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 https://www.winthropdc.com/blog.
If you go by pemdas your supposed to add before you subtract… giving you -17
Hi Mindy
PEMDAS means Parentheses, Exponents, (Multiplication/Division), (Addition/Subtraction). The Multiplication and the Division are performed at the same time and but before the Addition and Subtraction which are performed at the same time.
However, even if I perform the addition first, the answer is still -13.
3 – 3 x 6 + 2 = 3 – 18 + 2 = 3 – 16 = -13
because -18 + 2 = -16 not -20
Think of the sum as 3 + -18 + 2 if that helps.
Please see the third post in the series which discusses this further:
https://winthropdc.wordpress.com/2016/02/15/conclusion-only-for-genius-3-3-x-6-2/
David
One:
3 – 6 x 3 + 2
= 3 – (6 x 3) + 2
= 3 – 18 + 2
= 3 – (18 + 2)
= 3 – 20
= -17.
Two:
3 – 6 x 3 + 2
= 3 – (6 x 3) + 2
= 3 – 18 + 2
= (3 – 18) + 2
= -15 + 2
= -13.
BEDMAS does NOT identify the order of the operations of Addition and Subtraction. You need to do “Left to Right Association” yourself. Many would argue that Addition comes BEFORE Subtraction. In such a case, they will get a different answer if they do NOT see the minus sign as negative 18 [Addition of a negative: 3 + (-18 + 2)].
So you’re not a Genius for know the rule of Left-To-Right Association which American teachers do NOT teach
.
Hi Bleh
Solution Two is correct. Well done.
For Solution One you made a fundamental error. When you added brackets you failed to change the sign of the 2 when you moved it inside the brackets which have a minus sign in front of them. If you must add the brackets you MUST also change the sign. Then the calculation will work.
3 – 6 x 3 + 2
= 3 – (6 x 3) + 2
= 3 – 18 + 2
= 3 – (18 – 2)
= 3 – 16
= -13.
Maths is an exact science and will ALWAYS give the same answers as long as you don’t break any of the rules.
David
Yes. I showed it to an engineer at lunch today and he said -17. However, that was after he said 2, which is what I say. This is not how you measure IQ anyway. A person with high IQ figures the problem out without knowing any pre-existing rules.
Hi Sandy
Can I suggest you ask your engineer to read this blog article and its comments?
David
hi Mindy!
you’re right, PEMDAS is the rule in every equation which means
3 – 3 X 6 + 2 =
3 – (3 X 6) + 2 =
3 – 18 + 2 =
-15 + 2 = -13
because -18 + 2 = -16 and not -20
Initially this equation definitely reduces to
-13 = ??.
But if you interpret it as a trick question (which many of these viral Facebook math problems are) then it’s also possible to apply a square root on each side of the equation (in order to reduce the two question marks into one). Due to the trickiness of extracting the square root of a negative number, the resulting equation ends up requiring a complex number like this:
? = √13⋅i.
At least now we have left the confines of primary school math, but I don’t know if it qualifies as “genius”.
Hi Simen
I think you are over thinking this one. I don’t think that the use of complex numbers was ever in the plans of the person asking the question. I think it was just an over use of punctuation that seems common nowadays!!!!!!!!
David
Or bodmas…. same answer.
Hi Anthony
Look at the first post in the series:
https://winthropdc.wordpress.com/2016/02/09/trending-only-for-genius-3-3-x-6-2/
It has 12 variations of the order of operations mnemonics, depending on the terminology you were taught.
What answer did you get?
If you got -17 then you have incorrectly added -18 + 2. You cannot ignore the minus sign.
If you got -13 then well done.
David
To prove you’re a genius, you have to figure the problem out without prior knowledge of the rules. Going left to right, the answer is 2. You may have the right answer because you know the “rule” but that doesn’t make you a genius.
Hi Sandy
I just took the image from the internet which had the wording “Only for genius” already on it. I do agree that figuring out the problem is important.
