this. I guess that makes me terribly elitist for considering notation that sloppy as 'do math stupidly, get variable answers'.

[Lnxgeek]

Yes, notation like this:

31884

should make it better

[zombiescometh]

So after searching the web I have learned 3 things.
1. There has not always been a consistent convention or rule that is the standard for solving equations
2. To solve the equation correctly you must know what convention or rule the writer of the equation is using.
3. If you don't know the answer to point number 2 then there will always be more than one possible answer.

[223to45]

OK here is a question

After you perform the first problem inside the Parenthesis you are left with 6/2(3)=x

Now there is still math equation involving Parenthesis, do you do that first then go L to R??

[Lnxgeek]

OK here is a question

After you perform the first problem inside the Parenthesis you are left with 6/2(3)=x

Now there is still math equation involving Parenthesis, do you do that first then go L to R??

the parenthesis rule is to solve what is inside them, once you have (3) that is just a simple
multiplication.


6/2(3)

becomes

6/2*3

all we done is substitute the parenthesis for the multiplication symbol.

Multiplication and Division are at the same 'level' that is why you go left-to-right.

[Ryno12]

So after searching the web I have learned 3 things.
1. There is not a convention or rule that is the standard for solving equations.
2. To solve the equation correctly you must know what convention or rule the writer of the equation is using.
3. If you don't know the answer to point number 2 then there will always be more than one possible answer.

So it turns out that we all have the right answer.

That is incorrect. There are defined rules for solving mathematical equations because there can only be one correct answer.

I'm surprised this is even still being debated. The rules for solving the equation properly have been defined and the correct answer of 9 has been given.

[Clint]

PEMDAS says that multiply goes before divide.

That's why the answer is 1


PEMDAS is the order of operations: Parentheses, exponent, multiply, divide, ad, subtract. I don't remember multiplying and dividing being on the same hierarchy. It was specifically in the PEMDAS order.

6 / 2(1+2) = x

6 / 2(3) = x

6 / 6 = x

x = 1


the parenthesis rule is to solve what is inside them, once you have (3) that is just a simple
multiplication.


6/2(3)

becomes

6/2*3

all we done is substitute the parenthesis for the multiplication symbol.

Multiplication and Division are at the same 'level' that is why you go left-to-right.

[Lnxgeek]

PEMDAS says that multiply goes before divide.

That's why the answer is 1

http://en.wikipedia.org/wiki/Order_of_operations

Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. PEMDAS is often expanded to "Please Excuse My Dear Aunt Sally", with the first letter of each word creating the acronym PEMDAS. Canada uses BEDMAS, standing for Brackets, Exponents, Division, Multiplication, Addition, Subtraction. Most common in the UK and Australia[8] are BODMAS and BIDMAS.

In some English speaking countries, Parentheses may be called Brackets, or symbols of inclusion and Exponents may be called either Indices, Powers or Orders, which have the same precedence as Roots or Radicals. Since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BOMDAS. The original order of operations in most countries was BODMAS which stood for Brackets, Orders, Division, Multiplication, Addition, Subtraction. This mnemonic was used until exponentials were added into the mnemonic.

These mnemonics may be misleading when written this way, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would also give the wrong answer to the problem:

10 - 3 + 2

The correct answer is 9 (and not 5, which we get when we do the addition first and then the subtraction). The best way to understand a combination of addition and subtraction is to think of the subtraction as addition of a negative number. In this case, we see the problem as the sum of positive ten, negative three, and positive two:

10 + (-3) + 2

To emphasize that addition and subtraction have the same precedence (and multiplication and division have the same precedence) the mnemonic is sometimes written P E MD AS; or, simply as PEMA.

All of these acronyms conflate two different ideas, operations on the one hand and symbols of grouping on the other, which can lead to confusion.

[zombiescometh]

That is incorrect. There are defined rules for solving mathematical equations because there can only be one correct answer.

I'm surprised this is even still being debated. The rules for solving the equation properly have been defined and the correct answer of 9 has been given.
Didn't read all the way though post has been corrected.

[Whiskey_Bravo]

No, 2(X) meaning, "X" multiplied by "2". You got it right. I think this is why people using digital devices to solve the problem get 9, and those using the paper/brain get 1. When I first looked at it, I got 1. But if, in fact, multiplication and division are equal and are prioritized left to right, then the answer has to be 9.


I did it in my head and came up with 9.


But then again it's been a long time since I have been in school so I couldnt 100% tell you why I did what I did.

[FromMyColdDeadHand]

It's almost like they are mixing two ways of writing equations.

if :- is divided by

6 :- 2(1+2)

Why isn't it written 6 :- 2 x (1+2)

If you want to say 2(1+2) isn't a distinct term, then you have to be consistent with the multiplication and division symbols. If you have the term 2(1+2), you need to have 6/2(1+2), as a fraction, which is consistent.

