Answer: Only for genius ?? 3 – 3 x 6 + 2 = ??


David Meego - Click for blog homepageAfter posting Trending: Only for genius ?? 3 – 3 x 6 + 2 = ?? yesterday, I had to post a follow up article with the correct answer.

Even with the hint about remembering the order of operations, people still got it wrong on my poll. If you haven’t done the poll yet, click on the link above and respond.

The question was

Maths_Question

The correct answer is as follows:

  1. Question: 3 – 3 x 6 + 2
  2. Multiplication first: 3 – 18 + 2
  3. Left to right: -15 + 2 (or Addition first: 3 – 16)
  4. Answer: -13

[Start Edit] I have been asked in the comments numerous times, why step three just calculates left to right? “Shouldn’t you do addition first?”. So I am adding this explanation section to the top of the article (it is similar to information in the linked related posts).

Order of operations (excluding the first two parts of Parenthesis/Brackets and Exponents/Orders/Indices) is [DM] or [MD] followed by [AS] or [SA]. So, Multiplication and Division can be done at the same time and then Addition and Subtraction can be done at the same time.

Try calculating the following examples from left to right:

Multiplication & Division: 4 x 3 / 2 = 6 and 4 / 2 x 3 = 6 …. The order is irrelevant.

Addition and Subtraction: 10 – 5 + 2 = 7 and 10 + 2 – 5 = 7 …. The order is irrelevant.

In fact, Division is just Multiplication of the inverse number. For example: Dividing by 2 is the same as multiplying by 1/2.

Also, Subtraction is just Addition of a negative number. For example: Subtracting 10 is the same as adding -10.

Maths is exact, that is one of the beautiful things about it. As long as you do it correctly you will always get the same answer.

For those of you who still insist on doing addition before subtraction:

  1. Question: 3 – 3 x 6 + 2
  2. Multiplication first: 3 – 18 + 2
  3. Addition next: 3 – 16
  4. Answer: -13 … the same answer as before.

Please note that -18 + 2 is not -20, it is -16. You cannot ignore the minus sign in front of the 18.

Also, 3 – 18 + 2 is not equal to 3 – (18 + 2) it is equal to 3 – (18 -2) because there is a minus sign in front of the brackets to the sign of the 2 must be changed when moving it inside the brackets.

If you don’t believe me, try solving 3 + 2 – 3 x 6 or 3 + -3 x 6 + 2 which are equivalents to the original equation.

All numbers (except for zero) are either positive or negative. Negative numbers have a minus sign in front of them and positive numbers have a plus sign in front of them. But, because we are lazy, we normally don’t write the plus sign unless it is between two numbers.

So 3 – 3 x 6 + 2 becomes +3 -3 x +6 +2 = +3 -18 +2. Now you can use a Number Line to finish the calculation.

using-a-number-line

The Answer still is and will always be -13.

[End Edit]

So what do you get if you type it into a calculator (physical or app)?

That depends on if the calculator is simple and calculates as you type, or if it is smart and waits for the entire equation to be entered and the equals button pressed.

On my Windows 10 Mobile phone, the calculator app can behave in both ways.

In Scientific mode, it allows the entire equation to be entered and so correctly calculates the answer as -13 using the “Order of Operations” rules (same as above).

In Standard mode, it calculates as you type and so incorrectly gives the answer as 2. The way to think of it is that it inherently presses equals each time you press an operation button. This is just left to right calculation and ignores the “Order of Operations” rules.

  1. 3 = 3
  2. 3 – 3 = 0
  3. 0 x 6 = 0
  4. 0 + 2 = 2

If your calculator behaves in this simple way, you would need to apply the rules yourself. Here are the buttons to press:

  • 3 x 6 = MS
  • 3 – MR + 2 =

If your calculator has brackets or parentheses buttons you can use them instead of the Memory buttons to achieve the same effect.

