Why is the acronym pemdas misleading

Associativity tells us that it doesn't matter if you multiply from left to right, or right to left. This property of the real numbers allows us to multiply in whichever order is easiest, and we will get the same answer no matter which order we take. Furthermore, our numeral system is borrowed from Arabic, and Arabic is written from right to left!

The issue with this problem is that division is not associative. Which division sign do we do first? Regardless of what our elementary schoolteacher told us, we can't assume that the problem's author intended us to work from left to right.

The only reason that we can forgo writing parentheses with long strings of addition and multiplication is because of their associativity. For division, we must specify which operation to do first. It could mean two different things. The only way we can know which was intended by the auther, is to ask for clarification.

Ambiguous statements are not exclusive to mathematics. The following question is similarly upsetting:. Once again, the author's intent is unclear. Which woman does each instance of "she" refer to?

Next up is multiplication and division from left to right. This simplifies our equation as follows:. Finally, all we need to do now is solve the remaining addition and subtraction from left to right :. The final answer is Don't believe me? Insert the whole equation into your calculator written exactly as it is above and you'll get the same result! We'll go over the answers after. This math problem is a fairly straightforward example of PEMDAS that uses addition, subtraction, and multiplication only , so no having to worry about parentheses or exponents here.

We know that multiplication comes before addition and subtraction , so you'll need to start by multiplying 5 by 6 to get If this math problem looks familiar to you, that's probably because it went viral in August due to its ambiguous setup. Many people argued over whether the correct answer was 1 or 16, but as we all know, with math there's almost always! This problem has parentheses, division, and multiplication. While most people online agreed up until this point, many disagreed on what to do next: do you multiply 2 by 4, or divide 8 by 2?

PEMDAS can answer this question: when it comes to multiplication and division, you always work left to right. This means that you would indeed divide 8 by 2 before multiplying by 4. It might help to look at the problem this way instead, since people tend to get tripped up on the parentheses remember that anything next to a parenthesis is being multiplied by whatever is in the parentheses :.

The correct answer is This math problem has parentheses, an exponent, multiplication, division, and subtraction. But don't get overwhelmed — let's work through the equation, one step at a time. All that's left now is multiplication, division, and subtraction. Remember that with multiplication and division, we simply work from left to right:.

Once you've multiplied and divided, you just need to do the subtraction to solve it:. Shame on you for perpetuating bullshit. That is the definition. This is not where the ambiguity is. It is that the notation is ambiguous and experience shows that that it is a source for errors and misunderstandings.

Now, the question is whether there is a definite rule which tells, what is right. Because they have been taught so. Now, if you look at the literature and history, then it turns out that there is no definite answer what is right. And if this is the case, we call it ambiguous. But this makes things only more complicated as we have now three different interpretations. Everything else can produce misunderstandings. You are not the only one who feels very strong and become emotional about it.

Question: I am a Maths teacher and recently came across a particular question on PEMDAS kindly check the attachment where the students got two different answers 6 and My answer: There are two ambiguities in this problem and yes, all answers given by students should be graded as correct. Also here, there are no definite rules.

Both answers 6 and 66 are correct in the total. So, here are the four possible answers. But it also illustrates what can happen if "colloquial language" is used to describe arithmetic operations as this can can lead to other ambiguities. The article already has comments. Similarly as for years on social media, the fight goes on there. The most interesting thing is how certain most are that they are right, on all sides.

Which points again to ambiguity. The title of the article is "Millions fail at this math equation! The author of that video, Presh Talwalker, gives in his blog the reference Lennes, N. One should better read that article.

But it also states the "established rule" "All multiplications are to be performed first and the divisions next". It is the business of the lexicographer and grammarian to record, not what he may think an expression should mean but what it is actually understood to mean by those who use it.

The language of algebra contains certain idioms and in formulating the grammar of the language we must note them.