However, there are some basic maths rules which are needed to make it work.
For example: If you reorder the equation, what answers do you get when calculating left to right?
3 – 3 x 6 + 2 = 2
2 + 3 – 3 x 6 = 12
2 – 3 x 6 + 3 = -3
–3 x 6 + 2 + 3 = -13
If you follow the order of operation rules ALL of the above equations give the same answer = -13.
David
Nothing about the question makes you a Genius, whether you know what BEDMAS (or PEMDAS depending on where you live) is or not. Going left to right, the answer is 2, unfortunately that’s not how you do math equations. Order of operations has been around since at least the early 1600’s; its argued that its been around much longer though, as Greek and Romans did not use symbols to do math. I would need to do more research to say for sure, but we can safely say its been around for minimum 400+ years.
In the end its a very basic Elementary Math question that is making fun of how many people in the world cant do basic math. Which is funny given that you need to answer an Order of Operations question for almost every contest/lottery reward. I assume so they don’t give the money to idiots who would waste it. I would recommend remembering how to do this, it could be important in anybody’s future.
Hi Bob
Great comment. After that I do hope you got the correct answer. 🙂
In my related post (see link below), I came up with 12 variations of the order of operations mnemonic depending on whether you use parenthesis or brackets and whether you use orders, indices or exponents.
https://winthropdc.wordpress.com/2016/02/09/trending-only-for-genius-3-3-x-6-2/
David
Hi Sandy
Try this:
You are an apple farmer. You can sell apples individually or in a carton of 6 apples.
You have 3 apples available when a shop asks for 3 cartons to be supplied.
You give the individual apples you have to the shop and promise to supply the rest.
2 more apples are now ready for picking and so you also supply those to the shop.
How many apples do you still owe to the shop?
David
3-3×6+2= -13
I see 3×6=18
But how does it turn to -15
Hi Ed
I could not work out how to get -15, but it was in the list of answers I saw on the original Facebook post. I think it comes down to just not being able to do addition.
David
hi Ed!
-15 derives from adding the first number which is 3 to -18 which derived from (-3 X 6) where when you add 2 with -15 will give you -13 as the answer.
Why the two ??
Hi James,
The two question marks are on the image that was doing the rounds on the internet. I did not create it and don’t know who did. If you can identify the creator you can ask them !! 🙂
David
A teaser. What if ? represents x in algebra
-13=??
-13=?squared
?=square root of -13
?=3.60555126 i
Or impossible because you can’t have the square root if a negative number.
Hi Clancy, The creator of the original image got over excited with the question marks, but I am glad you have solved for a single question mark. The use of imaginary numbers based on the square root of -1 (represented as i) is allowed. 🙂
Why would you do the subtraction before the addition of the addition comes first in order of operations? I came up with -17 by doing the addition first.
Hi John
The order of operations mnemonic is designed to ensure that you perform the multiplication and division before the addition and subtraction. The actual order of multiplication and division (or division and multiplications) will not affect the answer. Also the actual order of addition and subtraction (or subtraction and addition) will not affect the answer.
Your calculation error is covered in my final post on the topic: https://winthropdc.wordpress.com/2016/02/29/the-last-word-only-for-genius-3-3-x-6-2/
Basically you jumped from 3 – 18 + 2 to 3 – 20. The mistake is that -18 + 2 is not -20, it is -16. When you add to a negative number, you make it less negative. See my post above for a full explanation.
David
Why don’t you apply “BODMAS” rule?
Hi Thabiso
I did apply BODMAS. The answer is still -13.
Note that Division and Multiplication can be performed at the same time as long as they are executed before Addition and Subtraction, which can also be performed at the same time.
However, if I do it exactly in BODMAS order you still get -13.
3 – 3 x 6 + 2 = 3 – 18 + 2 = 3 – 16 = -13
I suspect you are thinking I did the addition wrong, but when you add -18 + 2 you get -16 not -20. Just draw a number line and move 2 places right from -18 to -16.
