They're expressing it in a way you would seldom see it (in my opinion). Why would you say "3 divided by (1 divided by three)"? Why would you express the divided-by symbol in one instance and the fractional symbol in the same operation.
I picked up on it right away because I am watching out for a "trick" in that kind of post, but, seriously, you probably haven't seen that kind of operation expressed that way since you were in school when they were trying to emphasize that kind of operation to get you to pay attention to all the signs.
Anyway, it is good practice so as to not miss an operation when working through a survey problem.
@fl/ga
Our university physics professor who taught both Engineering Physics I and II had been locked away for months with the rest of the crew designing a couple of BIGGGGGGGGG surprises for Japan in 1945. He was a great lecturer and instructor with a fantastic sense of humor with which to befuddle a lecture hall of 400 geeks and nerds.......and me. But, every once in awhile he would slip up and take a massive equation that filled half a chalkboard (for young people substitute the term whiteboard or smartboard) and then announce, "From this expression it is intuitively obvious that this simplifies to A = B+C." Or some similar extreme simplification. We would all look at each other with looks that suggested we were thinking, "That's a bunch of BS." Within two minutes he would prove to us that what he said was absolutely true. Before long we, too, could find these enabling shortcuts.
He was very good at keeping incredibly boring information interesting. One favorite demonstration was the equivalent of a bowling ball on a cable suspended from a loop in the center of the ceiling. The length of the cable was set so that he could pull it tight while standing with his back to one wall and the ball would be touching his nose. Then he would release his grip on the sides of the ball and watch the ball swing to within inches of the other side of the lecture hall then return to within an inch or two of his nose while he stood perfectly still. Pendulum effect. Then he would attempt to recruit some egghead out of the front row to do the same thing. Of course, on the first release he would hold the ball and then pretend to shove it, which Mr. Egghead realized would be bad and would jump away. He would then promise to do it correctly on the second attempt. And he would, while Mr. Egghead about soiled his linen as the ball swung back at him.
Another fun one was watching as he would have the equivalent of a large sheet attached to the far wall and then drooped out in a certain way. He would have a bowl full of fresh eggs. He would throw a few, one at at time, as hard as he could into the droopy sheet with no injury to any of them. Here again he would recruit a young, athletically-built nerd to throw several eggs to prove that an even more powerful thrower could not break an egg in this manner. That was great until he recruited a fellow I knew from my home area of the State, a future PhD in Electrical Engineering. He missed the entire sheet with his first show, causing the geeks nearby to be showered with egg remnants.
BTW, I tried to always sit in the back row so I would be unnoticed as I worked the crossword puzzle in the daily student newspaper.
Was his last name Feynman?
CouldnÛªt have been Oppenheimer because he was too busy foolinÛª around with his secretary.
Dudley Williams
you were fortunate!
See, this stuff is hugely important for anyone who writes formulas in spreadsheets, computer programs, or calculators, especially RPN calculators.
Some interesting information in video format that is relevant to the original post!
I was one of those kids in math class who the other kids wanted to strangle, especially if the teacher believed in grading on the curve. It was fun. You found out if you solved the problem correctly or not. There were no opinions about correctness. It either was or it wasn't. If incorrect, learn from your mistake and move on. Most of the memorization occurred in the lower grades with things like multiplication tables and such. Meanwhile, boring social studies classes were entirely based on memorization. You didn't LEARN IT, you MEMORIZED IT long enough to get through the next test. And, that dreadful subject called Handwriting was graded entirely on the teacher's opinion. How much more unfair can you get?
skwyd, post: 372591, member: 6874 wrote: Some interesting information in video format that is relevant to the original post!QUOTE]
Good video. It might be a lesson to write an equation, if it's for someone else, with the appropriate parentheses when it could otherwise be interpreted ambiguously. Of course we aren't very often writing equations for some legal purpose, which would be the time to try to eliminate ambiguity. But you can apply the same principle to legal descriptions. I learned in "Wattles", for instance, that if it's not specified, that going from a straight line to a curve (or curve to a straight line) is always tangent if not otherwise noted. I always thought "why not note it either way"? One is a lesson if someone doesn't note it, and the other is a lesson for when writing it. (of course in this example, you can usually figure out the original intent by looking at the closure, bearing of the radius or chord, or other means, just commenting on the example)
skwyd, post: 372591, member: 6874 wrote: Some interesting information in video format that is relevant to the original post!QUOTE]
Good video. It might be a lesson to write an equation, if it's for someone else, with the appropriate parentheses when it could otherwise be interpreted ambiguously. Of course we aren't very often writing equations for some legal purpose, which would be the time to try to eliminate ambiguity. But you can apply the same principle to legal descriptions. I learned in "Wattles", for instance, that if it's not specified, that going from a straight line to a curve (or curve to a straight line) is always tangent if not otherwise noted. I always thought "why not note it either way"? One is a lesson if someone doesn't note it, and the other is a lesson for when writing it. (of course in this example, you can usually figure out the original intent by looking at the closure, bearing of the radius or chord, or other means, just commenting on the example)
The thing that is so often missed in teaching PEMDAS is that .multiplication and division are done in the order that they appear in the problem. Multiplication does not always precede division. If you put the ambiguous examples from the video into an Excel formula, Excel will see no ambiguity.
PEMDAS. This seems to me to be a strictly academic principle. Who in the world would write such an equation without using brackets?
PEMDAS is an academic crutch, but the concept it represents is crucial to consistent interpretation of equations. But such a simple acronym leaves something out , so it's not as good as its fans imply. Like FOIL, a similar crutch for multiplying binomials, it is supposed to give an anchor to less-able students.
As a teacher, I despised such constructs. They impeded learning by reducing concepts to procedures and were often applied in totally unrelated and inappropriate places. I had never heard of either of them until I began teaching at age 56.
Part of the problem is the number of poorly qualified math teachers. They learn the crutches without learning the math and then pass on their own misunderstanding.
I wish I had a cure, but until a teaching career becomes attractive to large numbers of smart young people, it will remain problematic.
Wow! I remember botching this one by quickly, and wrongly, reading one-third of three. Apparently it's an easy one to miss.
