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Even if you did the parentheses first, you'd still get 2(9) + 2(3) (distribution), which is 24. Then you'd have 48 ÷ 24.
It depends on which system you were taught.
That's what it is the way they taught it to us in school, too. There was even a little chant for it (that I totally forgot about until this moment...): Parentheses first! Multiply, divide, add, and subtract!
Quote:
Originally Posted by SoCal_Native
The correct order of operations is PEMDAS. First process the parens. Then when the equation is purely multiplication and division, process FROM LEFT TO RIGHT.
=48/2*12 = 24*12 = 288.
288 is always correct.
2 is always incorrect.
Google, Matlab, HP Calculators, and Excel all return 288.
You can't exactly fault someone and act like they're dumb for doing math the way they were taught to do it... it would be like making fun of someone from England because "no, it's spelled 'color' without a U."
Quote:
Originally Posted by silibran
I have trouble with math too. But you have a calculator on your phone, no?
Quote:
Originally Posted by Cida
Well, if you get a good calculator, you're okay.
A calculator doesn't solve everything. For example, if you're interested in learning about physics and a concept is explained in equations, a calculator isn't going to help you. That's my biggest problem.
To be honest, this is not a math problem; it is "order of operations" gotcha
It all depends whether there is a difference between "/" and ":". In some approaches ":" represents a divisor line, thus having all before it as "top" and everything after it as "bottom". That's why it is advisable to always use parentheses. Otherwise even calculators take it differently :
That's interesting. Casio must be an odd ball. Thanks for posting that.
I consider myself a smart person. I pick up on things and can learn jobs fast but whenever I have to figure out anything mathematical with pricing (which is rare since it usually auto populates or I just add a percentage) I get confused and need to have my boss or a coworker walk me through it. In HS I was behind in math and never got passed algebra. Never took physics or calculus. Always had a tutor. I remember only one teacher that was able to explain algebra a certain way that I got it. Now I even have trouble with simple math. I couldn’t even remember old school division. Why is it so hard for me to grasp. I feel like I have to read things 10 times if I have a convoluted price issue at work and I still don’t get it. Luckily my job rarely entails this but when it does come up. I feel stupid.
I went to grammar school in the 1960's when they taught normal arithmetic.. then came "New Math" and it was similar to algebra. At that time, they lost me.. and even now when i took an easy class in math, i did not get it either.
However, ironically my profession is accountant. I learned on the job. I work with numbers but a lot of times the computer system we use figured things out.
You might not be wired to do math skills.. but you probably are stronger in other skills, maybe you are very creative and excel in art and creative things like cooking, or whatever.
I'm saying - you are not the only one who has your problem. You might be able to some fun logic games, that will exercise your brain and you might be able to figure out math things better.
i didn't know how to do math until i had a practical reason to use it. i also was discouraged from counting with the "crossed tics" way to calculate an answer, though it's acknowledged nowadays as a less 'abstract' approach to getting a math answer. my point is that there is more than one way to learn math, and also more reasons to be 'turned off' to it. i grew up with a father who *loved* math, and disappointed that i was more interested in (and maybe
better equipped to do) art. i kept trying to learn math; it probably didn't help that he felt upset if i 'didn't get it faster' (stressful experience). it took a gentle, understanding math teacher later on to patiently let me go through "steps" to an answer, and accept questions about the process, etc. i didn't necessarily like math more, or have more talent, but at least i realized it was okay not to be a "quick study" either. (ironically, my father wanted to do art around the same time, but not necessarily for the experience itself.)
It's a purely man made construct. It does NOT answer everything and is NOT the answer to unexplained things. Which math often tries to answer.
There's always an extra zero. And some things can only be explained without thinking in numbers. Math might be useful for some things but I consider many other things MUCH more useful. Therefor my interest in other things is higher there and lower when it comes to math. So as a result my knowledge about other things is higher while math is lower.
I can do simple addition, subtraction and multiplication. A little division. And that's it. That's enough for me. Why would I want to know more then that? If I want to do something more complicated this is the 21st century and we got computers that can do faster calculations then the human brain.
I can see math being useful for things like game balance though. Stats that need to be changed. Health. Damage. Stamina. Food/water drain. etc. I'd be surprised if anyone can do that without having computers do the math though. Some of the math you do yourself obviously but there comes a point things have to be automated. And when things get automated they suddenly become much less certain. Which is maths biggest flaw.
I don't know much about history either. But a lot of that could be false as it's written by the victors and much of it is assumptions and theories. No one was actually around 1000 years ago so you can't know if that rock is actually that old. If anything I feel smarter with this in mind. History has shown we can be wrong about things over and over. So my faith in that area is limited. Too many myths are believed. Math isn't as bad there but it does still have its quirks. Mainly from people that make assumptions (theories) about things like the big bang and how "large" the universe is (again, this comes back to "age"). The former might not have happened and the later could well be endless without limit. yet math I crammed in to "explain" those things regardless. Despite our very limited knowledge and lack of space travel. We measured light then we discovered dark matter. Who knows what else is out there that can interfere with the travel of what we perceive as light? There's probably the equivalent of glass somewhere in space that redirects or otherwise dims light travel that we currently don't see. How many factors are at play? How much do we actually know compared to what we do know?
