Why does pemdas matter

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. The matter is not logical but historical. Yes, it is a very interesting topic, especially in connection with computers. You are right that with calculators one has to be even more careful and needs to put more brackets.

One of the reasons, why HP calculators had a lot of success is because they used reverse polish notation allowing to skip many brackets. I was never in that HP camp but like you used TI calculators. It is actually very interesting. I also agree that the PEMDAS ambiguity is not a flaw of mathematics as it is often presented, it is just a matter of fact that some expressions need more clarity meaning brackets to be meaningful. What is a bit offsetting is that there are so many around who believe that there is a definite way and only their way is right.

It is also quite amazing how long this discussion is still going on. But that makes it even more interesting. There is not only a mathematical or linguistic side, there is also a social aspect to the story. And as you mention as an engineer, it can be crucial. If one writes a program guiding a robot and overlooks something like that, it just does not work. I learned early on that programming something is the ultimate test of understanding.

It is harder than to read or write or teach a subject. If a procedure does not work, it is proof that there is something, that one does not understand yet.

This is the reason why people continue to argue about it. The answer 1 is the answer most people get. The answer 16 is what most computers get. This is a question on whether the division or multiplication is done first. It is a matter of fact an observation when looking what people write on the web that there are some who believe one of the answers is right.

To use the site, please enable JavaScript in your browser and reload the page. Enable contrast version. TutorMe Blog. Andrew Lee March 30, Online Tutoring ,. It's just a convention to simplify reading and writing.

Changing the convention wouldn't break anything, we'd just need a lot of parenthesis to express what we want. One place where polynomials occur organically is in field extensions. One could actually do quite a bit of Galois theory without ever explicitly writing down a polynomial.

Similarly, polynomials occur organically in linear algebra one can use tensor products to abstract abstract away things like characteristic polynomials. It would be harder, but equally powerful.

But this helps to justify why we care about polynomials and why we might want to write them down. This is really a linguistic question, so the answer is a typical linguistic answer: the order of operations is as it is because it made communication more efficient.

We change the format of our notation to suit our needs. In the case of operator orders, it was generally found that formulae were more readable with the order of operations likely due to the reduction in number of grouping symbols.

Sure, but it's harder. Over the years, mathematicians found the current order of operations to be extremely convenient, so they stick to it. The real answer is that this is a linguistic ambiguity which exists because it hasn't been important enough for the greater body of mathematicians to agree upon it.

If it ever actually became important, we'd decide one way or another. Always use to remove all ambiguity if you are the person writing the equation or expression. Even though there is a fairly good reason for the current convention, there is no longer any really any good to reason to rely on the reader to remember it and correctly interpret an equation or expression using it.

When everything was on paper this was a reasonable way to save space in texts and therefore money by reducing paper and printing costs. Later, when computers had tiny memory capacity it also made some sense.

I would claim that any time saved in typing or writing the extra characters would be more than offset by mistakes and the extra time spent to decipher it without the. Currently, most things are on the web and we have plenty of computer memory so there is no longer an excuse to introduce any ambiguity by omitting. The fact that there are many pages on the web regarding the PEMDAS convention is evidence that many people find it confusing and it often leads to unnecessary mistakes.

Mistakes that could be avoided just by typing a few to avoid any ambiguity and confusion. When writing computer code it is very important to include. Many extremely hard to find and fix bugs could be avoided by typing a few. Likewise exponentiation are forms of representing Multiplication and Division at least for integers exponents Parenthesis is on the other hand a way of explicitly prioritizing an operation, so it should be well Mathematics started solving problems like these.

So it was natural to try to write the bill calculation as short as possible. To avoid a ton of parentheses, the merchants decided to give multiplication a higher priority than to addition. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.

Create a free Team What is Teams? Learn more. What is the reason behind the current Order of Operations?