Order of Operations 48/2[9+3]

Video response for the two trolls that keep hitting this video.

[damncritics]

You cannot separate the 2 from the brackets. This is what all of my friends and teachers tell me.

[Harazi]

Follow the rules, multiplication always goes before division, man! It means that correct answer is 2.

[ExploitedWorker]

This answer is indeed 288. I'm not quite sure why people insist on stubbornly pushing different answers, regardless of having the correct method explained to them over and over. PEMDAS is split up as such. {P}{E}{MD}{AS} Multiplication and Division are on the same step, so they are solved from left to right. Addition and Subtraction are on the same step, so they are also solved from left to right. 48/2(12) cannot be re-written as 48/(2(12), because that is changing the problem entirely.

[pauluk]

But surely the '2' can't go with the '48' because it must pulled into the parenthesis '(9 +3)'?

You can distribute the '2', because that does not represent the 'evaluation', and you will have:

'48' divided by '(18+6)'

This has removed the previous ambiguity and the parenthesis now has precedence, leading to:

'48' divided by '24'

No?

[PreVaylMusic]

There are 48 apples total. Only 2 apples can fit in a box. How many boxes do the 48 apples fill up? 24. If a truck can only carry 12 boxes. How many trucks will you need? 2

[Mathbyfives]

I originally made the video as a response to a fb coment. I did not understand at that time that it was a controversial topic on the internet. I will make another video to address the 2 trolls soon.

[nexusg]

It depends on how it's written (e.g. 2^-2 has precedent over 2/8). There is a standard in mathematics regarding the order of operations; however, PEMDAS can be oversimplified in some cases. Though equations in which it is too simplified to work could most likely be written in a more proper way.

Barring the ability of being able to have an equation rewritten, there are more complex rules such as the rule of juxtaposition which would apply to the case in this video which would make the answer 2.

[SpaceCWByu]

His teaching style should be, Instituted in every math class from grade school to college and for the GRE . This guy is a blessing to me and Iam 39 and always hated math til I found him !  

[scottpi]

Wrong. 2(12) is not 2x12. It is (2x12). THAT is how you get rid of (). So the answer is 2.

[marial.n.b.]

Ok, I’m going to help everyone out here with a (math basics) lesson, which for some is ACTUALLY (and understandably) confusing.

So, for many people, they claim that their answers are indicative of the formula PEMDAS (which YES is the formula you need to be using to solve this equation) but unfortunately there is some confusion on how the formula works.

First let’s break down PEMDAS

P: parentheses
E: exponents

M: multiplication
D: division

A: addition
S: subtraction

So far so good right.
And so far everyone seems to be getting the first part right, which is to do whatever is in the parentheses FIRST. no confusion there (9+3). = (12)

The confusion to most people come from the last two parts of PEMDAS which is the M/D, A/S.
What people are reading here is that you have to do multiplication FIRST before division and then comes adding before subtracting. HOWEVER, what you SHOULD be reading here is a bit more complex and something I agree they don’t make clear enough when first teaching you this formula.

What you should be reading is...
1: if there are parentheses in your equation then no matter what they should always be done first
2: after solving all known parentheses, any exponents should be taken care of before moving onto multiplication and division
3: next you need to take care of any multiplication and or division in your equation (DEPENDING ON WHICH ONE COMES FIRST) that means that the equation must be read from left to right and if there is a multiplication sign first than that’s the one you solve first, but if the division sign is first then that is the one you must solve first. In this regard the multiplication and division signs are actually interchangeable in the PEMDAS formula, depending on which one is presented to you first. In this case it’s the 48/2 that is presented first so that is the one that must be solved first =(24)
4: And lastly, addition and subtraction must be treated BOTH with the same rules as multiplication and division. The two in the PEMDAS formula are interchangeable depending on which one comes first in the equation. (Read from left to right). BUT must only be done AFTER you finish all multiplication and division answers.
UNLESS, like in the very beginning of PEMDAS states, if the addition and subtraction equations are inside parentheses then they must be dealt with first, no matter what.

I hope this was helpful in clearing up any confusion.
(I used to be a math tutor)

Answer: 288



Ok, so some of you aren’t 100% sure why the above equation = 288.
It seems there are some issues with understanding how PEMDAS works and many of you seem... unmoved by my explanation.
But it also seems that this whole problem stems from one incorrect assumption...
48/2(12)
Many of you when you see this above equation immediately think that because the 12 is still in parentheses then it’s still counted towards the PEMDAS rule which states that everything inside parentheses must go first. So...
48/2(12) Becomes 48/(2x12)
And many of you are adamant that THIS is the way to solve the equation. And I’ve seen many confused videos that state this as an issue and why the equation should be either marked as two or no solution. But.... that couldn’t be further from the truth. In fact, I’m not only here to claim that 288 is the right and ONLY answer I’m also here to claim that (I CAN PROVE IT).

and it’s really easy to do so too. With a little equation I like to call...

THE...
PEMDAS PROOF OF CONCEPT EQUATION
Also known as the....
GROUPING PARASITE EQUATION
2x10-2+8/4(1+1)

This equation is meant to prove weather you fully understand the PEMDAS order system or not.

So let’s start off by answering this equation the WRONG way.
(Just to prove a point)

The ones who insist that the top answer is 2, their intuition is that the parentheses of the singular number (12) carries over to the two beside it. Coincidentally making it 48/(2x12). For people who use this logic, the numbers seem to round off easily and thus there seems to be no visible problem with the way they solved the equation. But looks can be deceiving. So... let’s plug in this Mathematical logic into our equation and see what it comes up with. For those of you who are smart, you’ll pick up on the problem relatively quickly...

