Hi, this is Presh Talwalkar Can you solve this problem which went viral in Japan? A recent test found that only 60% of Japanese 20 year olds were able to get the correct answer This is alarming, because it is down from 90% – which was the accuracy rate in the 1980s Can you figure it out? To get started, I´m going to over a common mistake Many people will input this expression into Google or into a calculator In order to do so, you have to convert the fraction 1/3 into an inline expression Many people write out the equation in the following form Now, you will interpret 1/3 as being grouped together However I will discourage you from writing expressions in this form It is not clear that the 1/3 should be grouped together – – because this expression using both the division symbol and the division slash – – which are the same mathematical symbol of division Although you want the 1/3 to be grouped together – – this expression is going to be evaluated by a calculator – by converting this division symbol into a division slash This will NOT be equal to the original expression The calculator is going to look at the 3 divided by 1 divided by 3 as one term and it is going to evaluate it from left to right Now a calculator would properly evaluate this 1/3 it´s going to evaluate the 3 divided by 1 first, – then it is going to divide 3 divided by 3 – and then it is going to do 9 minus 1 plus 1, which will give you the result of 9 If you were to transcribe it on a calculator – you want to make sure that the fraction of 1/3 maintains grouped together So instead of writing THIS expression – – you would like to write an expression which GROUPS the 1/3 as one group Now a calculator will properly evaluate this 1/3 – and this whole term: 3/(1/3) in a proper order 3 divided by (1/3) is equal to 9 – and now we have 9 minus 9 plus 1, which give us the correct answer of 1 The problem is a good reminder of the order of operations These can be remembered by the acronyms PEMDAS or BODMAS These relates to the order of operations of Parenthesis or Brackets – Exponents / Orders – then Multiplication – Division – and finally Addition – Subtracton Another important rule, is that if you have – – operators of the same precedence – – you want to evaluate the expressions from left to right So let’s get to that We have no parentheses or brackets in this expression, we also have no exponents or orders We do have a division here, which is 3 divided by 1/3 So let’s evaluate this first – 3 divided by 1/3 is the same thing as 3 multiplied by the reciprocal of 1/3 which is 3 We now has a multiplication of 3 times 3 – – which we also evaluate before anything else 3 times 3 is equal to 9 And now we have an expression with only addition and subtraction So how do you evaluate this expression? How do you know what to do? If you have something of the same precidence – addition and subtraction – you want to evaluate the expression from left to right So our first evaluation of 9 minus 9 which gives us 0 – then you evaluate the 0 plus 1 which gives us the correct answer of 1 Did you figure it out? Thanks for watching this video and please subscribe to my channel I make videos of math and game theory You can catch me on my blog MindYourDecisions which you can follow on FaceBook, Google+ or Patreon You can catch me on social media as @preshtalwalkar And if you like this video, please check out my books – there are links in the video description.