  • 3 – ( 3 x 6 ) + 2

Looking at the poll results from the previous article, there are a number of incorrect answers being selected, so I thought I would try to identify the actual equations that would give those incorrect answers (changes highlighted in red):

  • -17 = 3 – ( 3 x 6 + 2 )
  • -17 = 3 – 3 x 6 2
  • 0 = ( 3 – 3 ) x ( 6 + 2 )
  • 2 = ( 3 – 3 ) x 6 + 2
  • 8 = 3 – 3 + 6 + 2
  • 13 =  3 + 3 x 6 2
  • 17 = + 3 x 6 + 2

Hope this all makes sense. Here endeth the lesson. 🙂

Have a look at the other posts in the series:

Enjoy

David

03-Dec-2016: Added additional explanations at the top of the article.

05-Dec-2016: Added more additional information on number lines.

This article was originally posted on http://www.winthropdc.com/blog.

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173 thoughts on “Answer: Only for genius ?? 3 – 3 x 6 + 2 = ??

    • Hi Wisdom

      There are rules in mathematics which specify the order of operations. These rules say that Multiplication and Division must be performed before Addition and Subtraction.

      If you obey the rules you get -13. If you don’t obey the rules you get the incorrect answer of 2.

      David

      Like

    • As mentioned above, maths is a precise science at most times, but leaving the door open for ambiguity and error by omitting brackets is NOT a precise way to offer a formula to calculate. It is not a matter of precision to state that an external fact – that an externally designated order of precedence – must prevail as it is a matter of convention. If I were to ask someone to calculate something I would maximise the chance of getting the right answer by supplying brackets. I was, when younger, a 1st class mathematician, so this is not some way to avoid calculations.

      Like

      • Hi Neil

        Maths is precise ALL the time. People doing incorrect maths and getting wrong answers does not make maths any less precise.

        Order of Precedence or Order of Operations is not some external guideline. It is part of the laws of mathematics. It cannot be applied optionally.

        Yes, adding brackets can help make it easier and less ambiguous but they are not required in any way. Note that brackets/parenthesis are included the order of operations rules.

        If you look through the comments, most people actually do correctly do the multiplication first, but then fail to add three numbers 3, -18 & 2 together because they don’t understand how to add a negative number.

        I even had one comment that indicated that negative numbers can’t exist and that the equation was not possible to solve!

        David

        Like

      • My point is that it jeopardises precision by omitting brackets. The practical offshoot of the omission is to expose the less capable to more errors. It is precise to give this calculation as the fare on a bus, but would the bus operator trust that all would get it right? Being explicit with non-mathematicians is the wiser path to take. Mathematicians can and should take all appropriate shortcuts of notation.

        Like

      • Hi Neil

        You might be right, but where is the fun in that?

        The challenge of the puzzle was to see who remembered what they were taught in their primary/elementary school maths classes.

        Asking ((3 – (3 x 6)) + 2) = ? makes it too easy.

        David

        Like

  1. Hi,
    I came across this 3-3*6+2=?? on my facebook timeline and was interested in the various answers that were put forward which piqued my interest so I looked a little deeper and I ended up on this page.

    Now I am a pensioner so 50 plus years past schooled maths and my vaguely remembered priorities of actions (PEDMAS/BODMAS) started to explain just how people came to all these various answers.

    So sorry to be contradictory but to quote you “Maths is exact, that is one of the beautiful things about it. As long as you do it correctly you will always get the same answer.” is really not true and should probably really read “as long as you do it this one way (apply the same rules) you will always get the same answer” which in reality probably holds true for all of the other methods employed.

    The item in question 3-3*6+2=?? is devoid of periods and parenthesis or punctuation (unless you want to argue that the mathematical qualifiers are punctuation) which I think is quite deliberate from the perspective of the person that set it as they were exhibiting their arrogance in their mathematical superiority, so if I apply your “maths is exact” and read it exactly as it is I arrive at 2 and not -13.

    So your opening statement of “The correct answer is” is in reality incorrect and should more like the correct answer can be, or the correct answers are.

    You mention phones and calculators applying different methods of achieving the answer so does that not really mean BOTH answers are correct in their own way as no matter how many times you try, the answer will always be the same as long as you apply the same method?