2x10-2+8/4(1+1)
First we do the parentheses, adding one plus one.

2x10-2+8/4(2)
Oh, it’s 2... but what’s this? The two was left inside the parentheses? What do you suppose we should do about that?

2x10-2+8/(4x2)
The four is close to the two and should be considered one equation? Put it inside the parentheses you say? Well... I guess if you insist...

2x10-2+8/(8)
Oh, I guess we got 8 now. Nothing too hard I suppose... oh... hmmm.... wait a minute. We just solved an equation inside a parentheses. So now the 8 is Inside a parentheses too... well... might as well do the same thing too... wouldn’t want to be inconsistent now would we...

2x10-2+(8/8)
Ok, by now you’ve probably picked up on what’s going on. If not, stay tuned for the right way to solve this equation. Or just stay to read the hilarity that’s about to ensue.

2x10-2+(1)
So we got another one (rim shot) inside a parentheses (see what I did there?) XD
You know what that means right?

2x10-(2+1)
Yup. PUT IT IN WITH THE NEAREST EQUATION!!! XD

2x10-(3)
oh hey look, this equations starting to look a bit more familiar now isn’t it?

2x(10-3)
I’m having a déjà vu moment right now. Anyone else?

2x(7)
Well from here on out the equation SEEMS right... but we know better by now don’t we.

(2x7)
(14)
And here’s the completely incorrect answer for your absolute amusement. You can see here that the parentheses in this type of equation became like a parasite. And slowly spread through its closest counterparts to FEED off the answer. This is the reason, In math, when we see a singular number in parentheses (x) we treat it as just that, a singular number. This helps avoid confusion in the future.

Ok, ready for the real answer?

2x10-2+8/4(1+1)
Here’s our starting equation. So first, how about we get rid of that parasite.... I mean parentheses.

2x10-2+8/4(2)
And since it’s a singular number in parentheses why don’t we treat it as such this time. After all, it’s not like the 4 is INSIDE the parentheses with the two, so why should IT be treated special. This would especially not make sense if... say... you had an equation like this 2(4)8 who would get the special treatment here? Both, none? And when?

2x10-2+8/4x2
Ok. Thank goodness. That seems so much more manageable. Now back to PEMDAS.... finally. Now let’s focus on the multiplication and division side of things. Now everyone say it with me... WE! READ! THE! EQUATION! FROM! LEFT! TO! RIGHT! AND! SOLVE! WHATS! FIRST! Got it? Good. Now let’s do the multiplication and division side of the equation first.

2x10-2+8/4x2
20-2+8/4x2
20-2+2x2
20-2+4
Ok. We got rid of all the multiplication and division. Now the equation looks much cleaner. Now it’s time to focus on adding and subtracting. Remember, the same rules apply, it doesn’t matter which one comes first as long as you’re reading it from left to right.

20-2+4
18+4
22
And there you go, now you have the correct answer. Now wasn’t that much easier and way less confusing? I sure think so. You know... Sometimes it takes a longer equation to make a smaller one easier.

[pauluk]

Oops, my typo! The answer would be '288' of course (not '2') - which was the whole point of this example!

[ornaelchacon]

Stop and think, divide any quantity by itself and the answer is one. It does not matter how i express that quantity, It is up to you to understand what the math is asking you to solve.

When you have 4/4=1 divide 4 by 4 any way you want and the answer is 1.
Watch
(4)/(4)=1
1(4)/1(4)=1
2(4)/2(4)=1
3(4)/3(4)=1

[CharlieTVS]

I tutor math. No textbook would use this entire problem as an example. In fact, one of my students just started learning the distributive property, and the first examples his teacher game him were like 2(x-2).

The ONLY reason someone would be shown 2(9+3) as a distributive property example would be to explain why it works, that 2*9 + 2*3 will give you the same answer as 2(12). But to call 2(9+3) a factored expression would be just silly.

[jdouglasusn]

48÷2x = 48/2x = 24/x = 24/(9+3), witch in this case is 2
48/2x does not equal 24/x It is simply 24x

Left-associative operators: a1*a2*a3*...*aN = (((a1*a2)*a3)*...)*aN
Since multiplication and division are left-associative, that means when you mix them, you get: a1/a2*a3/...*aN = (((a1/a2)*a3)/...)*aN

[CharlieTVS]

How to solve this question:

1. Walk up to whoever gave it to you
2. Ask if the question has a numerator and a denominator

This has no real-world application, else it would be more clear. I guarantee this was made by someone on 4chan or 9gag just to see people with inferiority complexes squirm when they hold steady to whether this is 2 or 288. If someone gave me either answer and explained it with clear, sound logic, I'd probably accept it. A ring theorist from Berkley said the same thing.

[ed-odsd]

is it left ro did he say "RIGHT to left" which one is correct?

[Alanflamer]

I'm following the order of operations. The question is "when we eliminate the parenthesys?". It's seems there's some problems to interpret that.

That problem seems like a problem in digital sintaxis. Couse in the calculator we use the bar to simbolize the division, and on handwriting we use the Two points :

And on handwriting, this would be expressed as a fraction, if the intent was to divide first. On writing with one line there could be that problem with interpretation.

[nitramdh]

I've must add to you answer. A division is esscentially a multiplication by somthing with a negative exponent. So, everithing to the right have a -1 exponent wich makes it the denominator. Nuff said, answear is 2.

[jackhuntr]

Not sure if anyone pointed this out, but exponents and roots are the same level of OoO.

[nexusg]

In junior high and high school mathematics, it would be expected to work 1/2X from left to right (as students are taught -- well, i should say as we were taught in the 80s and 90s). I was taught the same in several different schools across the United States, so it wasn't just a specific teacher or school system that was at fault.