Hey, this is Presh Talwalkar. What is the value of this mathematical expression? This math problem has gone viral and it has received millions of comments on Facebook, Twitter, Youtube, and other social media sites. In this video, I’m going to present the correct answer. The problem is an example of the order of operations. These are commonly refered to as PEMDAS or BODMAS. This refers to evaluating the parentheses/brackets, then the exponents/orders, Then multiplication and division And finally, addition-subtraction. You have two operations of the same precedence, you want to evaluate them from left to right. The first of the problem has no controversy. This expression contains a parenthetical expression which must be evaluated first. 1+2 is inside the parentheses, so we’ll evaluate 1+2 to get 3. Now, the question is what to do next. If you this into google, wolfram alpha, or pretty much any scientific calculator, the thing that’s going to happen next is all of these will interpret the parentheses as an implicit multiplication. So this two parenthesis three will be converted into 2 times 3. Now we continue the order of operations. This expression only contains multiplication and division, These are operators of equal precedence, so we’ll evaluate them from left to right. Starting on the left, we have 6 divided by 2 6 divided by 2 is equal to 3 We then have 3 multiplied by 3 – one final multiplication. And that gets us to the correct answer of 9. This is, without a doubt, the correct answer to this expression as written according to the modern usage of the order of operations. So why did this problem cause so much controversy? Well, there is another answer that you could argue from a historical perspective, so I actually found some documentation that the order of operations did have a slightly different understanding in certain texts in 1917 or before. So the first part of the equation is the same as before: we have a parenthetical expression and this should be evaluated first we have 1 plus 2 and that becomes 3. The debate then centers around this division symbol. So what does it mean that we have 6 divided by 2 parentheses 3? While there were textbooks and there was a lot of usage that if you had this division symbol where you had something on the left divided by something on the right, this was understood to mean you want to divide the entire product on the left by the entire product on the right. So, for example, if a textbook wrote “x divided by 2y” with this division symbol they actually did mean x divided by parentheses 2y. You wanted to take 2y as the entire product and have that as your denominator. So under this historical usage – which is a special exception to the order of operations (and we don’t use it anymore) – you would want to take this product on the right as your divisor. So applying this rule would then lead to the expression 6 over 2 x 3. We will now convert the multiplication in the denominator so that 2 times 3 is equal to 6 and we now have one division which is 6/6 and that’s equal to 1. So, many people argue that one is a correct answer, and there is some historical justification of this because of the way that texts used to use the division symbol. I would suggest this is probably because of some historical artifact about typesetting: it would have been much easier to write the division symbol and have the understanding you want to divide everything on the left by everything on the right; you wouldn’t need to have an expression where you write a numerator over a denominator that would take a lot more vertical space and you also would need to keep putting parentheses everywhere. This would be just something that would be understood. Today we don’t use this practice, because it can be confusing. Instead, we follow the order of operations. If we want to have a fraction, we will put it as an expression like 6 over 6 which is written here. So the correct answer to this problem is 9, but there is some historical justification for the answer 1, but it’s not how we’d interpret the problem today. Did you get to the correct answer of 9? Thanks for watching this video. Please subscribe to my channel. I make videos on math and game theory. You can catch me on my blog “Mind Your Decisions” which you can follow on Facebook, Google+ and Patreon; you can catch me on social media at Presh Talwalkar and if you like this video, please check out my books! Links in description!