I believe the math world would do better by eliminating PEMDAS. Language assumptions have no place in mathematics; 80% of the world is not English speaking and has no idea what the3 acronym means. Proper use of nested parentheses and brackets are much more reliable.
In the 1960’s we learned “My Dear Aunt Sally” and that operations were performed in that order. When did the (MD/DM) order rule come in the change the rule?
Always. It has never been correct to treat all four letters in MDAS as separate steps, one after the other. Even a simple example like 3-2+1 will show you that.
Teaching the order of operations is stupidity in practice. It was imposed by typesetters because it was too hard to typeset non ambiguous expressions. Typesetting no longer has these limitations and hasn’t for 100 years. You will rarely find ambiguous expressions in any printed work nowadays. PEMDAS et al are obsolete. The only place it is used is in employment tests to determine if a candidate can follow rules without question. It is not a measure of the ability to do math. In fact, no real mathematician would write such an expression. The focus should be on teaching students how to express themselves in a non ambiguous manner.
Teaching the order of operations is not stupidity in practice, although there's a lot of stupidity in the WAY it is commonly taught - and it probably needs a better name than "order of operations", if it needs a name at all. The basic precedence hierarchy that's involved here - exponentiation has higher precedence than multiplicative operations, which in turn have higher precedence than additive operations - has been the way mathematical notation works for a few centuries now. It is ubiquitous and fundamental to the way mathematics is written. Failing to teach that would be stupidity in practice. Stupid acronyms like PEMDAS and their stupidly rigid calculation process can get in the bin though. Students do not have a hope of expressing themselves at all, let alone unambiguously, if they don't know the elementary grammar of the language. That would be like expecting them to express themselves clearly in English before you've told them how commas and full stops are used. I'd be astonished if PEMDAS appeared in an employment test. It's mathematics for 10 year olds.Who is going to be using that in their recruitment process, and what roles are they recruiting for???
I am from an older generation. The entire educational system, in those days, was geared toward cataloging people instead of educating students. Students who had idyllic memories received an A, were labeled ABOVE AVERAGE- GENIUS LEVEL but had no more understanding of the underlying principals involved than the students who received poor grades. When math was "taught" in those days, the curriculum was MEMORIZE, MEMORIZE, MEMORIZE. The testing system was essentially MUSTIPLE CHOICE- PLUG AND CHUG, as opposed to understanding the underlying concepts and knowing how to set up the solution process. The emphasis was getting a correct answer and a high grade instead of understanding the subject matter. If a multiple choice question was answered correctly, how the answer was obtained was of no consequence. A correct answer could be obtained with a lucky guess, cheating, or a knowledge of how to solve the problem. This means that 2/3rds of the students who were considered to be knowledgeable were, in reality, clueless. In fairness to the educational system at that time, the one teacher-30 student to a classroom educational model with limited resources, had practicality issues that had to flush overwhelming numbers of students through the process. At that time there was no other way for the educational system to work. Now we have computers, the internet, and UA-cam in particular, that can provide a path for positive changes in the way people can be educated. In my opinion the old system has been rendered obsolete due to courses, like this one, offered on the internet. The goal of a student can now be shifted from getting a high grade at any cost to understanding the subject matter.
Given the amount of effort that teachers seem to have to put into "unteaching" the M before D or A before S misconceptions, which arise, completely understandably, from these silly acronyms, I'm surprised it hasn't occured to more of them that perhaps they should just not teach those acronyms in the first place.
-24 is the wrong answer….. it is of course -39. Even PEMDAS says so. First parentheses then exponents then multiplication THEN division then addition then subtraction. These rules apply also between parentheses. The mathematical operations multiplication and division are NOT equal and the rule to do whatever comes first is wrong.
absolutely not. This right here is why my old teacher didn't teach it as PEMDAS he taught it as PEMSA (Please Excuse My Smelly Ass if you love mnemonics) How it works: 1:) treat division like a fraction and use the reciprocal rule (example 7 ÷ 4 is the same as 7 * 1/4. Since we have the whole number of 4 we turn it into a fraction by giving it the denominator of 1) 2:) x - y is the same as -y + x 3:) -x - y is the same as -y + -x Apply that here: (8 ÷ 4 * 2)² becomes (1/4 * 8 * 2)² 1/4 of 8 is of course 2 then 2 * 2 is 4 and finally the exponent of 2 so 4 * 4 which is 16 Now the second set of () (5 * 2³) we do exponent first so 2 * 2 * 2 is 8 then 8 * 5 is 40 Finally put it all together -40 + 16 = -24
-24
I have to say :
"Thanks to PEMDAS !"
I believe the math world would do better by eliminating PEMDAS. Language assumptions have no place in mathematics; 80% of the world is not English speaking and has no idea what the3 acronym means. Proper use of nested parentheses and brackets are much more reliable.
16-40
-24
note replace "÷4" with "×(1/4)"
and mutiplication order is important;
8÷4×2
=8×(1/4)×2 =4
=8×2×(1/4) =4
=2×8×(1/4) =4
=(1/4)×2×8 =4
-24, of course!! :)
Answer: -24
-----------
(8➗ 4 x 2)^2-(5x2^3)
Following PEMDAS,
(4^2)-(5x8)
16-40= -24
4² - 40 = -(40 - 16) = -24.
For me I remember PELMA, subtraction or division can be taken as negative addition and Inverse multiplication respectively...!
we called it PEMSA cause of the mnemonic Please Excuse My Smelly Ass
same concept.
In the 1960’s we learned “My Dear Aunt Sally” and that operations were performed in that order. When did the (MD/DM) order rule come in the change the rule?
Always. It has never been correct to treat all four letters in MDAS as separate steps, one after the other. Even a simple example like 3-2+1 will show you that.
