6÷2(1+2) = _ _ Correct Answer Inside Finally Solved!!

Okay, so in this video I am going to be discussing this problem here which is 6 divided by 2 open bracket 1 plus 2 and it just seems as though this problem has completely taken over the internet. It's just good to see so many people debating this from students, even teachers and academics Okay, so generally we find that people are getting two answers, getting either 9 or 1 as shown on these two calculators here. I'm just going to try it on my calculator, I'm getting 1. I'll try it on my other calculator, I'm getting a 9. And that is quite strange when you say it because calculators don't disagree, do they? Or they shouldn't? Okay, so the reason why a lot of people disagree with the answers is because of the way they tend to work it out. In the UK we use something called BODMAS and this is what we were taught as the order of operations when we were in school. So I'm just going to very quickly work this question out, explain to you how we get to the answer using BODMAS. So we start with brackets as you can see, it's 1 plus 2, that gives you the 3. Orders, so things like indices comes next and there are none, so we skip the step. Division comes next, so it's 6 divided by 2 gives you 3. And then obviously multiplication next and that gives you the answer as 9. The other common way is called PEMDAS and that is very common in the USA for example. It starts with parentheses again, gives you 6 divided by 2 times 3. There are no exponents so we skip that step. We do multiplication which is 2 times 3 which is 6 and then we do the last step which is division. And that gives us 1. So that's interesting. So this explains to us why we are getting two answers. So which one is correct? Well the first thing we have to do is rule out the ways which are not correct. Okay, to rule the first thing out is a long time ago this division sign here meant everything on the left divided by everything on the right. So this expression a long time ago would have meant you have ax plus b plus c divided by 2. On the left divided by the right. But obviously we don't use this convention anymore. This is the sort of correct way we would interpret this. So I'm going to rule that particular one out straight away because this doesn't apply to the modern way of doing math. Okay so the thing that we do agree with is we certainly do the brackets first. So no one has a problem with this. So 6 divided by 2 then times by 3 because we do the brackets first and the brackets gives you 3. And if I take you back to here we get this situation on both BODMAS and PEMDAS. But this is where things get interesting. With one you divide first and with the other you multiply first. So now we have to ask which one is correct. So at this stage what some people do is they decide that division and multiplication they have the same precedence. And what that means is they have the same ranking. One is not more important than the other. So a lot of people what they say is at this stage where you have the same precedence you go from left to right. So here they would do 6 divided by 2 first which is 3. Then you times by 3 and you get to 9. So is that the correct way? Well it's not. Certainly not and I will show you why. So look at this term here. X divided by 4A. Look at the way it's been written. How would you see this? I'm pretty sure 99% of people will see this as X over 4A. That's the way that we are used to working with. But if you consider this left to right same precedence convention. It would state that you divide first because it's from left to right and then you multiply. So it would become X divided by 4 first then times by 8. Then you get to AX over 4. Is that the way we see this? Do we see this as AX over 4? Question marks. So this doesn't necessarily apply. So is that the correct way? Well it's certainly not. And this would create a huge amount of problems. And this is why this sign is not used in higher level mathematics. For example if you look at this. This is something called the quotient rule. If you want to differentiate a function over another. It's not written like this. It would never ever be written like this. It's written like that. And at the same time if you have an indefinite integral. This division sign is not used. It's not written like this. It's written like this. There is no ambiguity here. And that's the reason why this sign is not used in higher level mathematics. I just want to show you a page from Wikipedia. It's about an article on order of operations. And as you can see it talks about the fact that there is ambiguity. With the way that this sign is used. And also more importantly it just says here. Please note that many academics consider PEMDAS as non-applicable. In these kind of scenarios. So however to really get to the correct answer. We have to look at it from a strictly mathematical point of view. And the correct answer is this. There is no solution. This is the most correct answer from myself. As someone who teaches mathematics. Who has studied mathematics at university. And a lot of academics would agree with this answer. And the reason why it is no solution. Is because of the way this question has been written. It creates ambiguity. This problem does not ever appear in higher level mathematics. Because we are not allowed to make ambiguous statements. And this is why there is no solution. And also that is what makes maths such an interesting subject. So that's it. There's your answer. Anyway thank you for watching. Remember to like and subscribe for more interesting maths videos.