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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 + 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.

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

      • It doesn’t make you right still, there are no parenthesis, therefore there are no negatives in this equation

        Like

      • Wow, that’s a new direction for Mathematics: Cannot have negative values with parentheses. Sorry, I am correct as -13 is the one and only possible answer.

        Like

      • You are wrong, Sir.

        “There are no parentheses… [therefore] there are no negative values…” – note* the 2 “no”’s…

        However, in your faux-rejection of the commenter’s statement, you maintain only a single “no”…

        Make sense?

        In other words, where there are two negatives, we can eliminate both, as each counters the other. This is also true in math……… However, and again, in your faux-rejection (which I write that way bc it fails) you do away with only one negative. You may not take two negatives for a single negative. For, that is incorrect.

        Similarly, as incorrect is your math.

        If your assumption of the negative value is true, you cannot insert a subtraction symbol as well. Note the interesting parallel between your English logic and your math. In English you take two negatives and make one; in math you take zero negatives and create one negative. Astounding!

        For, to show a counterexample, and prove how you are indeed incorrect, mathematically speaking,
        -> IF 3-3×6+2 meant ‘negative three multiplied by six’, THEN the three that we can *SEE* , written prior to the negative three we are assuming — by your assumption, evinced by your entire post — we would have ‘three multiplied by negative three multiplied by six, plus two’…. That is not what we have though. Since our assumption — your assumption — led us to a contradiction, your assumption is therefore wrong. You put the quarter in the jukebox, you get to listen to the music….

        What we do have, in truth, is an equation that states ‘three subtract three multiplied by six add two’. Note that my connective words map princely to the terms in “PEMDAS” (aka Order of Operations), such that we know what steps to take, and when to take each step, such that in this case Multiplication comes first; Addition, second; Subtraction, third.

        For these reasons, we can rewrite our equation — “three subtract three multiplied by six add two” — as (with parentheses now, for ease) “three subtract ((three multiplied by six), add two).”, and I’ve written that way to indicate the Order of Operations. PEMDAS: in this case M, A, S; Multiplication, Addition, Subtraction.

        Therefore, we can rewrite our equation as “three subtract twenty”. This brings us correctly and truthfully to negative seventeen.

        Like

      • That is a long explanation that is still wrong. Type the equation into any search engine (Google, Bing, Yahoo, Wolfram Alpha, etc.) and they will confirm the answer is -13.

        Like

      • The length of an answer does not determine its validity…

        However, I have discovered that I am nonetheless WRONG… I am wrong and your answer (-13) is CORRECT. SO, again, I admit that I am wrong and you are right.

        However, that does not answer the reason of why I am wrong.

        I am wrong because subtraction does supersede addition in cases where — barring any parentheses (which in this case there are none) — the subtraction sign is written prior to the addition sign. In other words, if the subtraction sign comes before the addition sign (reading the equation from left to right) then you do subtraction first.

        You could have easily just said that, “subtraction before addition when written first and no parentheses.”…

        Thank you

        Like

      • Thank you for your update.

        The parenthesis/brackets in the order of operations just forces you to calculate that part of an equation before the rest of the equation, this overriding the normal sequence. Without parenthesis/brackets you still have to perform multiplication and division before addition and subtraction. However, multiplication and division can happen at the same time (left to right) and then addition and subtraction happen at the same time (left to right). But Order of operations is not where you went wrong by saying the answer is -17. After correctly multiplying 3 by 6 first you are left with 3 – 18 + 2

        If you calculate left to right, you get 3 – 18 + 2 = -15 + 2 = -13. But you can still calculate right to left and get the correct answer of -13.

        The issue is that 3 – 18 + 2 is not 3 – 20. It is 3 – 16 which then give -13.

        You can see this if you think about the equation in different ways.

        Subtraction is the same as adding a negative number, so 3 – 18 + 2 becomes 3 + -18 + 2 = 3 + -16 = -13

        Adding parenthesis/brackets (remembering that if there is a minus in front, you must flip the signs inside), so 3 – 18 + 2 becomes 3 – (18 – 2) = 3 – 16 = -13

        Changing the layout of the sum also gives the correct answer 3 – 18 + 2 becomes the sum of (3, -18 and; 2) …. Note: extra zeros added to help with formatting tens and units.

        003
        -18
        002 +
        —
        -13
        —

        That’s why all the number line examples are provided in my article. I hope that explains more, and thanks again for your correction reply.

        David

        Like

      • Yes. The equation and result make a lot more sense now. Thank you for sharing all your work.

        It took me a while to see how you were getting 3 – 16 but I see you:

        3 + (-3×6) + 2 : 3 + (-18) + 2 which gives either,

        3 – 18 + 2 : -15 + 2
        Or,
        3 + (-18 + 2) : 3 + (-16) : 3 – 16

        Like

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  5. You clearly need to go back to grade school pemdas buddy 3×6 first then minus your answer which would be 18 by 3 which wiki give yo 15 then add 2 for a final answer of 17

    Like

    • Victor, I am sorry but you are WRONG.

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

      You cannot ignore the minus sign in front of the second 3.

      Try summing this… in vertical format:

      3
      -18
      2 +
      —
      ?

      David

      Like

    • Sorry sir, am not still convinced -13 is the answer. In the roles of BODMAS we have to respect the arithmetical signs from left to right, and each sign have to be delt with separately one after the other. So i still think -17 is the correct answer.