I know I don't have the answers to these questions. But that makes me a hell of a lot smarter then people that state theories as if they're facts. What disappointments me is that these theories aren't taught AS theories. And therefor people believe them to be facts. That's the equivalent of raising someone religious. Both science (which has a lot of math) and religion have the same flaw in that regard. Do that by all means but don't treat it like it's "the one and only answer". Be it in or out of the field you're in (science being one field. religion being another).
I've given this way too much thought. Still, I think people use science and math as excuses a lot. Often happens with religion too. math and science try to prove things but it does a poor job of it at times. And that's from people that are supposed to be smart.
Last edited by Taramafor; 08-11-2019 at 06:25 AM..
I consider myself a smart person. I pick up on things and can learn jobs fast but whenever I have to figure out anything mathematical with pricing... I get confused and need to have my boss or a coworker walk me through it.
To be honest, this is not a math problem; it is "order of operations" gotcha
Agreed.
Quote:
Originally Posted by SoCal_Native
The correct order of operations is PEMDAS. First process the parens. Then when the equation is purely multiplication and division, process FROM LEFT TO RIGHT.
=48/2*12 = 24*12 = 288.
288 is always correct.
2 is always incorrect.
It certainly wasn't incorrect when I was taking calculus and physics. I'm taking this directly from my Algebra I book:
If no parentheses are present: 1) Find the value of any numbers with exponents first. 2) Do any multiplications or divisions in the order in which they occur, working from left to right. 3) Do any additions or subtractions in the order in which they occur, working from left to right. 4) If an expression has a fraction bar, do all work above and below the bar separately, and then simplify is possible
NOTE: doing the fraction bar is #4 on the list, after multiplications or divisions.
If parentheses are present: use the rules above within each set of parentheses, starting with the innermost and working outward.
Part of learning what multiplication is, means you learn that you can drop the X for multiplying, so instead of using 3 X z you can just use 3z and people automatically know that it means 3 times z. So when I see something like 2(9 + 3), I know it stands for 2 X (9 + 3). That's why when it says to do any multiplications or divisions in the order in which they occur, you can't take 2 and divide it into 48. You need to do the complete multiplication problem which is (9 + 3) first, THEN multiply it by 2 and then divide that number into 48. Even if you wanted to divide only the 2 into the 48 and set the problem up that way, it would look like this:
48,,,,,,,,,,,,,,,1
-------X-----------
2,,,,,,,,,,,,(9 + 3) and that is
(48)(1)
--------
2(9 + 3)
If the problem really were 48/2 only, then I'd expect to see it set up like this:
48,,,,,,,(9 + 3)
---- X ---------
2 ,,,,,,,,,,,1
And in fact, if you see this kind of problem in textbooks, this IS how it's set up.
Edited to add: sorry about the commas - need them there for spacing.
Last edited by rodentraiser; 08-11-2019 at 11:13 PM..
You'd be surprised how many engineers and mathematicians think 48÷2(9+3) = 2. (It doesn't.)
You'd be surprised how many like to play that "gotcha" trick. Problem is, it's actually ambiguous which makes it a "gotcha." The question becomes when do you switch from order of operations to simply left to right arithmetic. BIDMAS or PEMDAS. Does division come before multiplication or multiplication before division or are they equal rank? Is the division symbol a grouping symbol and therefore a "parenthesis?"
I've never known any engineers and scientists to depend on BIDMAS outside grade school. Instead they would avoid the ambiguity and write what they actually mean:
Even if you did the parentheses first, you'd still get 2(9) + 2(3) (distribution), which is 24. Then you'd have 48 ÷ 24.
It depends on which system you were taught. I was always taught to replace the symbols with their equivalents. In this case, I'd replace the divided sign by / (or rather a straight line) and then 48 would go on top and 2(9+3) would go underneath. After that, you work the parentheses and then the math. Engineers have been doing it this way for centuries. If buildings start collapsing in the next couple of years, you know why.
...
Quote:
Originally Posted by kanonka
To be honest, this is not a math problem; it is "order of operations" gotcha
It all depends whether there is a difference between "/" and ":". In some approaches ":" represents a divisor line, thus having all before it as "top" and everything after it as "bottom". That's why it is advisable to always use parentheses. Otherwise even calculators take it differently :
Instead they would avoid the ambiguity and write what they actually mean
Yes, exactly this. Outside classroom arithmetic "math problems" exercises this isn't an issue. The notation here functions like grammar - technically "I prepared dinner with my mom, a chef and a pastry artist" and "I prepared dinner with my mom, a chef, and a pastry artist" are the same sentence with or without an Oxford comma, but the first statement is ambiguous whether there were four people in the kitchen or two, so a good writer would either rephrase it or add the comma, depending on meaning. A good mathematician would similarly rephrase that sort of ambiguous mathematical sentence.
Even if you did the parentheses first, you'd still get 2(9) + 2(3) (distribution), which is 24. Then you'd have 48 ÷ 24.
But if you did the parenthesis first, you'd be adding 9 + 3, so you'd no longer be calculating 2(9) or 2(3).
When our state had the CAHSEE (California High School Exit Exam), this type of problem would be an example of a "tricky" question for students who forgot about PEMDAS. One of the answers would be 2, which of course was wrong; the correct answer being 288.
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