The person writing 2(1+2) is being a math 'That Guy" by trying to make it look like a unified term, but then insisting it is something else.

2(1+2) is the math equivalent of the Sig Arm brace.

It's like mixing Common and IUPAC naming for chemicals.

[6933]

Answer is 1.

[Lnxgeek]

Answer is 1.

Do you agree the original question can be expressed like this?

31899

[Outlander Systems]

It's 9.

All day long, and twice on Sunday.

[6933]

Let me back up and state why I feel it is 1. The equation seems to be written deliberately obtuse in that it can be read several ways..each possibly correct. I feel this was done intentionally(obviously).

I will also concede that 9 is a possible answer.

Anyone with advanced math under their belt automatically assumes there is a single correct answer; unless we are talking operations that are designed to give a set of points, etc.

This is where I feel the trick is. Not necessarily in arriving at one definitive answer, but that the equation can be read two diff. ways and each answer may be correct.

I agree with 1 and I now can see arriving at 9. The joke is on us. Someone, somewhere is laughing knowing the type of people that would have some steam come out of their ears thinking about the answer.

That was the object of the equation, not getting a right answer.

[Ryno12]

Let me back up and state why I feel it is 1. The equation seems to be written deliberately obtuse in that it can be read several ways..each possibly correct. I feel this was done intentionally(obviously).

I will also concede that 9 is a possible answer.

Anyone with advanced math under their belt automatically assumes there is a single correct answer; unless we are talking operations that are designed to give a set of points, etc.

This is where I feel the trick is. Not necessarily in arriving at one definitive answer, but that the equation can be read two diff. ways and each answer may be correct.

I agree with 1 and I now can see arriving at 9. The joke is on us. Someone, somewhere is laughing knowing the type of people that would have some steam come out of their ears thinking about the answer.

That was the object of the equation, not getting a right answer.

Here's the skinny though. There are very defined rules for solving mathematical equations since there can only be ONE CORRECT ANSWER. There are no tricks, there are no additional ways to "read" an equation, there are no other "possible" answers; there's only one. If people think that there is, they need to go back to school... and not the one that Sam went to. (Sorry Sam, couldn't resist ;) ) That's not meant as a dig to anyone but can you imagine trying to calculate critical information and coming up with two different answers? NASA anyone??? If you come up with different answers to an equation, something so being calculated incorrectly; a rule is not being followed.
Believe it or not, calculators can be wrong. See my post above or Google it. The OP's "trusty" calculator... wrong.

[Frailer]

...Anyone with advanced math under their belt automatically assumes there is a single correct answer...

The more advanced math one has, the less likely he or she is to assume there is a single correct answer to anything.

But that's neither here nor there. The purpose of this problem was to demonstrate knowledge of order of operations. As such, there is only one answer in the domain of real numbers, and that answer is 9.

[steyrman13]

The answer is 1. The 2 and numbers in the parenthesis are tied together. That is done first. Or another way to look at it.
6/ 2(1+2)=x
6/ 2(3)=x
6=2(3)*x
6=6*x or 6=6x
6/6= x
X=1
Or faster
6/ 2(1+2)=x
6/ 2(3)=x
6/6= x
X=1

[Ryno12]

The answer is 1. The 2 and numbers in the parenthesis are tied together. That is done first.


That is where your mistake lies & led you to the incorrect answer.

[Frailer]

The answer is 1. The 2 and numbers in the parenthesis are tied together. That is done first. Or another way to look at it.
6/ 2(1+2)=x
6/ 2(3)=x
6=2(3)*x
6=6*x or 6=6x
6/6= x
X=1
Or faster
6/ 2(1+2)=x
6/ 2(3)=x
6/6= x
X=1


9 is a common core type answer

"Tied together"? What the heck does that mean?

The parenthesis following the 2 indicates 2 is to be multiplied times the numbers within the parentheses. In other words, this could be written as:

6 divided by 2 times (1 plus 2)

Since division and multiplication have equal priority they are executed left to right.

By your logic I would first distribute the two, leaving me with:

6 divided by two plus four

Which would equal 7

Bad news: the *correct* answer is 9.

Good news: you're not required to like it.

[tb-av]

6 / 2 X 3 = 9 --- left to right

6 / ( 2 X 3 ) = 1

6 / ( 2 ( 1+2 ) ) = 1 --- now they are tied together

It's an optical illusion. It's confusing shorthand. If you make no assumptions though and simply rewrite it, the answer is 9.

Six divided by two times, one plus two, equals what? The "times" is presented in a manner that makes the equation seem as though the number two is connected to the bracket number, but that is not the case.

The missing "times" symbol ... X or * ... is understood. Adding brackets ( 2 (1+2) ) to tie the 2 to the (3) is not understood... everyone recognizes a multiplication symbol is implied. There is no such further implication so don't assume one.

[steyrman13]

That is where your mistake lies & led you to the incorrect answer.