Did you look at the other articles in this series which explain why the answer is always -13? Especially the “Last Word” article.
Yours Mathematically
David
in my opinion it should be 0 because in badmas rule. first + ad – is solved then * and /.
no matter what the order is.
until u use brackets and explain the question.
why we are suppose to solve the * first. we must not as the brackets are not present
Hi Muhammad
You have two “a”s in your mnemonic. The second letter should be I (indices), O (orders) or E (exponents).
Mulitiply and divide are always performed before addition and subtraction.
Look at the other articles, especially the last one which has links to online sites solving the sum.
I understand why it is -13 but using the same method used to get -13 if you do the addition then the subtraction you get -17
3 – (3×6) + 2 =
3 – 18 + 2 =
3 – 20 = -17
And you can’t say that right to left the answer is -13 because saying that is -18 is to assume
3 (-18)+2 or
3 – (-18) + 2
Hi RicknMorty (great show)
Ok, you agree that you need to do 3×6 first to get 18. Except that it is actually -3×6 = -18.
So 3 – 18 + 2 = -15 + 2 = -13
Or 3 – 18 + 2 = 3 – 16 = -13
Or 3 – 18 + 2 = 5 – 18 = -18 + 5 = -13
Regardless of the order you do the addition and subtraction the answer is the same -13.
If you think about it as the following it might make it easier, especially if you use a number line:
3 – 18 + 2 = 3 + -18 + 2
Don’t subtract 18. Add negative 18.
Regardless as long as you do multiplication and division before addition and subtraction the answer will always be -13. The order that you do the multiplication/division in is not important: 3 x 6 = 6 x 3 = 18. The order that you do the addition/subtraction in is not important: 2 + 3 = 3 + 2 = 5 or 3 – 2 = -2 + 3 = 1.
David
I just want to know how you know that it is negative 3 because i see it as 3 minus 3??
Hi Keith
The order of operations rules say that you must perform multiplication and division BEFORE addition and subtraction. So even though there are no brackets you must treat it as though there are brackets around multiplications and divisions.
3 – 3 × 6 + 2 = 3 – (3 x 6) + 2 = 3 – (18) + 2 = 3 – 18 + 2
Now have a look my previous comment response to see how 3 – 18 + 2 = -13
Also look at the other articles in the series which provide more details.
David
I will be
3 – 3 × 6 + 2 = ????
3 – 3 = 0
6 + 2 =8
Now 8 × 0 = 0
Hi Rumi
Sorry but your answer is incorrect.
Mathematical principles say you MUST calculate the Multiplication and Division before Addition and Subtraction.
David
But of there are no brackets don’t you skip that part?
Hi Yoshi. Order of operations says multiply and divide before addition and subtraction. No brackets needed.
(3-3)*(6+2)=0
Sorry Raj but that was not the question asked and so is not the correct answer.
If you must put brackets/parenthesis around part of the equation then it must be around the multiplication as Multiplication and Division must always be performed before Addition and Subtraction.
3 – (3 x 6) + 2 = 3 – 18 + 2 = -15 + 2 = -13
Why is it not 3-18+2 = 3-(18+2) = 3-20?
You do the addition before subtraction. So you add 18 and 2.
You do not add -18+2 as the minus sign should be outside the brackets. You only use it once so you are taking the sun of (3×6)+2 away from 3.
If it is (-3×6) then suddenly your sum becomes 3 (-3×6)+2. This would be -54!
Hi Ian
Order of operations says that Multiplication and Division should be completed before Addition and Subtraction. However, Multiplication and Division can be performed at the same time as can Addition and Subtraction.
3 x 4 / 2 = 4 / 2 x 3 = 6
3 + 4 – 2 = 4 – 2 + 3 = 5
The order is not important. if you really need to add parenthesis/brackets:
3 – 3 x 6 + 2
= 3 + -3 x 6 + 2
= 3 + (-3 x 6) + 2
= 3 + -18 + 2
= -15 + 2
= -13
David
I thought using bedmas addition would be first so 3×6+2-3=17??