    Liked by 1 person

    • Hi Neville

      Thanks for your in-depth thoughts.

      Mathematics has rules to follow. One of those rules is order of operations, which specifies that Multiplication and Division must be performed before Addition and Subtraction.

      In the absence of brackets to change the order of operations, you must fall back to the rules and perform the multiplication first. If you follow the rules the answer will always be -13.

      A simple calculator does not understand rules as it can only work with two numbers at a time. It relies on the operator to perform the calculations in the correct order (ie. do Multiplication first). If the operator does not obey the rules, you will get the incorrect answer of 2.

      A more advanced calculator which can have the entire equation entered before calculating the solution, understands order of operations and will get the correct answer of -13.

      I still stand by what I said, “Maths is exact”. You must obey the fundamental rules of maths including order of operations. If you don’t, you will likely get an incorrect answer.

      There might be multiple answers (such as 2, -17 and -13), but only one is correct and that is -13.

      Regards

      David

      Like

  2. You are wrong. The mathematical sequence is always BODMAS (brackets first, then OF, if it is a worded equation, then division, followed by multiplication, addition and lastly subtraction) In this equation you do the multiplication first which is 3×6 = 18, then you do the addition 18+2=20 and lastly you do the subtraction 3-20 = -17

    Liked by 1 person

  3. But remembering a rule of math is not IQ. To know this question does not require intelligence just a good memory from school. So though most didn’t get the answer correct it only proves lack of good education in math (failure of the school system) or poor memory skills. When was the last time as an adult at work someone asked you what is 27-6*11+3= is there a big call for this. Sorry I cant find my equals key I have a Japanese keyboard [Ed: I fixed it for you].

    Like

  4. I found this when searching for something else, a computer algebra package called genius, and this is just so stupid that I cannot help to comment on it. There are rules in mathematics that are taught at school (in an early (!) year of elementary school when pupils advance from addition to multiplication). Multiplication has priority, that’s just it. No way to get a wrong result, as there is no ambiguity. I do not understand why you publish such a scrap (sorry) in the internet.

    Like

    • Alexander,

      I posted an entire series of articles based on this simple maths question after many people could not answer it correctly. I know that there is no ambiguity, but if you look at the comments (and the poll on the first post), you will see that most people get that multiplication should be done first but then they fail to add negative numbers. Then they argue with me to about their incorrect answers. My article is trying to help people get the correct answer and the information in it is accurate.

      David

      Like

      • Hi David,

        I think I know what you mean. This is incredible. Good luck.

        Alex

        PS: instead of -18+2 you may as well calculate 2-18, if there is no sign-changing key
        on the simple computer

        Like

  5. K sir i agree with your comment that -18+2=-16
    But In simple calculator we don’t have options to write -18+2. Then how students are agree practically?

    Like

    • Hi Goudappa

      On a simple calculator there is usually a sign changing key that looks like a plus and minus sign on it. You need to use this key to enter minus eighteen.

      Press (1) (8) (+/-) (+) (2) (=) and it will show -16.

      David

      Like

    • Hi Ethan

      Did you read the article? The order of Subtraction and Addition is not important. Subtraction is just adding a negative number.

      You will get the same answer whether you add or subtract first.

      Since when does -18 + 2 not equal -16?

      Like

  6. This is a great article, I found this equation on my facebook and I arrived at -13 but I wanted to make sure I was correct as the comment section seemed to have every number under the sun and it made me question my answer haha. Keep up the good work there David !

    – James

    Like

      • I thought it was 17 because you multiply first then you add then you subtract that bodmas formula but scratching my head on that one

        Like

      • Hi Ben

        Using BODMAS is correct, but it is actually BO[DM][AS]. Division and Multiplication can be performed at the same time going from left to right. Addition and Subtraction can be performed at the same time going from left to right.

        However, if you want to do addition then subtraction or subtraction then addition you will also get the same answer if you do the maths correctly … which means NOT ignoring the minus sign in front of the 18.

