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

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.

 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:

Enjoy

David

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

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

1. Do I get points for a wrong answer if I didn’t learn this in school? Lol
I don’t get how it can be a negative number though. How did the 18 turn into a negative?

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• Hi Tina

Did you not learn to multiply first at school? They should normally spend some time discussing order of operations. PEMDAS or BODMAS or something similar.

Now 18 did not turn negative, it was always negative because the 3 was negative.

Subtracting a number is the same as adding a negative number. So if you think of the question as 3 + -3 x 6 + 2 = ?. Then -3 x 6 = -18. So it becomes 3 + -18 + 2 = ?

Then use a number line (negative on left, zero at the middle, positive on right). …, -4, -3, -2, -1, 0, 1, 2, 3, 4 …. etc. Subtract positives or adding negatives moves left on the line. Adding positives or subtracting negatives moves right on the line.

Starting at 3 add -18 (or subtract 18) = -15. Then add 2 = -13.

David

PS: Sorry no points for wrong answers. Maybe half points if you show your workings. 🙂

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• Hi Peter

You just solved 3 – 3 x 6 – 2 correctly. Now can you solve 3 – 3 x 6 + 2?

Addition and Subtraction can be performed at the same time and you will always get the same result if you do it correctly. The order is irrelevant as long as it is after Multiplication and Division (which can also be performed together).

So you have 3 – 18 + 2

Subtraction first (Left to Right): 3 – 18 = -15, so -15 + 2 = -13

Addition first (though it is not required): -18 + 2 = -16, so 3 – 16 = -13

Your issue is that the sum is NOT 18 + 2 = 20, but is -18 + 2 = -16

If you don’t believe me, solve 3 + -3 x 6 + 2… which IS the same as the original equation.

David

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2. In public school I was taught BEDMAS, meaning addition before subtraction. If there were brackets around a value with addition being the verb, that would change the + to a -, however, there were no brackets around the remaining “3-18+2”, so why would we not add before subtract in this case?

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• Hi Shannon

The order you perform the addition and subtraction in is irrelevant, the answer will be the same. Subtraction is just adding a negative number.

The mistake many are making is to ignore the fact that the middle number is -18 not 18.

David

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• If this is the case, should there not be brackets around the (-18+2) portion of the equation, leaving 3-(-18+2)?? That would give 3+(-16) ? Or would that change the answer to -19 because the plus & minus would cause a minus??

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• Then shouldn’t there be brackets in order to get -13? Otherwise, would we not add before subtract as in the case of BEDMAS?

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• Hi Shannon

6 – 3 is the same as -3 + 6 equals 3.

The order of subtract and addition is irrelevant. You will always get the same answer regardless of which you do first.

David

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• Hi Shannon

There is no need for brackets to control addition and subtraction as the order they are performed does not affect the result.

It is actually BE(DM)(AS). As division and multiplication can be performed together and addition and subtraction can be performed together.

David

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3. Terrypayne
3-3 is 0 you can’t use x because it comes before the 6 plus 2 answer is 8

This one for you , (in old money before desimalisation ) 5 shillings – 3 Pencader plus 6 pence

What coin in the UK before desimalisation had a Robin on it

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• Hi Terry

You can do the multiplication of zero, as any number times zero is zero.

However, you have ignored the Order of Operations rules which state that you must perform multiplication and division before performing addition and subtraction. So the answer is not 8.

I don’t remember pre decimal coins in the UK, other than in coin collections. I did look up online and see that there was a “Robin” Farthing coin.

https://en.wikipedia.org/wiki/Farthing_%28British_coin%29

David

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• Hi Lynn

Adding the brackets changes the equation entirely. It now says 3 multiply the contents of the brackets rather than 3 subtract the rest of the equation.

3(-3×6)+2 = 3(-18)+2 = -54+2 = -52

David

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4. Maybe this is European, but what I remember from math ed. in Germany is, the equation should read this way: 3 – (3 X 6) + 2 = -13 > that’s grade 6 math, certainly not genius stuff.
Multiplication & Division: 4 x 3 / 2 = 6 and 4 / 2 x 3 = 6 …. The order is irrelevant.
That’s what I wanted to know and didn’t get. The forward dash in the above equation, 4 x 3/2, stands for = 4 x 3 divided by 2. In Europe we would write it this way: 4 x 3 : (2). Sometimes the division sign is also written with a forward slash between the two dots. Matter of language, then, not loss of memory.

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• Hi Jackie

The slash symbol / is the same as the division symbol ÷

It represents a numerator being over a denominator, such as 1/2 = 1÷2 = a half.

The / is used on computers for division in the same way * is used for multiplication.

Even though this is primary school level maths, the number of people who get it wing amazes me.

David

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• Thanks David. So, this single forward slash hanging between numbers being recognized as a division symbol is a computer age change then, or was it used and understood here in America before, say, in the 1960ties? As I said, that’s the thing which threw me, having come across it yesterday.

Regarding your astonishment about general lack of math skills, et al, just remember that something around 20% of people are ‘functional illiterates’, according to stats from government. Add to that the ‘Peter Principal’ with another 50%, give or take > and so on; we should not be surprised > sadly.

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• Hi Abigail

As multiplication and division can be performed at the same time, the order of M and D can be switched without affecting the results. Division is just inverted multiplication.

The same goes for Addition and Subtraction, they can be performed and same time and so the A and S can be switched. Subtraction is just negative addition.

Some people learn the menomic as BI[MD][AS], with the brackets indicating that multiplication and division can be performed together as long as they are done before addition and subtraction (which also can be performed together).

David

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