Negative 9???
Well, an alarming number of people think chocolate milk comes from brown cows, so you are in good company.
fat fingered answer the question
.
So you are asserting that 6 ÷ 2(1+2) is not the same as 6/2(1+2)?
I don’t buy that.
Im just asking. Im just a dumb contractor
Correct. See my prior example above where I explain the difference.
In the first case it is:
6 divided by 2 times (1 plus2) =
6 divided by 2 times 3 =
3 times 3 =
9
In the second case it is:
6 over 2 times (1 plus 2) =
6 over 2 times 3 =
3 over 3 =
1
How it is written makes all the difference in the world if you have studied math and/or engineering.
True, but having studied maths to a reasonably high level I’d say the latter approach is correct (including replacing the division sign with “over”).
Try 6 over 3. That’s the same as 6 over 1 times 3. Did 2 just become 18?
This, and the earlier 288 vs 2 problem come down to construction of the question rather than maths. If someone says to me 6/2(1+2) = (6/2)(1+2) it makes my eyes bleed. Ditto 6/2+4 (which gets you to 7), I immediately see it as 6/(2(1+2))
Your right. There is about a 100 precedent that a multiplier by brackets takers precedence over other orders of operation.
6 ÷ 2(1+2) =9
6 / 2(1+2) =9
Thats the way i undsrstand it, thats the way the pretty lady next to me (who has a math degree) understands it, and just for shits and giggles…wolfram alfa agrees and so does my calculator.
I was thinking along the same lines. I would answer 9 for the original equation (and that is how almost , but I would answer the following
6 ÷ 2(a+b)
as 6/(2a+2b)
Hmm…
I saw that too. Distributive property, if I recall.
Answer is 1 when doing it this way.
I’m going with 1. If it was written as 6 “over” 2(1+2), you would simply finish 2(1+2)=6. Then, 6/6= 1
And your way also gives us 1.
Although, at first glance, I had 9. Lol. Then after thinking about it, I like 1 for reasons above.
6 ÷ 2(1+2) =9
6 / 2(1+2) =9
Thats the way i undsrstand it, thats the way the pretty lady next to me (who has a math degree) understands it, and just for shits and giggles…wolfram alfa agrees and so does my calculator.
You keep on understanding it that way. Nobody’s perfect.
Nope. AS WRITTEN, there is only one answer, which is 9. Every solution that is not 9 makes an assumption not present in the express terms of the equation, as written.
I explained this in my earlier response.
In your example, you replace the divided by symbol with / which alters the equation.
This is a classic SAT questions that tests the ability to contemplate the equation as written, not as interpreted.
Based on the distributive property, which could be acceptable to use, answer is 1.
Doesn’t matter if it’s a divide sign. I would think when someone interprets 2(1+2) as 2 x (1+2), that assumption is what makes the answer 9, but would also not allow us to use the distributive property and thus, changed the question.
If ever there was a thread waiting for Dr Tigerchik to rule it like. Queen…
But obviously 1. Mathematicians don’t really use a “divided by” sign. They’ll write the expression as a fraction. I’d write that with everything after the divided by sign on the bottom of the fraction; it would just be plain odd to multiply the bracketed expression by the 6, given the way it’s presented.
/\ /\
this
am surprised how many think the answer should be 9
6 ÷ 2(1+2) =9
6 / 2(1+2) =9
Thats the way i undsrstand it, thats the way the pretty lady next to me (who has a math degree) understands it, and just for shits and giggles…wolfram alfa agrees and so does my calculator.
You keep on understanding it that way. Nobody’s perfect.
consider for a moment that being arrogant doesn’t necessarily make you right
Do you have an HP calculator? The scientific one not the business type? It uses a reverse (polar?) logic, different from traditional calculators. I plugged the equation into my old HP 11. Here are the keystrokes:
6 -enter button
2 -divided by button
1 -enter button
2 -plus button
Add button
Times button
Answer is 9
But my gut and schooling tell me it’s 1.
I have used this calculator now for over 30 years, so it pains me to agree with you…
When I first saw the equation my answer was 1, I learned my math back in the 60’s and 70’s. Then I read the article in the link and it appears the entire answer is up for interpretation. Too bad because math is one of those things that I was always was taught to be absolute and you could count on it, no pun intended.
Funny though that people are still arguing about their answers when they can all be right. Argument should really be about the process in interpetiting hierarchy of the symbols.