Hi Cameron
The sum you state does calculate to 17, but it is NOT the sum in the question.
3 – 3 x 6 + 2 = 3 – 18 + 2 = -15 + 2 or 3 – 16 = -13
In your bedmas, division and multiplication are performed together before addition and subtraction are performed together.
The issue is that -18 + 2 is -16 not -20.
David
Why wouldn’t you solve like this: 3-[(3*6)+2] ?
Don’t you have to do Addition before Subtraction?
Hi Nick
3-[(3*6)+2] is not the question.
3+[(-3*6)+2] is the question if you add brackets.
Please see https://winthropdc.wordpress.com/2016/02/29/the-last-word-only-for-genius-3-3-x-6-2/ which explains that the order of Addition & Subtraction and Multiplication & Division is irrelevant as long as Multiplication & Division is performed before Addition & Subtraction.
Doing Addition before Subtraction or Subtraction before Addition will ALWAYS give the same result if you do it correctly.
David
The answer cannot be -17 it is -13 and the reason is because of pedmas. Parenthesis exponent division multiplication addition then division. So 3-3×6+2=? U start with -3×6 which gives you -18 so the new equation is 3-18+2=? Next we go -18+2 =-16 New equation is then 3+-16=-13. If we say 3-3=0 is it not the same as 3+-3 = also 0. Another way of looking at it is 3-3×6+2 is the same as 3+-3×6+2=? Same operation -18 +2=-16 3+-16 still equals -13. That’s where the confusion lies because you can’t do 3-3×6+2=? And think you do 18+2= 20 therefore 3-20 = -17 it makes no sense that way because you forget it is already -3 to begin with not 3
Why not: 3 (-3×6)+2? =-52 how do you know whether it’s just 3 not -3?
Hi Danielle
The question is 3 – 3 x 6 + 2 = ?, which could be written as 3 + -3 x 6 + 2 = ?
This is not the same as 3(-3×6)+2=? as you have effectively written 3x(-3×6)+2=? which changes the + sign after the first 3 to a x sign.
If you must add unnecessary brackets then the question is either
3 – (3 x 6) + 2 = ? or 3 + (-3 x 6) + 2 = ? both of which give the answer -13.
David
Do none of you realise the order is Brackets, Order, Division, Multiplication, Addition, Subtraction in that order?
So, as it should go is as followed:
Multiplication: 3×6 = 18
Addition: 18+2 =20
Subtraction: 3-20= -17
That is straight forward mathematics that is taught to 11 year olds in schools….
Hi Dwayne
You are correct on the order, but forgot to note that Addition and Subtraction can be performed together, or any order and the answer will always be the same… if you do it correctly.
Your issue is that you changed the sign of the -3 value.
Multiplication: -3×6 = -18
Addition: -18+2 = -16
Subtraction: 3-16 = -13
or
Multiplication: -3×6 = -18
Subtraction: 3-18 = -15
Addition: -15+2 = -13
Try solving 3 + -3 x 6 + 2 as this is the same as 3 – 3 x 6 + 2 but will help you keep the sign.
Multiplication: -3×6 = -18
Addition: 3 + -18 = -15
Addition: -15 + 2 = -13
Look at https://winthropdc.wordpress.com/2016/02/29/the-last-word-only-for-genius-3-3-x-6-2/ as it shows that Google and Bing say -13 is the answer.
David
Lalu,jika memang -18+2= (-16)….bagaimana cara untuk mengkalkulasikan hasil -16 dengan 3…bisa dijelaskan…karena tanda (-) sudah anda ambil sebelumnya di penjumlahan -18+2 ,come on
Translated: Then, if it is -18 + 2 = (-16) …. how to calculate the results of -16 with 3 … inexplicable … because the sign (-) is already before you take on the summation -18 + 2, come on
caknories
Subtracting a number is the same as adding a negative number.
