Hi u/Otherwise-Special521,
Please read the following message. **You are required to explain your post and show your efforts. _(Rule 1)_**
If you haven't already done so, please add a comment below explaining your attempt(s) to solve this and what you need help with **specifically**. See the sidebar for advice on 'how to ask a good question'. Don't just say you "need help" with your problem.
**This is a reminder for all users.** Failure to follow the rules will result in the post being removed. Thank you for understanding.
*I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/askmath) if you have any questions or concerns.*
My guess is something like this is what their looking for (not a unique solution, there are infinitely many options, but I like this one.)
Right side 40=100-60 and 60-35=25
Left side: 40=50-10 and 10+15=25
Its a question for a 9 year old. I guess just find numbers that fit it. I think its from left up and down and from right up and down. Who knows it's a kids exercise i guess
Edit: didnt look at the pic well so changed pretty much all the comment
I think I've been overthinking it.
On the right side, have the middle value be 40
40-0 = 40
40-15= 25
On the left use:
-15 - (-55) = 40
-15 + 40 = 25
Double check if this makes sense though.
Started doing this:
X + Y = 25
X - Z = 40
2X + Y - Z = 65
M - N = 40
M - L = 25
2M - N - L = 65
This gets me no where
I think you’re right. My stoned ass was confused like *what number that can be subtracted from to equal 25 also works for subtraction to 40*. Clever.
Goddamn it Jim Foxworthy, you got me.
I like your take and I was thinking of doing a similar one too what with the negatives, as I knew the right side would be easy with one direction, but honestly the whole thing is ridiculous. 40 - 0 is easy to make 40 with but the opposite of 0 - 40 just get us -40. We’re given no sense of direction so we can only assume the math goes this certain way and then the math will only work that certain way. I don’t know what the point is when it comes down to giving this to a 9 year old, but it perhaps it just promotes creative thinking. Like how will they solve this? Sure they got a variety of answers or just nothing. Personally I’m awful at math so I’m always giving a ..creative answer
They have learned negative numbers, rjght? Because then you can just fill in two random numbers on either side, and fill the rest in accordingly. Without negative numbers, this is not solvable.
It's not solvable either with that, it's a circular equation of four terms of which two of those are already distinct.
This question makes no sense whatsoever. Someone tried to be clever and made a mess of a question.
We have agreed on the "intended interpretation" of this notation, see my other comment. Questions like these often do not follow standard notation. The only problem is that that has not been made clear either in the question, or in the post. But luckily, the diamond shape is quite suggestive.
We have agreed on the "intended interpretation" of this notation, see my other comment. Questions like these often do not follow standard notation. The only problem is that that has not been made clear either in the question, or in the post. But luckily, the diamond shape is quite suggestive.
Agreed. Maybe I am reading it wrong, but the only answer I can come up with is "false".
Am I wrong to view this as: 25 = x + y - z = 40 = a - b - c = 25
In that case you end up with infinitely many solutions, so you can pick whatever number you want in respect to another number.
40=x-y+z,
25=z+y-x,
x=y+7.5,
y=Any number you want,
z=32.5,
40=a-b-c,
25=c-b-a,
a=c+7.5,
b=-32.5,
c=Any number you want,
Maybe I'm missing the rules of this diamond, but the idea is to find numbers (in clockwise direction, starting at 11 o'clock)
a f
b e
c d
such that b-a=40, b+c=25, e-d=25 and e-f=40, right? Or are there more requirements?
The interpretation of the diamond I used was different that this. I have another comment in this chain that explains that I for instance read this first subtraction in the opposite order. So in that case, you do need negative numbers. But then again, if the question doesn't explain its notation, who knows at this point what it means.
Doesnt ask for a unique solution. These equations are enough to come up with some solution. Tho a bit of a hassle without knowing some linear algebra lol.
I recommend refusing to answer this nonsense and writing a note that your household refuses to recognize the validity of poorly structured questions such as this one.
It's not like the grades of a 9-year-old really matter, so as long as they actually understand addition and subtraction rules, there's really no harm in taking the opportunity to make a statement.