      Like

      • The Order of Operations rules take precedence over left to right. Anyhow, you must have used to rules to get to the 3 -18 + 2 stage. But if you then do left to right how do get -17? 3 -18 + 2 = -15 + 2 = -13 or 3 – 18 + 2 = 3 – 16 = -13. Just add together 3, -18 & 2 it equals -13.

        Like

      • PEMDAS.Multiplication first 3×6=18. The addition 18+2=20. The subtraction 3-20 =-17 You made up your own rules to get to -13.

        Like

    • Hi Linda. I agree, but you still need to understand how to perform operations in the correct order if there are no brackets used. Anyhow I think more people are getting the subtraction and addition part wrong than those not performing the multiplication first. David.

      Like

  9. When I did the problem I came to the answer to being 17.I got 17 because I did addition before subtraction.So my question is,”even though I got a different number could the answer be 17?,”

    Like

    • Hi Jamie

      It makes no difference whether you do subtraction before addition or addition before subtraction. your mistake is that you ignored the minus sign.

      3-3×6+2 = 3-18+2
      3-18+2 = -15+2 = -13 or
      3-18+2 = 3-16 = -13.

      -18+2 is -16 not -20 and 3-20 is -17 not 17.

      If you don’t make mistakes there is only one correct answer and that is -13.

      David

      Like

  15. what if you say so 3-3 (9) x 6 = 56 + 2 = 58 -3 = 55 and or,
    3-3 x 6 + 2 = 2
    3-3 x 6 +2 = 36 + 2 = 38 – 3 = 35 …….so many variable crap 55,2,0,35 -17 , – 13

    Like

  16. The answer is 17 ok apply bedmas ‘I was taught it was “brackets exponents multiplication division addition subtraction’
    3 x 6 = 18 18 – 3 = 15 15 + 2 = 17

    Like

  17. 3-(3×6)+2=
    3-18+2=
    3+(-18)+2=
    (3+(-18))+2=
    -15+2=
    -13
    Or
    3-(3×6)+2=
    3-18+2=
    3+(-18)+2=
    3+((-18)+2)=
    3+(-16)=
    -13
    Or
    3-(3×6)+2=
    3-18+2=
    3+(-18)+2=
    3+2+(-18)=
    (3+2)+(-18)=
    5-18=
    -13
    Is There anything wrong with solving the problem this way?

    Like

    • Math needs wide imagination.. in order to do that you have to solve it only in imagination step by step verbal by mouth.. 3-3=0×6=0+2=2
      Take note .. this is only simple equation. Not at algebraic… Just imagine by adding bracket your changing the problem.. that’s why Einstein’s iq are too high because of deep imagination..

      Like

      • Don. By not solving the equation as a whole you are using your imagination to change the equation and hence get the wrong answer. The question is not (3-3)x6+2, but that is what you are solving. Solve the equation asked, not one you made up.

        Like

    • Hi Frank

      Because it is not 18 add 2. It is -18 add 2. You cannot ignore the minus sign.

      Change the sum to 3 + -18 + 2 which is the same as 3 – 18 + 2 if that helps.

      Also additional and subtraction have the same order of operation precedence and should be performed from left to right. 3 – 18 = -15 + 2 = -13.

      David

      Like

  20. Odd because I don’t see the negative numbers in the equation. I see it as
    3 minus 3 times 6 plus 2 = 2
    Not: 3 minus -3 times 6 plus 2=
    Which by reason should look like: 3- -3×6+2=? not 3-3×6+2=?

    Like

    • Hi Charles

      Subtracting a positive number is exactly the same as adding a negative number of the same magnitude.

      Eg: 10 – 6 = 4 or 10 + -6 = 4

      So 3 – 3 x 6 + 2 could be expressed as 3 + -3 x 6 + 2

      In your example you doubled up the negative and two negatives cancel to make a positive which means you have changed the equation.

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

      The solution is -13, it always has been and always will be. Type either “3 – 3 x 6 + 2” or “3 + -3 x 6 + 2” into google.com or bing.com and it will tell you -13.

      Like

  22. Seriously.. What if you solve it by mouth..step by step verbal expression.. 3-3= 0 ×6=O+ 2..
    Math is beyond imagination ….this is only simple equation not algebraic..

    Like

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  26. yepp i got – 13 because in BODMAS the addition and subtraction do not go addition first it goes in the order of the question like wise with division first it isn’t it is only what comes first in question

    Like

    • Hi Ethan

      Multiplication and Division can happen at the same time as long as they are before addition and subtraction which can also happen at the same time.

      Division is just multiplying by the inverse of the number (1/number) and Subtraction is just adding the negative of the number (- number).

      The answer will be the same regardless.

      David

      Like

  30. 3-3×6+2
    So if you have in your bank £3
    Next day you have an birthday and 6 people give you £3 quid each in total sums up to £18 + £3 in bank total of £21
    Following day you decide to treat your self with the shoping and buy your self some sweets at supermarket. At the till bill comes to £21 exactly what you have. You decide to pay with cash and card but as you reach in your pocket you realise that there is an hole inside it and you lost your £18 but thank God bank let’s you go into overdraft so you end up with £-15 in your bank account and your treats. As day goes pass you are at your sofa looking for TV control but instead you find £2 quid which makes you now only £-13 worth. So answer is -13 and not always birthdays are good days 🙃

    Like

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