So 3 – 18 + 2 is the same as 3 + -18 + 2.
Now can you solve it correctly.
David
@dwyne pipe ,aku sependapat denganmu
Translated: @dwyne pipe, I’m in agreement with you
Hi caknories
Sadly, you are still wrong, as is Dwayne. -18 + 2 = -16 not -20
https://www.google.com/?gws_rd=ssl#q=3+%E2%80%93+3+x+6+%2B+2
How can the subtraction sign be used twice in this equation?
3-3×6+2
Not only are u using the subtraction as a minus for the 3-3 part but then you’re subtracting 3.. so really shouldnt it be written as 3 take -3 ×6 +2?
Hi Jake
I only see one subtraction sign in the original equation 3-3×6+2.
Subtracting a number changes the sign, so 3 take -3 x 6 + 2 will change the original equation to 3 – -3 x 6 + 2 which becomes 3 + 3 x 6 + 2
Adding a negative number is the same as subtracting a positive number, so 3-3×6+2 can be written was 3 + -3 x 6 + 2 without changing the equation.
Just solve the original equation, do the multiplication first, then do addition and subtraction together from left to right.
3-3×6+2 = 3-18+2 = -13
If you want to add brackets, try (3 – (3 x 6)) + 2 = (3 – 18) + 2 = -15 + 2 = -13
David
I don’t get why the number is negative, it’s just the subtraction symbol?
Hi Mr Me
What is the difference between 10 – 5 and 10 + -5?
Nothing, the answer is 5 for both.
Because, subtracting a positive number is the same as adding a negative number.
David
Thank you for the challenge of my brain😀
Hi.
Okay. I understand that you did the multiplication first, which left the equation as:
3-18+2=
What I don’t understand is why you then reverted to “left to right”. When I was at school, we would not have then gone “left to right” after the multiplication. We would have continued to apply BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction). That means we would then have done the addition 18+2. That reduces the equation to:
3-20.
Ergo, the answer is -17.
Was I taught incorrectly or has the process changed over the years?
Thanks,
Peter.
Hi Peter
The mnemonic is actually BO[DM][AS] as the Division and Multiplication can be done at the same time as can the Addition and Subtraction. That’s why some people know the mnemonic as BOMDAS.
Either way, your maths is incorrect, The addition is -18+2 = -16 then 3-16 = -13
I think that people believing the addition must be done before subtraction combined with ignoring the fact that 18 is a negative number is why so many people incorrectly get -17.
3-18+2 will always equal -13 regardless of the order you do the calculations.
3-18+2 = -15+2 = -13
3-18+2 = 3-16 = -13
3-18+2 = 5-18 = -13
3-18+2 = -18+5 = -13
David
Yes, demikian saya setuju (-17) is answer bro
Translated: Yes, so I agree (-17) is answer bro
Hi caknories
Both you and Peter are mistaken
https://www.bing.com/search?q=3+%E2%80%93+3+x+6+%2B+2
14
Hi Surjyamani
I have no idea how you got the incorrect answer of 14. Please tell us what you did, so we can work out your error.
David
PEDMAS = -13
3 – 3 x 6 + 2
3 – 18 + 2
-15 + 2
= -13
BODMAS = -17
3 – 3 x 6 + 2
3 – 18 + 2
3 – 20
= -17
Previously you have said the BEDMAS multiplication equals -18, this is incorrect. The negative number is the result of the subtraction not the multiplication. If it weren’t then the PEDMAS equation would equal 23 as it would be 3 minus negative 18 plus 2
3 – 3 x 6 + 2
3- -18 + 2
21 + 2
= 23
Quentin, How can you solve the same sum correctly once and incorrectly twice?
The first sum you solved was the original question 3 – 3 x 6 + 2.
The second sum you solved was 3 – 3 x 6 – 2 (Note sign on number 2 changed).
