Here is a math problem that seems simple at first, but it has generated quite a bit of debate on the internet for an unexpected reason. Can you find the solution, and if so, which side of the debate are you on?
Many of us learned the conventional way of solving problems like this, but we may make the mistake of thinking that there are no other ways to solve it. For example, not everyone follows the same rules for the “order of operations.” However, if we take a closer look at this problem, we may be able to deduce what the best solution is.
Study the problem shown below, come up with your answer, and then scroll down to see what all the controversy is about.
6² ÷ 2(3) + 4 = ?
Seems simple enough, right?
Probably a lot of people immediately thought back to the “order of operations” rules: “PEMDAS” is one acronym for remembering the order of operations: Parenthesis first, Exponents second, Multiplication and Division third and fourth, Addition and Subtraction fifth and sixth.
Note: when dealing with expressions of the same precedent, they are solved in the order from left to right.
That makes sense right? Here’s where the controversy lies.
Most people would probably solve it like this:
Probably many of us would make the correct assumption that the expression “2(3)” implies multiplication and would solve the problem using PEMDAS as follows:
6² ÷ 2 × 3 + 4 = 58
Using this method, the final answer is 58.
Using our calculators, we would get the same answer.
Here is a different interpretation with a different answer:
There are some people who resolved the problem by starting with the expression “2(3)” based on the assumption that it somehow takes precedence over the rest of the problem. Then, using PEMDAS and solving it from left to right, we get:
6² ÷ 6 + 4 = 10
And that gives us a final answer of 10.
So, which answer is right?
The first answer, 58, is correct. Here’s why:
According to an explanation by Dave Burton via Quora, “The notation used in the question is unconventional, and the expression is ambiguous.” What he means is that the expression “2(3)” isn’t usually used this way, and so it’s confusing, but that doesn’t give it any special treatment with respect to the order of operations. It’s misleading, but it doesn’t confer precedence.
“[T]he use of parenthesis […] is normally only used for a multi-part expression,” Burton explains.
To drive home the point, author and YouTube host Presh Talwakar compares this ambiguity in math to that in the English language, which illustrates that the problem is in the phrasing, and not in the rules of the order of operations. He gives the following example:
“I saw the man with binoculars.”
This could imply that (a) you used binoculars to see that man, or it could imply that (b) you saw the man who had binoculars, as per below:
(a) I saw (the man) with binoculars.
(b) I saw (the man with binoculars.)
To sum it up, this debate has nothing to do with inherent controversy in the rules or the math problem being difficult; it’s simply a matter of “bad writing.”
RELATED: Can You Solve This Controversial Math Problem?–Millions Have Tried and Argued Over the Correct Answer.
This viral math problem has generated an extraordinary amount of controversy because of an obscure yet perfectly valid point that you might not have heard of. Can you figure out what that highly contentious issue might be?
If you’re somewhat familiar with online math brainteasers like this one, it’s clear that this problem deals with what’s known as the “order of operations.” The acronym for remembering this is PEMDAS/BODMAS, which breaks down as follows:
And as a rule, any expression of the same precedence is dealt with from left to right.
Literally millions of people online have tried this math problem on various social media platforms, and it has sparked a massive debate over what the correct answer is. Despite how clearly the order of operations are understood in the community of mathematics, the debate has split netizens into two main camps, which we shall explore here.
So, go ahead and solve the viral math problem, shown below, for yourself before scrolling down to find out what all of the fuss is about. What answer did you get? And which of the two camps do you belong to?
When you’ve found the solution, scroll down to see what others have come up with online.
Seems pretty straightforward, right? Well, it’s not quite as simple as you may have thought.
Following the order of operations, the first precedent to be dealt with is the parenthetical expression (9 + 3), which is (12).
Next, we are left with the expression 48 ÷ 2(12). The parenthetical expression 2(12) is implicitly one of multiplication: 2 x 12. Then, if we follow the standard, modern order of operations as per above, multiplication and division are of the same precedent, and so, they are dealt, as per our rule, from left to right.
Also, that is exactly how any calculator would interpret such an expression—using the same order of operations as mentioned.
Thus, 48 ÷ 2 gives us 24, which is multiplied by 12, which gives us a final answer of 288. Was this your answer? Then that might seem like the end of the story, but it’s not, and here’s why:
Dating back to an earlier age, there is an obscure exception to the modern rules for the order of operations from 1917 that was once in use. According to this exception, parenthetical expressions that are implicitly multiplication, like 2(12), are not treated in the same way as 2 x 12 would be, as per the order of operations.
Rather, the expression 2(12) takes precedent over that of division and multiplication; it would be grouped in the same way the expression 2y would be, for instance. And the reason for this was one of expediency, as it would be simpler and easier to denote 48 ÷ 2(12) as such than it would be to denote the cumbersome expression:. Such an exception was thus applied.
Thus, going by the old rule from 1917…
The parenthetical expression 2(12) is not implicitly dealt with like multiplication and division, and instead takes precedent. So, 2(12) equals 24, and 48 ÷ 24 gives us our final answer: 2.
Depending on which rule is used, there are two completely different answers. Most modern schools teach the first method, the one that our calculators follow, but there are some people out there who continue to follow the ways of olden times.
Which camp do you belong to?
Photo Credit: The Epoch Times