(8 : 4 · 2)² - (5 · 2³) = ?
----------------------------------
1st term of the subtraction :
(8 : 4 · 2)² = ((8 : 4) · 2)² = (2 · 2)² = (4)² = 16
2nd term of the subtraction :
(5 · 2³) = (5 · (2³)) = (5 · 8) = 40
-------------------------------------
16 - 40 = (40 - 16) · -1 = -24✅
-24 is the answer
-24 👍🏻
= 16 -40 = - 24
Teaching the order of operations is stupidity in practice.
It was imposed by typesetters because it was too hard to typeset non ambiguous expressions. Typesetting no longer has these limitations and hasn’t for 100 years. You will rarely find ambiguous expressions in any printed work nowadays. PEMDAS et al are obsolete. The only place it is used is in employment tests to determine if a candidate can follow rules without question. It is not a measure of the ability to do math. In fact, no real mathematician would write such an expression.
The focus should be on teaching students how to express themselves in a non ambiguous manner.
Teaching the order of operations is not stupidity in practice, although there's a lot of stupidity in the WAY it is commonly taught - and it probably needs a better name than "order of operations", if it needs a name at all.
The basic precedence hierarchy that's involved here - exponentiation has higher precedence than multiplicative operations, which in turn have higher precedence than additive operations - has been the way mathematical notation works for a few centuries now. It is ubiquitous and fundamental to the way mathematics is written. Failing to teach that would be stupidity in practice.
Stupid acronyms like PEMDAS and their stupidly rigid calculation process can get in the bin though.
Students do not have a hope of expressing themselves at all, let alone unambiguously, if they don't know the elementary grammar of the language. That would be like expecting them to express themselves clearly in English before you've told them how commas and full stops are used.
I'd be astonished if PEMDAS appeared in an employment test. It's mathematics for 10 year olds.Who is going to be using that in their recruitment process, and what roles are they recruiting for???
Absolutely! PEMDAS has no function other than to make inadequates feel superior by giving schoolkids grossly ambiguous questions.
❤️ I couldn’t do this in high school , but at 73 , I love trying these problems.
I am from an older generation. The entire educational system, in those days, was geared toward cataloging people instead of educating students. Students who had idyllic memories received an A, were labeled ABOVE AVERAGE- GENIUS LEVEL but had no more understanding of the underlying principals involved than the students who received poor grades. When math was "taught" in those days, the curriculum was MEMORIZE, MEMORIZE, MEMORIZE. The testing system was essentially MUSTIPLE CHOICE- PLUG AND CHUG, as opposed to understanding the underlying concepts and knowing how to set up the solution process. The emphasis was getting a correct answer and a high grade instead of understanding the subject matter. If a multiple choice question was answered correctly, how the answer was obtained was of no consequence. A correct answer could be obtained with a lucky guess, cheating, or a knowledge of how to solve the problem. This means that 2/3rds of the students who were considered to be knowledgeable were, in reality, clueless.
In fairness to the educational system at that time, the one teacher-30 student to a classroom educational model with limited resources, had practicality issues that had to flush overwhelming numbers of students through the process. At that time there was no other way for the educational system to work. Now we have computers, the internet, and UA-cam in particular, that can provide a path for positive changes in the way people can be educated. In my opinion the old system has been rendered obsolete due to courses, like this one, offered on the internet. The goal of a student can now be shifted from getting a high grade at any cost to understanding the subject matter.
Negative 24
Thank you
8/4=2
2*2=4
4^2=16
2^3=8
5*8=40
16-40=-24
Although, to me at least, this is basic stuff, thank you for keeping my brain facile. It's a pleasure working out the problems.
-24
-24 correction
Now, is it “8/4” or “4*2,” that is the burning 🔥 question, isn’t it?
When reading from left to right, it's 8/4 first, and the quotient then multiplied by 2.
Given the amount of effort that teachers seem to have to put into "unteaching" the M before D or A before S misconceptions, which arise, completely understandably, from these silly acronyms, I'm surprised it hasn't occured to more of them that perhaps they should just not teach those acronyms in the first place.
Too long winded
Answer =-24
got -24 basic PEMDAS thanks for the fun. (2 X 2)^2 - (5 X 8) 16 - 40 = -24
Yeah! Does happy dance. 💃
Solved it via the thumbnail.
-24
Yay, got it.
too long
Follow PEMDAS and that's what you get, -24
-24 is the wrong answer….. it is of course -39. Even PEMDAS says so. First parentheses then exponents then multiplication THEN division then addition then subtraction. These rules apply also between parentheses. The mathematical operations multiplication and division are NOT equal and the rule to do whatever comes first is wrong.
absolutely not. This right here is why my old teacher didn't teach it as PEMDAS he taught it as PEMSA (Please Excuse My Smelly Ass if you love mnemonics)
How it works:
1:) treat division like a fraction and use the reciprocal rule (example 7 ÷ 4 is the same as 7 * 1/4. Since we have the whole number of 4 we turn it into a fraction by giving it the denominator of 1)
2:) x - y is the same as -y + x
3:) -x - y is the same as -y + -x
Apply that here:
(8 ÷ 4 * 2)² becomes (1/4 * 8 * 2)²
1/4 of 8 is of course 2 then 2 * 2 is 4 and finally the exponent of 2 so 4 * 4 which is 16
Now the second set of ()
(5 * 2³) we do exponent first so 2 * 2 * 2 is 8 then 8 * 5 is 40
Finally put it all together
-40 + 16 = -24
24
John the JACKASS, who has special ability to make a mountain of a molehill 🥸
ah youth today and their lack of discipline.
Negative 24
-24
-24
-24
-24
-24