        So 3 – 3 * 6 + 2 becomes 3 – 18 + 2 because we did the multiplication first.

        If you want to do Addition first then -18 + 2 = -16. So 3 – 16 = -13.

        If you want to do Subtraction first then 3 – 18 = -15. So -15 + 2 = -13.

        Subtraction is the same as adding a minus number, so you can think of the problem as 3 + -18 + 2.

        Now try thinking of it as summing those three values:

        3
        -18
        2 +
        ——
        -13

        David

        Like

    • Molly

      3 – 3 x 6 + 2 = 3 – 18 + 2 = -15 + 2 or 3 – 16 = -13

      The only way to get 17 is to lose the negative sign from -15 + 2.

      I have seen the answer -17 because people fail to add -18 and 2 … which is not -20 but -16.

      Remind me never to use any mechanical device made by you as it is bound to be unsafe.

      Like

  7. The comments on this post are ridiculous! The answer is -13, it is basic math that you are all disagreeing over. Instead of wasting your time trying to prove the answer is wrong with ridiculous reasons, just remember the guy only put the question on here for fun. Unless you understand what you are talking about, then don’t try and prove someone wrong – just a lesson that may probe beneficial to you in life in more important circumstances.

    3-3×6+2 BIDMAS (The actual order of division and multiplication DO NOT MATTER, neither does the order of MULTPLICATION and SUBTRACTION!!!!!!!!!!!!!!!!!!!!!!!! They are opposites of each other. For example, 2×3/4×5 is 6/4×5 = 1.5×5 = 7.5. Or treat differently such as 2x5x3/4 = 30/4 = 7.5. Or again could be 5/4x3x2 = 1.25×6 = 7.5. As long as you have the multiply next to the 2, the 3 and the 5 and the divide before the 4, you cannot get a different answer. The same works with addition and subtraction. Just do not do silly things like (2×3)/(4×5), as this includes brackets and so BIDMAS rule B applies first and is why then you would get 6/20 = 3/10 = 0.3. This example has been provided so you can see a different example than the question stated, so you can see why you were wrong and should apologise to the question provider for you rude comments. The answer is {-(-root 13)(-root 13)]/[(-1)^(13-1)]} lol ie -13 🙂

    Like

    • Hi Mbalenhle

      The mathematical rules for order of operations says you must perform multiplication and division BEFORE addition and subtraction.

      I suggest you try again.

      David

      Like

    • Hi Margaret

      Feel free to share my article and the related articles in the series.

      I am still amazed how many people get this wrong. It seems that most get the multiply first bit but then cannot add a negative number.

      David

      Like

  8. How do you know when you’re using the order of operations though. Clearly it could be 2 or -13 mr. Smarty pants you never specified to use order of operations which is not always used in all math problems

    Like

    • Hi Antonio

      Thanks for calling me Mr Smarty Pants. That’s a nice compliment.

      There are rules in Mathematics and one of those is Order of Operations. It is one of the principles that makes sure maths works the same every time. There is never a situation where it does not apply. If you need to override the default rules you use brackets or parenthesis, but they are still part of the rules.

      David

      Like

  9. In order to achieve your solution, one must assume there are brackets or parentheses around the numbers to be multiplied. It seems to me that the operation rules are to be taken literally, they do say to solve bracketed items first, they do not say to add brackets.

    Like

    • Hi Don

      The order of operation rules say to do multiplication and division before addition and subtraction. No need for brackets or parenthesis, only need them if you want to override the standard rules.

      David

      Like

    • Hi Gameadviceweeklyguy

      Sadly the answer can never be -17. We know that you need to do the multiplication first which gives you 3 – 18 + 2. You can decide if you want calculate 3 subtract 18 (3 add -18) or -18 add 2 first. Either way the result is the same -15 + 2 = -13 or 3 – 16 = -13.

      You cannot ignore the fact that the 18 is a negative number when adding 2. -18 + 2 is not -20. It is -16. This is explained in detail in the article.

