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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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 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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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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