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  • 8 months ago

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00:00Hey this is Presh Talwalkar. What is the value of this mathematical expression?
00:06This math problem has gone viral and it has received millions of comments on
00:12Facebook, Twitter, YouTube, and other social media sites. In this video I'm
00:19going to present the correct answer. The problem is an example of the order of
00:26operations. These are commonly referred to as PEMDAS or BODMAS. This refers to
00:33evaluating the parentheses brackets, then the exponent orders, then multiplication
00:38and division, and finally addition subtraction. If you have two operations
00:43of the same precedence you want to evaluate them from left to right. The
00:49first step of the problem has no controversy. This expression contains a
00:54parenthetical expression which must be evaluated first. One plus two is inside
01:00the parentheses, so we'll evaluate one plus two to get three. Now the question is
01:07what to do next. If you input this into Google, Wolfram Alpha, or pretty much any
01:13scientific calculator, the thing that's going to happen next is all of these will
01:19interpret the parentheses as an implicit multiplication. So this two parentheses
01:26three will be converted into two times three. Now we continue the order of
01:34operations. This expression only contains multiplication and division. These are
01:40operators of equal precedence, so we'll evaluate them from left to right. Starting on
01:47the left we have six divided by two. Six divided by two is equal to three. We then
01:54have three multiplied by three, one final multiplication, and that gets us to the
02:00correct answer of dyne. This is without a doubt the correct answer to this
02:06expression as written according to the modern usage of the order of operations. So
02:12why did this problem cause so much controversy? Well there is another
02:17answer that you could argue from a historical perspective. So I actually
02:22found some documentation that the order of operations did have a slightly
02:28different understanding in certain texts in 1917 or before. So the first part of the
02:38equation is the same as before. We have a parenthetical expression and this should
02:43be evaluated first. We have one plus two and that becomes three. The debate then
02:49centers around this division symbol. So what does it mean that we have six
02:55divided by two parentheses three? Well there were textbooks and there was a lot of
02:59usage that if you had this division symbol where you had something on the left divided
03:05by something on the right, this was understood to mean you want to divide the
03:10entire product on the left by the entire product on the right. So for example if a
03:16textbook wrote x divided by 2y with this division symbol they actually did mean x
03:24divided by parentheses 2y. You wanted to take 2y as the entire product and have
03:29that as your denominator. So under this historical usage, which is a special
03:37exception to the order of operations and we don't use it anymore, you would want to
03:43take this product on the right as your divisor. So applying this rule would then lead to the
03:52expression six over two multiplied by three. We will now convert the
04:00multiplication in the denominator so that two times three is equal to six and we
04:07now have one division which is six divided by six and that's equal to one. So many
04:14people argue that one is the correct answer and there is some historical
04:17justification of this because of the way that text used to use the division symbol.
04:23I would suggest this is probably because of some historical artifact about typesetting.
04:28It would have been much easier to write the division symbol and have the understanding
04:33you want to divide everything on the left by everything on the right. You wouldn't need
04:36to have an expression where you write a numerator over a denominator, that would take a lot
04:41more vertical space, and you also would need to keep putting parentheses everywhere.
04:46This would be just something that would be understood. Today we don't use this practice
04:51because it can be confusing. Instead we follow the order of operations. If we want to have
04:57a fraction we will put it as an expression like six over six which is written here. So the
05:02correct answer to this problem is nine but there is some historical justification for the
05:07answer one but it's not how we would interpret the problem today. Did you get to the correct
05:13answer of nine?
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