The third sum you solved was 3 – -3 x 6 + 2 (Note sign on number 3 changed).
The wonderful thing about maths is that if you do it correctly, it will ALWAYS give the same answer. In this case -13.
David
PS: PEDMAS and BODMAS are the same, just using Parenthesis vs Bracket and Exponent vs Order. It is a terminology difference only depending on where you live and what you were taught.
See the original post in the series which shows 12 variations of the mnemonic: https://winthropdc.wordpress.com/2016/02/09/trending-only-for-genius-3-3-x-6-2/
13 is not the correct answer.
The answer is – 17.
3-3×6+2=
3-(3×6)+2=
3-18+2=
3-(18+2)=
3-20=-17
There is no way you can subtract before you add.
There are rules that need to be followed.
So in that order you multiply, add then
subtract.
Hi Shanett
Sorry, you are wrong.
3-18+2 is not equal to 3-(18+2)
If you must add the brackets, it will become 3-(18-2) due to the minus sign.
3-18+2 is the same as 3 + -18 + 2
Whether you do subtraction or addition first the answer is the same -13.
Addition and subtraction are the same, just subtraction is adding a negative number. For example Subtract 2 is the same as adding -2.
Multiplication and Division are the same, just division is multiplying by an inverse number. For example Divide by 2 is the same as multiply by a half (1/2).
Type the equation into Google or Bing and you will get -13.
David
I can never understand maths. So difficult to understand. So confusing
Hi Kay
Basic maths like this is not that hard, you just need to remember to do multiplication and division before addition and subtraction.
Division is just multiplication by an inverted number and subtraction is just addition of a negative number.
David
Its an algebraic xpression. Therefore you would replace the x with () indicating cross multiplication the answer is zero. Your notitaion is wrong
Jim,
The x is a multiplication sign. If I wanted to I could have used *, but that is going to be confusing unless you work with software programming.
So, based on the fact that this is not an algebra problem, but a simple mathematics calculation, can you get the correct answer?
David
PS: I did not create the original image, so I take no blame.
PPS: Your spelling of “expression” and “notation” is wrong.
Dearest David your answer is completely wrong. Using BDMAs theory, add and subtract from feet to right as the principles occur , then multiply and divide from left to right, complete inside brackets first, then outside brackets. With this in mind, there are no brackets. Add and subtract first, 3 – 3 = 0 6 + 2 = 8, but any numeral times 0 = 0 the answer must be 0 by definition of the theory, you errored when you applied extrinsic brackets. Cheers.
Jack
You mentioned the order of operations (BDMAS … but missing the I, O, or E for Indices, Orders or Exponents), but then completely failed to implement them.
DM – Division and Multiplication occur at the same time but before AS – Additional and Subtraction which occur at the same time.
Multiply first so 3 x 6 = 18, so 3 – 18 + 2 = -13
David
2+6×3-3=21
Hi Landon
Firstly, the answer to the equation you listed is incorrect as you did not follow the order of operations and perform the multiplication first.
2 + 6 x 3 – 3 = 2 + 18 – 3 = 20 – 3 = 17
Secondly, 2 + 6 x 3 – 3 is not the same as 3 – 3 x 6 + 2
If you really want to reorder the equation, it would be 2 + 6 x -3 + 3
2 + 6 x -3 + 3 = 2 + -18 + 3 = -16 + 3 = -13
The answer is always the same if you follow order of operations and do the calculations correctly. Always -13.
David
In grade school they taught order of operations as: Please (parentheses), Excuse (exponents), My (multiplication), Dear (division), Aunt (Addition) Sally (subtraction)
By doing addition before subtraction it’s a different answer. Did it change at some point? When you say left to right was that the change? Why did you do subtraction before addition when we were taught that it was Aunt (addition) before Sally (subtraction)? I always love learning and looking forward to your response!
