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