Idk, you can make a stand here, but it’s likely that the teacher doesn’t know that this is a bad question in the first place. Elementary teachers are frequently bad a math, and so they probably just stick to their worksheets and do their best.
Next week will probably have another poorly structured exercise.
Rather than teaching your child to ignore their work, work on explaining what is strange here, talk to the teacher, admit that you will just try your best, and then move on.
Or you can teach them that your teacher is fallible, makes mistakes, and it can become a conversation between you, the teacher, and your child. You don't want to teach your children that every disagreement has to be where you plant your flag and pick a fight.
There's no one to "stand up to" in this situation. The teacher is just clueless here. You don't need to be a bully.
I disagree, in the early years is where you want to atleast get the fundamentals down. Like "here is how you set up and addition problem". Then you see this mess? I guess in the end I am not a teacher so I wouldn't know, but my gut tells me this is bad for learning. Hell i'd even consider a shape problem (Like if you have 10 apples and eat 1 how many apples do you have left?) like we used to do better, cause then at least it connects the kid with what you are writing.
9th grade is 4th. If i remember this is the age you should be doing fractions and negative integers. If you get lost early in math its pretty much impossible to do the harder topics.
Oh well i guess only for the part where it is like "its not like the grades of a 9-year old really matter". I think they do, in that education of fundamentals is pretty important, but its also important to know what the grade is tied to. If its tied to a meaningless skill/question then it is definitely meaningless and you should complain to give it meaning.
My point was that so long as they have the necessary knowledge, the grade itself doesn't matter as there are no ramifications from it. Hell, they can even get an F and nothing happens unless the parent(s) consent to holding them back or having them take a remedial course. Unlike in high school, their GPA doesn't actually affect anything - it's purely the knowledge itself that matters. The only reasons for even having grades at that level are to communicate the status of students with their parents and to begin teaching students to associate the quality of their work with grades, which if the assignments are good (unlike this one), will help ease the transition into high school later.
I think the intention is that you don't actually consider the series of operations, just 1 operation at a time. So, the circle represents the set of equations (if read in a clockwise direction):
40 = A - B; B - C = 25; 25 = D + E; E - F = 40
Though, since they're using explicit subtraction symbols, it's not at all clear which direction the operations are meant to be read. I've assumed clockwise here, but it could be some other ordering that was intended.
This is a problem for a 9 year old…which put this kid in the third or fourth grade.
The formatting is poor and very problematic for kids that learning about operational properties.
My questions to the teacher would be…
Since when is subtraction commutative?
I agree. Maybe some arrows that show the order of operations would be nice.
But if they have to come up with this "creative" stuff, why not make it like a cross word puzzle but with numbers. That avoid a lot of ambiguity.
On the left center, pick a number less than 25, and on the right pick a number greater than 40, then the rest is self explanatory, just remember that the number on the top left will be negative. See? Easy! Even a 9 year old could do it.
Only if you don’t treat each diagonal like it’s own expression.
I can see how it’s confusing when kids don’t understand and then take it home to parents who aren’t familiar.
It’s kind of ironic though because I feel like the lateral thinking skills these exercises are intended to teach are the exact same skills parents lack that make them bad at understanding math framed differently then they expect.
Definitely a catch 22 type situation
I can see how this might help kids think differently about math problems, but in a practical sense no one does calculations this way to solve actual problems. It seems counterproductive to avoid maintaining consistent notation when teaching introductory maths, since they'll have to relearn everything later.
For sure. I think with math being broadly exposed to a bunch of types of learning ultimately works best.
I’ve definitely seen the reverse thing happen where students are good at solving math problems presented on paper in a math class but fail to recognize how math is useful or see it’s application in day to day life
Plus who knows if questions such as this are helpful anyway. Particularly if it’s just frustrating parents and students it might be counterproductive.
I do think math needs to try harder to show that it’s basically an art form and the real math is recognizing and framing problems, showing that your answer is correct. And not memorizing that 9x7=63; or worse, the “order of operations”. So I understand the motivation to teach differently
I'm curious why you bring up order of operations, I tend to agree that memorizing tables of multiplication or division is not really teaching people to think, but how you perform operations is pretty important in any late high school or college math. I also see a lot of students struggle with basic algebra because of this.
