Last week, I posted a couple of articles with a maths problem that has been trending on the Book of Face. If you have not read them and answered the poll in the first article, please do that now:

The reason for this third article is that the poll shows that less than 50% of the respondents answered correctly.

Many of those who understand the concept of Order of Operations (do the multiplication or division first) failed to apply it properly and of those who did apply it correctly, then failed to perform the addition or subtraction parts correctly.

So here is the question again:

And here is the answer broken down into steps:

- 3 – 3 x 6 + 2

Apply the Order of Operations. The mnemonic I remember is BIMDAS (Brackets, Indices, Multiplication/Division, Addition/Subtraction), which for this simple equation just tells us to do the multiplication first:

- 3 –
**3 x 6**+ 2 - 3 – 18 + 2

Now we can just perform the addition and subtraction as I read the line (from left to right):

**3 – 18**+ 2- -15 + 2

Remembering number lines, with negative numbers on the left of the zero and positive numbers on the right. If I have a negative number and add a positive number to it, it will make the result less negative.

**-15 + 2**- -13

So the correct answer is -13.

The most popular incorrect answer was -17. This is the answer you will get if you correctly apply Order of Operations, but then incorrectly add 2 to -15. Below is an example to help you with this:

If I lend you $15, so you owe me $15. You then pay me back $2, you now owe me $13. Not $17.

[Edit] Also, I have seen 3 – 18 + 2 incorrectly written as 3 -(18 + 2) = 3 – 20 = -17, however there is a minus sign in front of the brackets and so just adding the brackets has flipped the sign on the number 2.

To be correct: 3 – 18 + 2 = 3 – (18 – 2) or 3 + (-18 + 2) = 3 – 16 = -13.

You can think of the sum as 3 + -18 + 2 if that helps.

The next most popular incorrect answer was 2. This is the answer you will get if you ignore Order of Operations and just calculate each part of the equation from left to right.

- (3 – 3) x 6 + 2 = 0 x 6 + 2 = 0 + 2 = 2

The last of the most popular incorrect answers I will discuss is 0. This is the answer you will get if you incorrectly apply Order of Operations and perform the addition or subtraction before the multiplication or division.

- (3 – 3) x (6 + 2) = 0 x 8 = 0

So why is this number line stuff so important… other than meaning that you can solve simple equations?

The reason is that it is the basis of accounting and that is what most of you reading my blog will be involved with in some way (Considering that I have based my career around ERP systems and specifically Microsoft Dynamics GP).

In my next couple of articles, I will discuss how I learnt accounting principles and the maths behind them (including number lines). I will also give you another maths challenge and see if more of you can get the correct answer.

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 = ?? Provides Answer and common errors
- Conclusion: Only for genius ?? 3 – 3 x 6 + 2 = ?? This article
- 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

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

**17-Feb-2016:** Added other explanation of why people are getting -17.

My Dear Aunt Sally. That’s the order: Multiple, Divide, Add, Subtract. That’s how I remember.

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Belinda, that mnemonic does not include brackets/parentheses or indices/orders/exponents.

My first article has mnemonics for all 6 operations.

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Correct. If there are brackets, then those are always done first.

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Thank you kindly, one is never too old to learn.

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