6 ÷ 2(1+2) =9
6 / 2(1+2) =9
Thats the way i undsrstand it, thats the way the pretty lady next to me (who has a math degree) understands it, and just for shits and giggles…wolfram alfa agrees and so does my calculator.
You keep on understanding it that way. Nobody’s perfect.
consider for a moment that being arrogant doesn’t necessarily make you right
This is why you cannot get the equation right. Being arrogant doesn’t make me right. Being right makes me arrogant.
People keep missing the point of the equation. It is written in a way no mathematician or engineer would write the equation. It is done so intentionally to force you to use linear math to get to 9. It is an SAT question to test your memory of high school algebra and the order of operations. It bears no practical purpose in the real world.
Edit to Add: It is also written in sentence format in an attempt to engage the left and right sides of the brain. Finally, it attempts to make you overthink the equation rather than looking solely at what is in front of you.
People keep missing the point of the equation. It is written in a way no mathematician or engineer would write the equation. It is done so intentionally to force you to use linear math to get to 9. It is an SAT question to test your memory of high school algebra and the order of operations. It bears no practical purpose in the real world.
Edit to Add: It is also written in sentence format in an attempt to engage the left and right sides of the brain. Finally, it attempts to make you overthink the equation rather than looking solely at what is in front of you.
I think this interpretation is correct. I think advanced mathematics moved away from the ÷ sign for this exact reason. In fact, there is a danger for people that had an especially long period of advanced mathematics to forget the intricacies of PEDMAS and instead interpret the ÷ sign as a / with everything on the left side getting divided by everything on the right.
Edit to Add: It is also written in sentence format in an attempt to engage the left and right sides of the brain.
Left brain vs right brain dichotomy is a myth.
Wiki (on Order of operations) has this to say:
Similarly, there can be ambiguity in the use of the slash (‘/’) symbol in expressions such as 1/2x. If one rewrites this expression as 1 ÷ 2x and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes:
With this interpretation 1/2x is equal to (1/2)x. However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1/2x equals 1/(2x), not (1/2)x. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash, and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.
Many academics consider the mnemonic PEMDAS as non-applicable with implied groupings that are ambiguous, such as 1/2x, where the lack of an explicit operator × between the 2 and the x implies a grouping of the 2 with the x.
Mnemonics
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 the mnemonic “Please Excuse My Dear Aunt Sally”.
Canada and New Zealand use BEDMAS, standing for Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
Most common in the UK, India and Australia are BODMAS meaning "B"rackets, "O"f or "O"rder, "D"ivision, "M"ultiplication, "A"ddition and "S"ubtraction. Nigeria and some other West African countries also use BODMAS. Similarly in the UK, BIDMAS is used, standing for "B"rackets, "I"ndices, "D"ivision, "M"ultiplication, "A"ddition and "S"ubtraction.
Besides noting that the “M” and “D” don’t have a universally recognised order in the mnemonics, the first section (to my mind) settles the answer as 1.
1/2x can only sensibly be understood to mean 1/(2x). If it is (1/2)x, you’d write x/2.
Try staring at 1/2x = x/2 and see how long it takes for you to put a line through the equation.
Do you have an HP calculator? The scientific one not the business type? It uses a reverse (polar?) logic, different from traditional calculators. I plugged the equation into my old HP 11. Here are the keystrokes:
6 -enter button
2 -divided by button
1 -enter button
2 -plus button
Add button
Times button
Answer is 9
But my gut and schooling tell me it’s 1.
I have used this calculator now for over 30 years, so it pains me to agree with you…
Reverse Polish Notation (RPN), also known as postfix (as in the operator follows (“post”) the operands). Most people use infix (operator is between the operands), and nobody uses prefix.
And you wouldn’t enter it in that order. You’d do 6 2 1 2 + * /. Which gives you 1.
Edit to Add: It is also written in sentence format in an attempt to engage the left and right sides of the brain.
Left brain vs right brain dichotomy is a myth.
I’m not advocating for any type of dichotomy. The term refers to the different types of interpretation employed to a task.
Edit to Add: It is also written in sentence format in an attempt to engage the left and right sides of the brain.
Left brain vs right brain dichotomy is a myth.
I’m not advocating for any type of dichotomy. The term refers to the different types of interpretation employed to a task.
The idea that tasks use left vs right brain is a misunderstanding of how the brain works. Perhaps lateral thinking is a better term to avoid confusion.