Sorry I saw the responses but not the original.
As I have written it, it would be 1. With the divided sign which my phone doesn't do per reason I saw the / sign as above me the divided sign changes the meaning and intent of the problem. Divided sign and / (over) are different in terms of writing out a problem. The answer would be 9. If you hadn't corrected me I would not have looked further to it. Reason 1 to read entire thread [emoji6]

[Double3]

I would say 1 every time and if that is wrong I would be wrong every time.

[TheBelly]

That is incorrect. There are defined rules for solving mathematical equations because there can only be one correct answer.

I'm surprised this is even still being debated. The rules for solving the equation properly have been defined and the correct answer of 9 has been given.


please explain. I'm not seeing the clearly defined rules of which you speak. (I'm not being sarcastic, I genuinely curious)

[RIDE]

6/2(2+1) = 9

6/(2(2+1)) = 1

Two different questions, two different answers.

The answer to the OP is 9.

[Jwknutson17]

6/2(2+1) = 9

6/(2(2+1)) = 1

Two different questions, two different answers.

The answer to the OP is 9.

This. The answer is 9.

[Lnxgeek]

please explain. I'm not seeing the clearly defined rules of which you speak. (I'm not being sarcastic, I genuinely curious)

Here is an example:

http://www.algebrahelp.com/lessons/simplifying/oops/pg2.htm

you can also find a lot more info here:

http://en.wikipedia.org/wiki/Order_of_operations

the Wikipedia article discusses the PEMDAS acronym we talked about in this thread, and it also has a section on calculators.

[tb-av]

I would say 1 every time and if that is wrong I would be wrong every time.


Just apply the most basic simple rules of math.

Left to right ... first work on the brackets and exponents.. Do you have a bracket? Yes... (1+2) ... Does it have any multiplication or division? No.... Then do the addition and/or subtraction left to right... One + Two = Three.
Now write out the remaining equation.

6 divided by 2 times 3

Now do you have any multiplication or division? Yes... then perform it left to right.

6 divided by 2 = 3

3 times 3 = 9

Brackets
Exponents and roots
multiplication and/or division ---- left to right, doesn't matter which it is.
addition and/or subtraction ---- left to right, doesn't matter which it is.

[Ryno12]

please explain. I'm not seeing the clearly defined rules of which you speak. (I'm not being sarcastic, I genuinely curious)

Lnxgeek has covered it but just to expand...

There needs to be a set of rules in place for properly solving mathematical problems (algebraic equation in this example) otherwise it would result in multiple answers as you see in this thread. We know, or should know, that only one answer can be correct. To solve for the correct answer, a person needs to follow the applicable rules of the equation. The people getting 1 as an answer to the OP's equation aren't properly following the rule to solve for the correct answer. In this case, the "Order of Operation" rule needs to be followed to solve for the correct answer, which in this case is 9.

You can Google "rules of algebra" or something similar and get tons of info.
Here's another simplified example of some rules:
http://www.sosmath.com/algebra/fraction/frac8/frac8.html

[VooDoo6Actual]

Risible.

[6933]

I feel so good right now. Love when I get something wrong and then jam myself up through overthinking. Makes me feel good to have done well in math at UT and then to flub this.

My two young children have been sick and I have barely slept lately; that's the ticket.:rolleyes: I will placate myself by repeating this endlessly today.

[rero360]

I personally read it as:

__6__
2(1+2)

Which would give the answer of one, however, as others have said, having it written in a single line the answer is 9

[Bulletdog]

I got 9 back at post number one... then I read the rest of this thread.

Can I have my 8 minutes back please?

[rdbse]

I hate that stupid division sign. In science and engineering, you never see the sign in the original post.
Also, in real world practice, one knows what you are dividing, multiplying, adding, etc.

Two different problems:

6
______ = 1
2 (1+2)


6
__ x (1+2) = 9
2

[Dead Man]

You can do it any way you want, but if you're doing math, it's 9.

The only part of this problem not done left-to-right is that which is INSIDE the parenthesis. The number that multiplies the number inside the parenthesis is NOT inside parenthesis - it's done AFTER being divided by the first number.

[Bowser]

The answer is that this is a poorly written math equation meant to bait and troll people, such as the retards who argue about it on facebook.

1.

[moonshot]

I thought the answer was 1, and posted my rational earlier in this thread. I looked at the expression and saw the 2(1+2) as a higher priority than the leading 6/. I forgot about order of operations. I was wrong.

[R0N]

Parentheses first, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right)

[chuckman]

My first answer was wrong. I had to ask my 11 year-old son to do it for me.

What's the definition of ironic? I do not do math well, yet here I am at work at 5 am, being called in on call, calculating medications to ensure my patient is pain-free and remains alive.

[jaydoc1]

Who opened the door and let Sheldon and Leonard in here?

[FromMyColdDeadHand]

Are we going on the assumption that the numbers are actually base 10?