-4 squared divided by 2 times - 2 Can You Find the ERRORS in This Work? Basic Math Mistakes!
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- เผยแพร่เมื่อ 16 ก.ย. 2024
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This is not a math problem but a math lawyer caveat .
I am an engineer. I use parentheses for these kind of cases. So everyone knows exactly what i mean and if inputing this to a computer or calculator I will get a consistent result.
If you are "wrong" here, doesn't mean you are bad at math.
So true. It depends where you set up the (
I always liked parenthetical expressions. What threw me was the Title "-4 squared" whereas it should have said "a negative (4 squared)". also, the "2 X -2" I saw as 2X -2, not 2 times -2. I suppose he clarified those in the verbiage but after a short while, it does become "blah bliblah bliblah blah".
@@thomasharding1838I came out of one of the top math programs in the country and I was one of the top students therefore one of the top math students in the country.
We were taught that when you write down an expression like this, you have written it down incorrectly.
So, to ask for an answer to this question is starting with an inaccurate premise.
Very easy. The result is
16
I'm proud that my 7 and 9 year old boys did it right. I put the problem on their plates a little earlier for breakfast as a "5-minute wake-up task". The 5 other children (between 5 and 16) had to solve other tasks.
Salutations des Caraïbes françaises...🙂
And one word as a postscript: This PEMDAS is in itself a provocation for errors, here the section "MDAS". Other countries solve this better: In many countries, the simple "dot before dash calculation" is the rule of thumb. "Dot" stands for multiplication and division, "dash" for addition and subtraction. It is easier to understand in order to keep to the correct sequence.
Well...PEMDAS is a good example of how such shortcuts can sometimes be counterproductive.🤔🤨
Fix the Title. It says "-4 squared" not "a negative (4 squared)". Before the puzzle is even opened, the mind is thinking "16".
I get that the first term is there to emphasise that there's a proper, accepted, way to parse such things, but outside of a test scenario would it not be better written with brackets, −(4²), to avoid ambiguity?
Because many people do lose track of the actual rules, using brackets of some kind is definitely preferred. But then there would be no point in publishing a video like this that reminds folks of what to do when there aren't surplus brackets making the solution trivial to work out.
If this was writing thusly, (-((4²)÷2))×(-2), then as long as the person doing the solution realizes that if you have nested brackets you resolve them from the innermost to the outermost, they'll get it right.
But this wouldn't let the teacher reinforce things like M and D being the same order of operations, done from left to right, and same with A and S, which is why BODMAS and PEMDAS both work the same even though one is DM and the other is MD.
Personally I think the mnemonics should always have been written like this:
PE(M&D)(A&S) or BO(D&M)(A&S). That are least would remind people - if they remembered the ( ) at all, that all "same order" operations are to be done in one pass from left to right. 🤷♂️
@@ernesthakey3396 Problem with nested brackets is that, just like multi-nested if...then arguments in programming, it can get a tad hard to parse once you have more than a couple of levels. I do agree regarding PE[MD][AS] though. Or even-shock! horror!-teach the order of operations without resorting to acronyms. That's how I was taught.
It's utterly ubiquitous and completely normal in algebraic expressions to write it without parentheses. For example, absolutely nobody writes a quadratic with coefficients -1,1 and 1 as
-(x²)+x+1
It's just
-x²+x+1
As such, it's completely normal in mathematics to write -(4²) as -4², because people who use mathematics to actually do things know what that means.
So while there's nothing wrong with writing this as -(4²) if you want to, I don't think that should be the teaching goal. The teaching goal should be for students to know what -4² means.
Part of learning mathematics is learning the language of mathematical notation.
@@dazartingstall6680I agree. I do wonder how many of the people who talk about using parentheses for everything have actually tried that for real. It might work for some people but often it seems like a bit of a knee-jerk reaction that hasn't been thought through.
There's a reason why some of the tools we use highlight the matching ( and ) as you type. It's hard enough keeping track of multiple layers of nested parentheses as you're writing it, let alone when you're reading it.
If using parentheses everywhere was generally better for everybody, then I doubt all of the conventions we have in mathematical notation that reduce the need for parentheses would have evolved in the first place.
I suggest you use ( ) instead of X for multiplication. I was thinking at first that I had to solve for X, which, after thinking about it made no sense.
Good point. Same thought here initially.
-4^2 ➗ 2 x -2
-(4^2) ➗ 2 x -2
-16 ➗ 2 x -2
Following the order of operations (PEMDAS) from left to right,
16 is the answer.
