After 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

The correct answer is as follows:

- Question: 3 – 3 x 6 + 2
- Multiplication first: 3 – 18 + 2
- Left to right: -15 + 2 (or Addition first: 3 – 16)
- 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:*

*Question: 3 – 3 x 6 + 2**Multiplication first: 3 – 18 + 2**Addition next: 3 – 16**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.*

*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.

- 3 = 3
- 3 – 3 = 0
- 0 x 6 = 0
- 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:

- Trending: Only for genius ?? 3 – 3 x 6 + 2 = ?? With Poll and Order of Operations
- Answer: Only for genius ?? 3 – 3 x 6 + 2 = ?? This article
- Conclusion: Only for genius ?? 3 – 3 x 6 + 2 = ?? Breaks down solution into steps
- The Last Word: Only for genius ?? 3 – 3 x 6 + 2 = ?? Explains ordering of DM and AS
- Viral: Only for genius ?? 3 – 3 x 6 + 2 = ?? Answer has gone viral and explanations

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.

Ans. 1st is 2

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Only if you ignore the order of operations rules… Which means you are incorrect.

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Ignoring the operation would result to a wrong answer. PEMDAS method is applicable and i think the answer for that is -13

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4-3×4+3=

#1 3×4=12

#2 12+3=15

#3 15-4=11

Perfect

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Luis, that is wrong. You can’t swap the order and you calculate left to right if no other order is specified.

3×4 = 12

4-12 = -8

-8+3 = -5

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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

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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

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Thanks, I never knew this. We can always learn every day.

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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.

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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.

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3-3=0

0×8=0

Definitely answer is zero

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Hi Anwar.

Please search Order of Operations on the internet or read my articles to learn why you are wrong.

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I agree with zero.

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Then you would be wrong. You must use order of operations, which means perform the multiplication and division before the addition and subtraction.

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I think it would help if you used the () in your problems it makes the problem clearer.

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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.

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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?,”

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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

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3(6+2)-3(6-2)=

Please solve that for me immediately

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Hi Emmanuel.

3(6+2)-3(6-2) = 3*8-3*4 = 24-12 = 12

David

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3(6+2)-3(6-2)

3(8)-3(4)

24-12

12

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Tks ! Love the explanation where it does not led one, to believe his not a genius ! Way to go ! Two thumbs up

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Hi Roberto

Thanks for the feedback.

David

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3-3*6+2=?

3-3(6+2)=3-3(8)

3-24=-21

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Hi irakozebrian

The sum you solved with the added brackets is correct, but it is not the question that was asked. By adding the brackets you changed the question. Try again without adding brackets.

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6

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Wrong.

Show some working so we can see where your mistake was.

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9

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Are you just picking random and incorrect numbers? Show us some working so we can see where you made your mistakes.

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3

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Just guessing now.

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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

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Hi James

There is only one answer if you follow the order of operations rules and perform the calculations correctly.

David

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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

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Hi Isabella

Sorry the answer is not 17. You cannot swap 3 – 18 to 18 – 3, that changes the equation.

3 X 6 = 18, 3 – 18 = -15, -15 + 2 = -13

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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?

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No, because you got the correct answer all 3 times. So glad you can do basic maths. 🙂

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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..

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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.

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3+3×6+-2=?

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3+3×6+-2= 3+18-2= 19. Why do you ask?

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In your example of addition first, why does 18+2 leave 16? 18+2=20 so 3-20 = -17

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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

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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=?

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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.

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Shouldn’t you follow the BODMAS rule

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Hi Emily. Exactly. The answer is -13 if you follow the order of operation rules.

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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..

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Hi Don. You could but you would be wrong. This is how a simple calculator would solve it, but that is because it has no understanding of the Order of Operations rules. David

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Its sort of cringe that you still try to trick people to reply with a false answer

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I am more worried about your user name. The answer is -13 and always will be. Just ask Bing or Google or anyone who understands mathematics.

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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

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If you follow the order of operations it is -17

3-3×6+2

3-18+2

3-20

=-17

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PEMDAS

PARENTHESES

EXPONENTS

MULTIPLE

DIVIDE

ADD

SUBTRACT

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Sadly Nicole you are wrong.

3-18+2 is not equal to -17

3-18+2 = -15+2 or 3-16 = -13

Add 3, -18 & 2 together gives -13

David

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I thought multiplication would go first using pemdas ( parentheses, exponents, multiplication, division, addition, subtraction).

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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

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