      David

      Like

  10. weird i understand the answer, however I’m always perplexed 3-3=0 anything after that is 0…i.e you can’t or should i say x a 0 as it will always be zero 🙂

    Like

  11. Think of it as old and New Testament and the equation being God. Two types of algebra being taught at two different times. Today’s algebra is different from algebra taught 50 years ago. For example: (New Testament) there are no brackets so that means multiplication first than either addition or subtraction. Division and multiplication has the same value and addition and subtraction has the same value and should read left to right. P-e-m or d(which ever comes first)-a or d(which ever comes first) meaning 3-3×6+2 equals -13. Implying that you multiply first and work the equation of addition left to right. -3×8=-18+3= -15 +2= -13.-3 gets made a whole number so to speak because of it being at the start of the multiplication or equation so to speak. the 3 gets added because it is a whole number and there is no need for a plus symbol. example for Old Testament implies that divison comes before multiplication or vise versa but is set and cannot change. Same goes for addition and subtraction but you cannot skip. for example: p-e-d-m-a-s meaning 3-3×6+2 equals 17. Because multiplication is first, 3×6 would be done first because of multiplication being first, +2 then -3 equaling 17. Both answers are correct but New Testament is the current method used in most schools nowadays. Correct me if I’m wrong. The equations might not make sense but the principle does.

    Like

    • Hi Mike

      The basic rules of mathematics have not changed for thousands of years. Brackets or Parenthesis just allow you to override the base order of operations. As long as you do multiplication or division before addition or subtraction you will be fine. Maths is exact and will ALWAYS give you the same answer.

      However, you also need to watch your negative signs.

      In your second calculation you multiplied 3×6 to get 18, then added 2 and subtracted 3 to get 17. But that is incorrect.

      You should multiply -3×6 to get -18, then add 2 and add 3 to get -13.

      The answer is always the same regardless of whether you add or subtract first.

      Just remember that subtraction is the same as adding a negative number.

      David

      Like

      • Hi David, the only reason I added 2 before subtracting 3 is because of the rule that many people follow being p-e-m-d-a-s, multiplication first. Not regarding the – sign as a negative number because M is before A and S. Addition comes before subtraction meaning A before S always. This is the misconception of order of operations. People interpret the word “order” and assume that the A before S is absolute. I researched and found out that the rule stating (division and multiplication), and (addition and subtraction) have the same value (so to speak) and reads left to right has always existed but was not enforced as a major constant until sum 70 or so years ago. The acronym pedmas was meant for reference so that people remembered. Not as a actual order to follow. Most Secondary (99.9%) and all further tertiary education enforced the correct rule at the time but elementary did not (80-90% did) , even though algebra is taught at an elementary level. Say if one teacher forgot the rule but remembered the acronym, then taught 30 students. And out of the students, 2 become teachers, cycle starts, misconception is multiplied because of rule not being enforced early. Most remembered but my teacher didn’t (incompetent for lack of a better word). I got taught Old Testament and I taught myself New Testament. That was the reason I posted both answers. 17 is correct relative to how I was taught using A before S as a constant (k) 🙂 this is the reason I left school.

        Like

      • Hi Mike

        There is no subtract 3 when you solve the equation regardless of whether you do subtraction or addition first. It makes no difference, the answer is always the same.

        Starting with 3 – 3 x 6 + 2
        Multiplication first gives: 3 – 18 + 2
        Addition first gives: 3 – 16 = -13
        or Subtraction first gives -15 + 2 = -13

        The best way to think about this is that subtraction is just adding a negative number.

        You could write this is 3 + -18 + 2

        So add or sum the following: 3, -18, 2

        There are no alternate answers here. Maths is exact and the answer is always -13.

        Note: PEMDAS should be taught as PE[MD][AS] because the MD can be swapped around and the AS can be swapped around as long as MD/DM is before AS/SA. However, it makes no difference as the result will always be the same.

        What I am seeing is that many people are having difficulty working with a negative number and do not understand that that

        -18 + 2 is -16 and NOT -20.

        David

        PS: To get 17, the equation you are solving is 3 x 6 – 3 + 2, which is not the question posted.

        Like

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