Hi Karen
There are many acronyms for order of operations, looks like you learnt PEMDAS. What schools don’t seem to teach is that it is really PE[MD][AS], as both the Multiplication & Division steps, and Addition & Subtraction steps can be performed at the same time.
So as long as you only have addition and subtraction left, you can just go from left to right.
Your error is ignoring the minus sign in front of the 18.
3 – 3 x 6 + 2 = 3 – 18 + 2
Addition first: -18 + 2 = -16, so 3 – 16 = -13
Subtraction first: 3 – 18 = -15, so -15 + 2 = -13
Note that 3 – 18 + 2 is not equal to 3 – (18 + 2), it is actually equal to 3 – (18 – 2). This is because of the minus sign in front of the parenthesis, which means to move the 2 inside the parenthesis you must change its sign.
Subtraction is the same as adding a negative number, so try solving the following which is the same as the original equation. This should help you keep the minus sign.
3 + -3 x 6 + 2
David
Why after you multiply 3×6 that iguals 18
And the math is 3-3 × 6 +2 why 3 -18 =15
When 3 -18 can’t be done
Hi Pete
3 – 18 can be done. It just results in a negative number -15.
Think of this example: If I owe you $3 and you borrow $18 from me. Then I owe you -$15… or (without the negative) you owe me $15.
To finish the last bit of the equation -15 + 2 = -13.
David
Saya berpendapat : 3-3×6+2 = 3-(3×6)+2=3-18+2= 3 – (18+2)=3-20=is Done (-17) MAS >>>MULTIPLICATION,ADDITION,and SUBTRACTION
#ping(x) >> poro(:) >> lan (+)>>sudo(-) …..pingporolansudo ( wong jowo as javanese people )
Translated: I thought: 3-3×6+2 = 3-(3×6)+2=3-18+2= 3 – (18+2)=3-20=is Done (-17) MAS >>>MULTIPLICATION,ADDITION,and SUBTRACTION
#ping(x) >> poro(:) >> lan (+)>>sudo(-) …..pingporolansudo ( wong jowo as javanese people )
caknories
Read the new additional section at the top of the article.
Your mistake is that 3 – 18 + 2 is not equal to 3 – (18 + 2) because there is a minus sign in front of the brackets, the 2 must change its sign when brought inside the brackets. 3 – 18 + 2 is equal to 3 – (18 – 2).
It is also the same as 3 + 2 – 18, +3 + -18 + +2 or 3 + (-18 + 2). All of which have the same answer … -13 regardless of whether you add or subtract first.
David
So where does it state that the ( – ) minus sign represents being negative? It doesn’t. Usually when a number is negative the symbol is in front of the number. 3-3×6+2 so it works go 3×6=18 then 3-18=15 and finally 15+2=17 so the correct answer would be 17 and not -13.
For that to be the answer the problem would have to be -3-3×6+2 and that would work out
3×6=18 and then -3-18=-15 then -15+2=-17
So then the answer would be -17
Hi Demetrius
All numbers are either positive or negative. Negative numbers have a minus in front of them and positive numbers have a plus 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 =
Left to right: +3 -18 +2 = -15 +2 = -13
or Add first: +3 -18 +2 = +3 -16 = -13
In your calculations, you are ignoring the minus sign sometimes and not other times. For example: 3-18=-15 not 15, -3-18=-21 not -15 and -15+2=-13 not -17.
Look at how number lines work to help you get the correct answer:
https://en.wikipedia.org/wiki/Number_line
I have updated the article with a number line example.
David
thank you all i have benefited a lot.
Thanks. It is nice to get some positive feedback.
The problem is that the question PRESUMES the application of a rule not defined in the question. It might be a convention to use bodmas or some such like, but the question does not state that. Schools really made a huge mistake not using brackets. It removes ambiguity and removes the need for an operator precedence memorisation and errors made applying it as is evident in the array of answers. If you program computers, you use brackets to ensure calculations proceed as expected.
It reads equally as three take away three, multiply by six and add two.