Try this Alt 0247 = ÷
-(4^2)×(1/2)×(-2)
-16×(1/2)×(-2)
-8×-2
16
This is how the problem would be written to avoid errors. The parentheses around the 4^2 preclude the "error" of -4^2 being treated as (-4)^2
@@awcampbell2002 this is one of those sat questions written by a smug academic who failed high school math.
@tomtke7351 Having a small amount of programming experience & spreadsheet experience I always put in the parentheses because the programmers of the language or of the spreadsheets showed no consistency. When I was an instructor in the army (very basic front end of electronics -ohm's law very basic trig & Pythagorean the rim stuff) I always put in the parentheses because I didn't want the math to be hard & based on the students varying backgrounds & previous instruction. With students from all around the country & each state having different standards to teach to this allowed me to specify what I wanted the student to do. Then they could learn the concepts & not get bogged down in the math
I find it to be difficult because your X and multiplication sign appear to to be the same. I was taught to make a distinction. We used a cursive to make the distinction.
-16
I do not like PEMDAS and BODMAS and all the variations of it. It is not always correct and does not cover all scenarios. It is just a way of simplifying things for primary schools
I totally agree. Avoiding brackets is just lazy, and causes unnecessary confusion. A math professor here in Norway said the same, and he even said there is no global agreement on the rules. So when the interviewer gave him an equation, he gave multiple answers as correct. Use () he said. Math is difficult enough, no need for making it even more complicated.
(-1)4^2. According to pemdas you square the 4 first. Then that is multiplied by -1 in accordance with pemdas order.
In science and engineering a/bx is always meant to be grouped a/(bx). Teaching PEMDAS as a hard and fast rule is wrong and does a disservice to young students.
I don't understand the presenter's almost fetishistic attachment to PEMDAS. This is the computer age. Brackets are cheap - USE THEM and eliminate all ambiguity.
@@HerlongianIf you rewrite it as (-1)4² then obviously the PEMDAS priority rules tell you that it's -16 not 16.
But in order to do that you have to know whether it's correct to rewrite it as (-1)4², and PEMDAS doesn't tell you that.
In order to evaluate -4² correctly, you need to know that the - symbol is a negation operator, not a character in the number -4, and you need to know that the negation operation has lower precedence than the exponentiation. PEMDAS doesn't tell you either of those things.
Evaluating -4² correctly is beyond the scope of PEMDAS.
- 4 squared - (4 x 4) or -4 x -4 is one mistake you could make
In what world is -8x - 2 = 16???
-8x = 2
x = -2/8
x = -1/4 (which is not the correct value for X
Note: -4² ≠ (-4)²=-1*4*4 = -16, NOT 16. (-4)² = -4 * -4 = 16 (which is the correct evaluation/nterpretation of that term)..
According to PEMDAS, the first term should be within parenthesis as follows for this problem to work out properly:
(-4)^2 / 2x -2
16/2x - 2
16=2*2x
16=4x
x=16/4
x=4
Check:
(-4)^2/2x-2=0
16/(2*4)-2=0
16/8-2=0
2-2=0
0=0 This verifies that the correct answer for x = 4, NOT 16.
Without the parenthesis or proper following of the PEMDAS rules, the fist term results in -16 (which is not correct, obviously). According to PEMDAS rules the power or exponent is calculated first & that = -1 * 4 * 4 = -16. Hence -16 / (2*16) -2 = -.5 -2 = -2.5. Hence the wrong answer for x according to the video.
Check:
-16 / 32 - 2 = 0
-.5 -2 = --2.5 (This proves that 16 is not the correct value for x.
its not a x like a missing integer..its the multiplication sign after all. i thought the same thing when i computed it.
@@mracjesstark3468 In that case, he should have used "/" as the division operator & "*" as the multiplication operator to increase clarity.
(-4) '2+2(-2)
I would expect the written Phrase, -4 Squared, to be +16 compared to the number -4^2 which is -16
Deu16.
- 4^2 : 2x(-2) (Forma correcta) = -16 : -4 = +4 RESULTADO CORRECTO. El resultado del vídeo, ¡¡¡UNA MIERDA!!!
-16 ÷ 2 x -2 = 1. multiplicar o dividir de izquierda a derecha el que aparesca primero
---------- 2. sumas o restas de izquierda a derecha el que aparesca primero
-8 x -2 = 16
+16
16
I thought it was 2x not 2 times. So, [-16 / 2x ] - 2
no equal sign so it is multiplication
Thx!
16 is the answer
--16
What a mess with "x-": no chance to get to Moon once more.
There's nothing wrong with that, other than it being preferable to use • for the multiplication, as a few people initially read the × symbol as a letter x for an unknown variable.
Ans =16
The answer is 16.
got it 16 thanks for the fun
Yesterday's errors were in the calculations. Today is about understanding notation.
