Have you seen this question going round on Facebook?
What do you think?
I recall the Order of Operation in an arithmetic equation was/is:
Parentheses - Power (Exponent, in some terms) - Multiplication/Division - Addition/Subtraction. This could be remembered by the memonic fo PPMDAS - Pretty Please My Dear Aunt Sally. M/D & A/S are worked from left to right in order.
Thus, the equation would go:
Yes, that is my final answer.
Others work out of 'left-to-right' sequence & come up with:
The correct answer is 1. The second way you worked out the equation was correct, Beetle.
But you work from left to right when conducting the mathematical operation when working the expression. Can you give me a reference that refutes the standard order of operation?
Further explanation addresses the Associative Properties as a computational strategy. The equation can be rewritten out as:
Six divided by two times the quantity of one plus two
Six divided by two times three
These can be grouped & yield the answers:
(6ï¿½2)*3 = 3*3 = 9 working left to right
6ï¿½(2*3)= 6ï¿½6 = 1 working right to left
Division indicates the multiplication of the inverted number, or written out:
6 * 1/2 * (1+2) => (6*3)/2 => 18/2 => 9
Want me to prove that zero equals one? Or how to work a slide rule?
Try the equation on a calculator that has the parenthesis. My Texas Instruments TI-30 SLR+ gives the answer as 9.
Final answer & I still don't need to call a friend or get audience voting.
LOL, how do we know the answer?
Is it posted somewhere or are we going by our Bella EXPERTS
I am so impressed with how Beetle just jumps in and figures stuff out - way to go Mr. Math!!!!
Had enough math in getting my degree... & all I wanted to do was fly, so I went the Aerospace route. Okay, I am a rocket scientist.
< addition: My studies came before desktop computers & cheap scientific calculators. It was pencil & paper crunching out the numbers. >
My husband is the math expert, not me, although I do help students with it in the private school I volunteer at. I will ask others at school about it Monday and will have my husband look at it again later when he gets home, but from what I have learned, it is worked in the following way.
You need to use distributive property in this problem. First things first, (1+2) =3 .
6 / 2(3)
6 / 6 = 1
You need to eliminate the parentheses before you can move on to dividing.
Well I'm definitely no rocket scientist, but I have stayed in a Holiday Inn Express! :)
I also had a middle school algebra teacher who REFUSED to let me sleep in his class (Thank you Mr.Brammer!)
I consulted [i]Basic Rules of Algebra, Algebraic Fractions, Laws of Exponents, and Roots/Radicals[/i] by Charles Ormsby.
He states "Letters or symbols should be considered placeholders for numbers...)
Let's replace the 2 inside the parenthesis with x and see how this problem works out
6 / 2(1+x)
6 / (2+2x)
or on a blackboard would be written
plug 2 back in for x and you get 1
You are correct Lisa
Using a variable forces you to keep the parenthesis and use the distributive property, which you should do anyway.
Mr.Brammer forced us to work hundreds of these on the blackboard in front of the class. (This was before schools worried about kid's "self esteem) He didn't care to berate you a little if you kept getting them wrong.
Thanks again Mr.Brammer, RIP
Odd thing to be going around on Facebook.
But the answer is 1.
In the right hand term, 2+1 in brackets equals 3, just as it does when it's not in brackets. Multipled by the 2 next to it, you get 6. 6 divided by 6 is 1.
Well we know to do the brackets first and 2+1 = 3
but when once you get
the question is, where do you go from there?
If it were written 6 / 2 x 3 the answer would be 9
but if the 3 were an x and it were written 6/2x, the answer would be 1
I believe that using the order of operations, the answer would be 9. PEMDAS (some say GEMDAS-G standing for grouping symbols) says that the order of operations = parenthesis, exponents, multiplications OR divisions-left to right-whichever comes first, finally additions OR subtractions -left to right-whichever comes first.
Beetlemess is right. The other ways of working it out, like the one on Facebook have mathematical flaws. They do not really follow the order of operations. There's a bit of math sleight of hand going on. Beetlemess elegantly listed all of the steps and reasons why it should be worked so that the answer is 9.
Tina, the Facebook thing is just not correct math.
"If it were written 6 / 2 x 3 the answer would be 9
but if the 3 were an x and it were written 6/2x, the answer would be 1."
6/2 = 3 and 3*x = 3x it does not equal 1 As a variable, x could equal any number.
if you had 3x/3x that would equal 1.
Some people think that PEMDAS means you do the multiplication first. Those folks would think that they would do the 2 * 3 first and then divide by 6. That would give them 1, but it would be incorrect.
