Debate: 48 ÷ 2(9+3) = ?

[Duffie]

... It's somewhat easy to process in my head, but...

It's so difficult to output it to people who can't process it, in a way that isn't terribly long or confusing. D:

 

[Defiant_Blob]

48÷2(9+3)
=48÷2(12)
=48÷24
=2

48÷2(9+3)
=48÷(18+6)
=48÷24
=2

48÷2(9+3)
=48÷2(12)
=2(24)÷2(12)
=24÷12
=2

48÷2(9+3)
=48÷2(12)
=48x[2(12)]^(1/2)
=48x[1/2(12)]
=48x(1/24)
=48/24
=2


HOW ON EARTH DO YOU GET 288

I was educated that when something is expressed as a(x+y), it is equivalent to (ax+ay), with the parenthesis. Therefore in this case, in the second step, 2(12) should be done first due the the brackets.

You have to follow the rule of Multiplication/Division goes from left to right.
It's easier to understand if you write it out as 48÷2*(9+3)
You then get 48÷2*12 (parenthesis first!)
Then you do M/P left to right
24*12
288

 

[Deleted member 4601]

That only applies when using variables, such as x or y!

When you see something, like 2(9+3), you can distribute ( Being what you've been doing there, multiplying the number next to the () into the (). ). But, it's best not to do that when it's like this.

Let me explain. When do you normally distribute? When using variables, such as x or y.

When you see an equation, like 2(x+3), you have to distribute, as you can't add together the x and the 3.

But, as you've done, you can add what's in the ().

Now, think about this; when you added those two numbers together, you formed one number. Now you can take that number out of the (). What does it look like now..?

48 / 2 * 12
tl;dr - Do what you do inside the (), take it out of the () and add it to the equation, since it's just one number.

Well, I think they're all correct. It all depends on what you are taught, and this equation is just a special case.

I messaged my teacher, and she said 2. Here's what she gave me:

48/2(9+3)=48/24=2

She reasoned that 48 divided by 2(9+3) would be 48 divided by (18+6), which gives 48/24.

Not that your argument doesn't make sense. I agree to it to a certain extent, but if that question came out during exams and I gave 288 as my answer, I'd fail that question.

It really depends on how you are educated.

If you want to resolve this problem, the only way is to write the question more clearly.

Either
(48/2)(9+3)
Or
48/[2(9+3)]

 

[Duffie]

Well, I think they're all correct. It all depends on what you are taught, and this equation is just a special case.

I messaged my teacher, and she said 2. Here's what she gave me:

48/2(9+3)=48/24=2

She reasoned that 48 divided by 2(9+3) would be 48 divided by (18+6), which gives 48/24.

Tell her to add the numbers inside the parenthesis first, then change the parenthesis to a multiplication sign.

 

[Deleted member 4601]

Tell her to add the numbers inside the parenthesis first, then change the parenthesis to a multiplication sign.

Did you see the rest of my post?

 

[superstein]

Both ways are right. If you're following distributing, then it will become 24 and consequently 2.

But if you divide by two then multiply by 12, it is 288. It's a weird equation, but both are right depending on the method used.

 

[Duffie]

Tell her to add the numbers inside the parenthesis first, then change the parenthesis to a multiplication sign.

Did you see the rest of my post?

Yes, but you're not supposed to distribute! Distributing is only for when you cannot add the numbers within the parenthesis! It works in most situations, but this situation, the multiplication has to be done after the division.

You don't use 2(9+3) as a number in its own, as it's not one number. It may look attached, but it's secretly 2 * (9 + 3), which is 2 * 12.

Both ways are right. If you're following distributing, then it will become 24 and consequently 2.

But if you divide by two then multiply by 12, it is 288. It's a weird equation, but both are right depending on the method used.

Actually, as I stated above, it isn't right when distributing.

The reason you distribute is because you cannot do anything more to whatever is inside the parenthesis, and you have a number multiplying into the parenthesis.

Ex; 2(5x+2)

You cannot add these two numbers together anymore, so you'd have to distribute.

---

Yes, you can normally distribute all the time, but this special case doesn't have the use of variables, such as x or y. That being so, the parenthesis is being treated as a solitary number, rather than a number and a variable.

 

[MarsKid]

Shit, where's X? I can't find it.

 

[Fruit]

Honestly, I love math. Why must you guys dislike it so much? :<

And one thing's for sure, wasn't I proven wrong with how to go about this process... But, not completely.

Duffie's Learning Time!

You see, what most people would do is distribute, right away. 2(9 + 3) would end up being 24. That's what the calculator would say, that's what the numbers would say. Right after that, just do 48 / 24, and you get 2. Simple as that.

But, if you look more closely, it is obviously wrong.

The correct way to do this is still under PEMDAS, more or less; just not in the way you originally learned it, I suppose.

Yes, you do the parenthesis first, being (9 + 3), resulting in a solid 12. With that, you now have the equation 48 / 2 x 12. From then on, you complete the equation from left to right. 48 / 2 is 24, then 24 x 12 results in the answer being 288.