The student's errors are treating -4² as (-4)², and giving multiplication higher priority than division.
The teacher's error is using the ÷ symbol for division instead of /. Or better still, writing division vertically, with numerator above the line and denominator below.
We can surmise that the teacher has made another error in the past, which was to use stupid, misleading acronyms like PEMDAS to teach the priority rules for different mathematical operations, which is the cause of the student's second error.
which is why I teach my students to turn division into multiplication and subtraction into addition that way there is no confusion. ( use negative exponents when converting to multiplication and remember that x - y is the same as -y + x for converting to addition )
👍🙏
We have -4² ÷ 2 ⋅ -2
1. Following the Orders of Operations, we go from left to right, so we’ll do -4² ÷ 2 first.
Note: -4² ≠ (-4)² -4² = -1 ⋅ 4² = -1 ⋅ 16 = -16
-16 ÷ 2 = -8
2. Now, we’ve simplified the expression to -8 ⋅ -2, which equals 16.
Final ans: 16
Ez
Use parentheses and eliminate ambiguity, then there won't be mistakes. What is this almost fetishistic attachment the presenter has with PEMDAS? This is the computer age. Parentheses are cheap - USE THEM.
Parentheses are not free. They have a cost in terms of readability. Nobody wants to have to write, say, a quadratic, as
-(x²)+(2•x)+3
when we can simply write it as
-x²+2x+3
The conventions that we use to make mathematical notation clearer and simpler have been with us for a long time. They evolved for a reason.
@@gavindeane3670 Yes, and the use of parentheses is part of that evolution. In the computer environment, where garbage in = garbage out, it is vitally important to make sure that there is no ambiguity as to how a mathematical statement is to be executed.
@@silverhammer7779There is no ambiguity in the expression in the video.
What you're concerned about is not ambiguity, it's scope for misinterpretation. That's a good thing to be concerned about. The point I'm making is that lots of use parentheses can cause that problem too, by reducing readability. And also by making the act of writing more error-prone in the first place.
Judicious use of parentheses is good. Blindly using them everywhere is not.
But that's all beside the point since the purpose of this video is to teach the grammar of the language without parentheses.
You have to bracket the 4 WITH the negative sign if you are trying to say -4 * -4. (If -4 where an x value though that you are plugging in to check your work then yes the - would apply)
Also they didn't use the proper order of operations.
PEMA or Parenthesis Exponents Multiplication Addition
so lets rewrite so it is more clear:
-(4²) * 2 ^ -1 * -2
-16 * -2 * 1/2
32 * 1/2
Final Answer is 16.
Wrong. x = 4
In what world is -8x - 2 = 16???
-8x = 2
x = -2/8
x = -1/4 (which is not the correct value for X).
Note: -4² ≠ (-4)²=-1*4*4 = -16, NOT 16. (-4)² = -4 * -4 = 16 (which is the correct evaluation/nterpretation of that term)..
According to PEMDAS, the first term should be within parenthesis as follows for this problem to work out properly:
(-4)^2 / 2x -2
16/2x - 2
16=2*2x
16=4x
x=16/4
x=4
Check:
(-4)^2/2x-2=0
16/(2*4)-2=0
16/8-2=0
2-2=0
0=0 This verifies that the correct answer for x = 4, NOT 16.
Without the parenthesis or proper following of the PEMDAS rules, the fist term results in -16 (which is not correct, obviously). According to PEMDAS rules the power or exponent is calculated first & that = -1 * 4 * 4 = -16. Hence -16 / (2*16) -2 = -.5 -2 = -2.5. Hence the wrong answer for x according to the video.
Check:
-16 / 32 - 2 = 0
-.5 -2 = --2.5 (This proves that 16 is not the correct value for x.
@@ab_ab_cThat's a multiplication symbol, not the letter x used for a variable.
I get the potential for confusion, hence why it's better to use • for multiplication, but if this was an unknown x value then arguing about it's value makes no sense. It's impossible to determine a value for x unless you're told that
-4² ÷ 2x - 2
is equal to something.
@@ab_ab_c lol I see your confusion the original problem isn't x the variable it is x for multiplication. Very confusing and why I ALWAYS use * to denote multiplication on exams I give my students.
@@gavindeane3670 Absolutely correct and the usage of X in addition to his ramblings and his usage of multiple choice in Math is why I do NOT subscribe to this channel, but I do defend him as he is a very kind teacher for giving partial credit and he doesn't make his students feel like idiots. Unlike my old teacher who wanted it 100% right, written fully and in the event of a variable fully proven too. Oh and also he would sneer at his "retarded students" while marking the "retarded" mistakes they made. (" " used to represent his exact words)
-16
16
-16
-16