The distributive property does need to be taken into account. However, first do what is in the parenthesis. Then, the division is completed. After that, you distribute the 3 times the 3 for an answer of 9.
go to [url=http://www.freemathhelp.com/distributive-property.html]free math help / distributive property[/url]
and type in 6/2(1+2)=x and hit solve
it will show you how they got their answer
I visited the above site and it worked. Go to the bottom of the page and type in the math problem, hit answer and the problem will be solved for you. Free Math Help
I stand corrected....
If you type in 6/2(2+1)=x and hit solve, the answer is x=1
If you type in 6/2(2+1) and hit solve, the answer is 9
...I give up!
I stand corrected....
If you type in 6/2(2+1)=x and hit solve, the answer is x=1
If you type in 6/2(2+1) and hit solve, the answer is 9
...I give up!
Yes, if it were written 6 / 2 x 3, the answer would be 9.
But it isn't written that way. And when you write 2(1+2), the whole thing is an expression that needs to be treated as a unit in terms of any other operations.
The expression 2(2+1) equals to 6 and needs to be treated as if it were the number 6.
If you were using letters a and b instead of the 2 and 1 in the parentheses, it would be 2(a+b). This is a tidy way of writing (2a + 2b) because it's treated as a unit. Plugging the numbers back in, it would be the sum of 2x2 (4) and 2x1 (2), i.e., 6.
6 divided by 6 is 1.
I'm not moved from my "9" stance.
6 divided by 2 times the quantity 1+2 is calcualted in that order...
Had the equation been
6/(2(1+2)) => then it would be 6 divided by the quantity of 2 time the quantity of 1+2.
But since there are no parens to define a calculated quantity for the denominator, only the numerical value can be used.
You don't have to put the 2(1+2) into further brackets, because without an operator between the 2 and the (1+2), it is always read as one expression which, in this case, equals 6.
Mona, I have to say that I do agree with you. I remember teaching my own kids algebra. According to the way they were taught and what the answer keys said, the correct answer would be 1.
I really do not see what all the confusion is about.
Beetlemess mentioned the "Order of Operations" which is very clear. The Order of Operations states that if there is a problem that has all of the following operations: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction, then the Operations must be performed in the order in which they are stated.
Therefore, 6ï¿½2(1+2)= 9
"It seems as though the answer depends on which way you look at the problem. But we can't have this kind of flexibility in mathematics; math won't work if you can't be sure of the answer, or if the exact same problem can calculate to two or more different answers. To eliminate this confusion, we have some rules of precedence, established at least as far back as the 1500s, called the "order of operations". The "operations" are addition, subtraction, multiplication, division, exponentiation, and grouping; the "order" of these operations states which operations take precedence (are taken care of) before which other operations.
A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction"."
See: Order of Operations
Math is an exact science. We cannot insert "what ifs" or "look at it this way" insinuations to arrive at the correct answer.
Phyllis, the confusion comes about because I was taught in school to do it so that the answer is 1. I taught my children to do it so that the answer is 1.
Today at school I asked a another lady that I worked with about this problem. She is also attending college at the moment and a lot of her work involves math. When I presented the problem to her, she immediately said that the answer was 9. I asked her why and told her that the way I had been taught to do it, the answer should be 1. What she told me really surprised me, because you are right - the rules of math should not change. Tara told me that the way she was taught to do this type of problem in high school was different than the way she was taught to do it in college. In high school, she was taught to do it so that the answer would be 1. When she did these same problems in college, she missed them all. Finally, she asked her professor to explain to her why she was missing them and he told her that they had changed the rules, the answer was now 9.
Because the rules of math should NEVER change is why I am so adamant that the proper answer is 1. What good does it do us to learn how to do all of this math if they can just up and change the rules on us? I realize now that it can be done either way, but I really feel that is wrong - it should only be able to be done in one way.
Yet the way I was taught, the answer is 9. The way I taught my children and the way they were taught in school, the answer is 9. I still hold to the fact that math is an exact science and a calculation is to be done in the order it is presented. I went to high school over 45 years ago and the way I was taught would give me the answer 9. I do not know what college or professor changed the rules, but I would sure like to see it written down in a current math book.
How odd. Changing the rules? If so, this hasn't made it here.
I've asked a few mathematically-literate friends about it. Everyone has looked at it and said "one" and given me a strange look that I couldn't work out anything so simple.
I finally asked was one of our math teachers. Answer: one. We discussed why. He said he would also always read the expression 2(1+2) as a short way of writing the cumbersome [(2x1)+(2x2]). Without an operator between the outside 2 and the brackets, it's one expression that you can't break up.
But he teaches children and giving the problem a second look, said some people might misread the whole thing as being equal to 9. But that would be incorrect? Yes. He suggested it would be helpful to enclose the 2(1+2) in further brackets so it wasn't misread. Would you misread it without the brackets? No. Has this changed over the years? No.