As the video above says, PEMDAS is morally wrong, but only to a certain justification to make things less confusing.

Also, PEMDAS means Parenthesis(), Exponents², Multiplication*, Division÷, Addition+, and Subtraction-. You can put Brackets[] with parenthesis, of course.

Duffie's Learn Time End

... And now that I look at it, I think I know why I got it wrong at first. The reason I'm so used to distributing first is the fact I usually see parenthesis when x is a factor in the equation, usually resulting in something like... 5(x + 2). From this, you would end up getting 5x + 10, considering you can't add x and 10 together, moving on from parenthesis to multiplication in PEMDAS.

Well, you know what they say, you learn something new everyday! (Hey, that rhymed!)

Thanks for that, davidjl123. I love you for bringing math here. <3

Oh I forgot about doing it in order from left to right :3 I didn't even distribute i just 2x12 after adding up what was in the parenthesis.

Actually wait.

Wouldn't you treat what was in the parenthesis like a variable?

 

[Sephhh]

Bleh. I do think only one answer is the purest, and basically it is Algebra's fault that messed our minds up and it gets coded into our brains. Much like grammar, it may sound right, it looks right, but it isn't really right sometimes.

It is also partly the problem's fault for being vague

 

[Duffie]

Oh I forgot about doing it in order from left to right :3 I didn't even distribute i just 2x12 after adding up what was in the parenthesis.

Actually wait.

Wouldn't you treat what was in the parenthesis like a variable?

I don't think I learned it that way.

No, if they are all real numbers in side the parenthesis, it stays a real number unless a variable is included through distribution.

Bleh. I do think only one answer is the purest, and basically it is Algebra's fault that messed our minds up and it gets coded into our brains. Much like grammar, it may sound right, it looks right, but it isn't right.

It is also partly the problem's fault for being vague

So true, in both senses. xD

This problem wouldn't be so difficult if it just added the numbers in the parenthesis for us, giving us a somewhat more normal problem.

 

[Suikae]

This is some seriously simple math, how the fuck are we getting riled up over this? xD

 

[Duffie]

This is some seriously simple math, how the fuck are we getting riled up over this? xD

Because the rules for mathematical equations are too vague...

Well, more like we take too many shortcuts.

 

[Fruit]

This is some seriously simple math, how the fuck are we getting riled up over this? xD

This equation has been debated for over 2 years, and the best conclusion I've seen is that there is no definite answer, like superstein said, both sides are correct.

 

[DKnucklehead]

http://www.mathsisfun.com/algebra/operations-order-calculator.html


mathisnotfunformeeee

 

[Jayfeather]

okoofkomeo
so golden valley was explaining this to me because this thread was starting to infuriate me:
because the division symbol is used in the equation it is unclear whether 2(12) needs to be done first or not, ignoring rules of PEMDAS you could arrive at 2 and still be correct. However, because I'm almost certain this is just a stupid facebook post like "90 percent of people can't get the answer" and David didn't expect people to actually know PEMDAS: 288 is the right answer if you use the division symbol and 48/2 interchangeably.
Edit: Tuna swears by it being 2 because of the reasoning above, but like I said, it's probably supposed to be 48/2 and not 48 divided by 2

 

[Duffie]

Order of Operations​

[ Brackets ] or ( Parenthesis ), whichever is the deepest inside the equation.​

Exponents ³​

Multiplication or Division, whichever is first from the left --Distribution, or numbers touching parenthesis, falls under here.​

Addition or Subtraction, whichever is first from the left​

Taking that into account, you can now look at the equation;

48 ÷ 2(9 + 3)

The first thing we'll need to do brackets. There are none, so we head to parenthesis.

When doing parenthesis, you do not take into consideration anything outside of the parenthesis. So, this is the problem you will see on this step;

9 + 3

Looking at this, the equation is simple. Just add them together to get the answer.

9 + 3 = 12

With that out of the way, we can go back to the full problem, keeping in mind the equation we just completed inside the parenthesis.

48 ÷ 2(12)​

Now that the step for parenthesis is done, we can move on to the next step, multiplication or division, whichever is from the left.

If you look at the problem, division is up first, then a distribution problem. To make things simpler, I will change the parenthesis to a multiplication symbol.

48 ÷ 2 x 12

Keeping in mind of the order of operations, division and multiplication go from left to right.

48 ÷ 2 x 12

Divide the 48 into 2, and you get left with this equation;

24 x 12

Now, just do the multiplication, and you get your answer...

288

... Now, any questions?

 

[RyanDodd]

PEMDAS

=

Please Excuse My Dear Aunt Sally

But in all seriousness, I am leaning towards it being 2. Since 2(9+3), is also 2(12), I'm pretty sure this would be considered in with the parenthesis step, since you're working to remove them. Therefore, you'd do everything to get rid of the parenthesis first, then work it out later, which translates to this:

48 ÷ 2(9+3)
2(9+3)
2(12)...keeping in mind that the parenthesis step isn't over until the parenthesis are gone...
48 ÷ 24
2


It's how I've been taught that in

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

That the "P" step isn't complete until you remove the parenthesis. Leaving them in the problem (which results in 288) is incorrect because you aren't actually solving them, in this case because they are connected to a multiplication problem.

 

[Awwwyea]

PEMDAS

=

Please Excuse My Dear Aunt Sally

But in all seriousness, I am leaning towards it being 2. Since 2(9+3), is also 2(12), I'm pretty sure this would be considered in with the parenthesis step, since you're working to remove them. Therefore, you'd do everything to get rid of the parenthesis first, then work it out later, which translates to this:

48 ÷ 2(9+3)
2(9+3)
2(12)...keeping in mind that the parenthesis step isn't over until the parenthesis are gone...
48 ÷ 24
2


It's how I've been taught that in

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

That the "P" step isn't complete until you remove the parenthesis. Leaving them in the problem (which results in 288) is incorrect because you aren't actually solving them, in this case because they are connected to a multiplication problem.

You solve multiplication/division from LEFT -> RIGHT. The equation after adding 9 & 3 is (48/2)(12). Or 48/2*12 and in both cases, you have to solve 48/2 first because it's just the way that math works.

Considering that anything can be written in parenthesis, much like I did just now (because math is freedom), it's not crucial to eliminate parenthesis, but to condense what is inside of them to the simplest form before continuing.

 

[Duffie]

Considering that anything can be written in parenthesis, much like I did just now (because math is freedom), it's not crucial to eliminate parenthesis, but to condense what is inside of them to the simplest form before continuing.

Unless the problem you have to solve includes parenthesis. Then consider checking out the parenthesis.

 

[RyanDodd]

I think this really has to do with how you were taught. I was taught that what I did above was correct. All of this other stuff looks wrong.

 

[Duffie]

I think this really has to do with how you were taught. I was taught that what I did above was correct. All of this other stuff looks wrong.

But if you look at it, you're multiplying 2 and (12) together, before dividing 48 and 2! :c

Multiplication and division do not come one before the other, but rather whatever is first in the equation.

 

[Samlen]

I took one look at this and got 288
You always do parentheses first, so (9 + 3) = 12
This leaves 48/2*12
Next, since you group both multiplication and division together, you read left to right, getting 24 from 48/2 and then 288 from 24*2.
The reason WHY multiplication and division are grouped together is what confuses people: Division is REALLY the multiplication of the inverse of a number, whilst addition is really just the addition of a negative number. In theory, there are only TWO basic mathematical operations, addition and multiplication.

 

[Duffie]

All right... Let's say we have this equation;

12 ÷ 12 x 2

Looking at this problem, you could easily solve it by working the equation left to right.

12 ÷ 12 x 2

1 x 2

2

Now, let's change things up a bit...

12 ÷ 12(1 + 1)

Looking here, I just split the 2 into two numbers, but keeping it in parenthesis to keep it as a 2.

This problem didn't change in the slightest; it just looks different, due to the fact the 2 is cut in half. The order of operations remains the same.

12 ÷ 12(1 + 1)

12 ÷ 12(2)

As you can see, adding the numbers back together, I get my number again; same as the problem I first showed you in this post.

This equations plays exactly like the other equation.

12 ÷ 12(2)

1(2)

2

- - - - -

Now, let me show you these two problems, side by side.

48 ÷ 2(9 + 3)_______48 ÷ 2 x 12

These two equations are the same. 9 + 3 does equal 12, and since it is inside the parenthesis, it is done first.

48 ÷ 2(12)__________48 ÷ 2 x 12

When a number is next to the opening parenthesis [ ( ], it is the same as saying you are multiplying to it. Here's how it would look like with a multiplication sign;

48 ÷ 2 x (12)________48 ÷ 2 x 12

Look familiar? They're the same problem. Now, let's solve...

48 ÷ 2 x (12)_______48 ÷ 2 x 12

24 x (12)___________24 x 12

288_______________288

The answers become the same, as you can see here.

When looking at the 2(9 + 3) part of the problem, it seems as if some people filter out the 48.

Just remember that distribution is a form of multiplication, and falls under the same operation as division, leaving you to a left to right normal equation.

I'm honestly running out of ideas as to how to simplify this problem. ;~;

I really hope I can convince you guys that this is the answer. I mean, even the calculators and Google itself is on my side. D:

Edit: RyanDodd, I'm trying to convince you that you're doing the order of operations wrong. D:

Please, let me help you. :c

I'm just saying that, when you did the 2(9+3), you didn't consider the 48!

What you essentially did was multiply from the end of the equation, rather than the beginning, doing the order of operations backwards (in that operation).

 

[Notme]

http://knowyourmeme.com/memes/48293 Hmmm....

(48 ÷ 2)*(9+3) I think its missing bracket lol.

It will be 288, but when written like: 48 /(2*(9+3)), then it will become 48/24=2.
Morale of story is: Use brackets to be unequivocal.