Have you seen this question going round on Facebook? 6ï¿½2(1+2)=? What do you think?
Hi Tina, as a child 'BIDMAS' was drummed into us
as being the order in which any mathematical conundrum is done with 'BIDMAS' standing for:
B - Brackets
I - Indices
D - then Division
M - followed by Multiplication
A - then Addition
S - and finally, Subtraction
Using 'BIDMAS' the answer would be 1. A great thread! (JOY)
Mona hit the nail on the head "without an operator between the 2 and the (1+2), it is always read as one expression"
There is one division sign. The number or sum to the left of that sign is being divided by the number or sum on the right.
Mona and Frank,
I wish I had seen your posts at the time you posted them - it would have saved me a lot of misunderstanding I have had with a friend.
Thanks for clearing this equation up.
first you solve small bracket then division operator and yhen multipication
for more welcome to this forum site
I think if we first divide then we will get the good results.
Although I am very week in maths, But I have heard that first we have to divide then subtract.
Time I dust off this thread & provide the answer as derived by two college math professors (One is a very close frind of mine & a retired Math PhD) er.jacob89 breaks it down above by doing the parened operation first...
*E*: left to right is the precedence for mult/div 6ï¿½2*3. Correct answer is 3*3 or 9.
*G*: Brad - *E* stated it correctly (no big surprise to either *E* or me). Math follows certain conventions and the left to right is one of them. I learned it (way back when) as : Add or multiply or divide, then add or subtract. In case of a tie go left to right. The Please Excuse My Dear Aunt Sally tells you to do what is in the parentheses first, then exponents then multiply or divide, then add or subtract (in case of a tie go left to right).
I'll now rest my case with an answer of NINE (9)
I so agree! Good job, Beetle. You have settled it once and for all. Yeaaaaah!!!!
Beetle, that's how I teach it. Your explanation a long time ago was brilliant. That's when I started reading your posts; it was so elegantly written.
I always had faith in you, Beetle.
[quote=Lisa - Fiction Writing]The correct answer is 1. The second way you worked out the equation was correct, Beetle. [/quote]
Yes It is As the ( have most prior then multiplication , then Division .
Fully agree that the parened (1+2) operation is to be handled initially.
Yet, Multiplication does not have a priority over Division and are conducted mutually in left-to-right ordered process, before any Addition/Subtraction... as Division is merely multiplication of the value's inverse.
How do you find the actual retail value of an even-money priced item that totals $30 cash when the sales tax rate is 12.5% ?
First of all, I'd find a way to buy online to avoid sales tax, or move to/buy at another locale with a lower tax rate.
Item retails for 'X'
At checkout, the tax is added at 12.5% of 'X'
Thus you are paying 1.125X, which is the stated $30. Equation would be:
1.125X = 30
X = 30/1.125 = $26.67 (actually $26.66666666...); but all depends on the tax charting for the range around $26.66 and $26.67
Oh, for crying out loud! How can you guys think so hard before it is even noon?
Very good, Beetle -- well done!
Hi Phyllis & Beetle
Well done Beetle -- you are most definitely quick !
We oversee a Mom & Pop motel in Volusia County Florida.
6.5% Sales Tax
6% Bed or Tourist Tax
Phyllis: It was the noon hour when I prepared my response. Time Zones are in effect during the holidays...
Burt: $30 for a motel room? Is that a per night cost or hourly?
<< the deviant mind prevails, again... >>
Standing joke is No Refunds -- sometimes it takes less than $5-$15min. -- Yikes !
Early '80's was buck-wild... I must have a hell of an immune system !
I had a dream last night that me and Kris Krsitoferson were hitin' the bars and his 'ole lady showed up and we had some steak and beer -- a lot of shake it but don't dislocate it !!
I got to clean the bathrooms... 30+ years now -- you've seen my current pic -- Yikes
Cabbage Patch cole slaw is lame compared to pure 'ole mud wresilin' girl on girl on Main St.
Those were the days my friend...
Even the math problem enters into the mud puddle discussion...
An Eagle flying over an Indian by a River is a mnemonic for what radical mathematical equation that got a German Professor kicked out of academia and had to support himself by teaching piano lessons because his proposal was 100 years ahead of his time ?
Hint: We could not be having this conversation if that mathematical equation was not being in use right now.
Would that be Georg Ohm?
I'm seeing E=volts; R=resistance; & I=amperage and this can be placed into Ohm's Law Triangle having E over IR to easily present the equation permutations; i.e. E=IR; I=E/R; & R=E/I
But of course...
Ohm's Law... E = Eagle (or Electromotive Force aka Voltage) I = Indian (Current or Amperage) and R = River (Resistance of the circuit) :0 :0
What a concept !!
Every trailblazer has a burden to bear.