It’s important to know. As are times tables.
But the order of operations is just an arbitrary convention to keep notation simpler in certain cases. There’s no mathematical reason behind it.
It gets worse when people mix in notation that rarely ever is used like the obelus for division and then post ‘problems’ that people argue over.
I think it creates a false impression that this is what math is, when in reality it’s like seeing colour and color can be spelled differently and then inferring “isn’t literature nonsense”
>But the order of operations is just an arbitrary convention to keep notation simpler in certain cases. There’s no mathematical reason behind it.
As someone who uses complex mathematics daily, I wholeheartedly disagree. The order of operations exists to provide a framework, without it you can interpret an equation multiple ways. There's a nice example given here https://en.m.wikipedia.org/wiki/Order_of_operations
Math has to be more exact than you make it seem, language is completely different.
The modern order of operations are just an arbitrary convention though, primarily so that polynomials can be written without parentheses.
It’s very useful for notation, similar to spelling rules.
Imagine say somebody programming a computer. The logical units of addition, multiplication, division, and exponentiation are all independent binary operations with no inherent presidence over each other.
When it comes to telling how to parse an expression like (3x + 2). We know to arrange these operations into the stack as add( multiply( 3, x ), 2). But we could have chose the convention to be strict left to right or something else.
The subjects of group, field, and category theory cover these topics, and discuss the properties of algebraic operations in depth.
Again the order of operations is great. It’s useful to be able to have a shared understanding of written notation but it doesn’t ‘have’ to be that way. And in fact in practice it isn’t. Division for example is typically written with a horizontal line which inherently parenthesis the numerator and denominator. This is again partially because polynomials are often found in radicals and we prefer to write them without parens.
This is why in math it’s important to understand why the set of rules you’re learning applies. What is the difference between 3(x+2) and (3x)+2. Why do we choose to recognize one as “the” 3x+2.
For the left side, we want a tuple (a, b, c) such that a + b - c = 40 and c - b + a = 25. There are infinitely many solutions (in particular, there is a solution for any choice of c) so we may simply plug in c = 0 and solve for a and b.
We have a + b = 40 and a - b = 25 => 2a = 65 => a = 32.5, b = 7.5
Solve the right side similarly.
Let’s try to avoid negatives as much as possible. I’m also going to avoid 0 just because.
This means that for the left side we want to write 40 as a - b where b < 25 because b + something positive must be 25.
If b = 24, a = 40 + 24 = 64, and for the left, we have this.
40 = 64 - 24
25 = 24 + 1
For the right side, we want to write 40 as a - b where b > 25 so that b - something positive = 25
If b = 26, a = 40 + 26 = 66, and for the right side, we have this.
40 = 66 - 26
25 = 26 - 1
In the end, it should look something like this
40
64 66
24 26
1 1
25
It took me a minute to notice this, but there's no indicator that the far left and far right squares would be the start of any computation. It might be the case that the "middle value" in each chain is just part of the chain, not anything special.
So, my reading of the left side would be that: 40 = a - b + c, and simultaneously, 25 = c + b - a.
By combination, 65 = 2c, so the bottom-left box is 32.5.
I'm a bit stuck on solving for A and B from there, and don't have a ton of time to dedicate to trying combinations at the moment (I presume subtracting the two equations would help in some way,) just wanted to pass along a different reading of the problem from what I've seen so far.
I think you're supposed to read the expressions starting from the left/right corner then going to the top/bottom corner, then solve that system of equations
So wait they want an answer to 40=x-y-z=25=a+b-c?
That's the dumbest question.
I'm thinking it's meant to be the far left and right numbers should have some number added or subtracted to give the two knowns, but still there are infinite answers to that so I say this is a bad question.
I think what it's asking is for you to find some numbers A,B,C,D,E,F such that B - A = 40, B + C = 25, D - E = 40, and F - E = 25.
This problem doesn't have a unique solution. To find a particular solution, choose any two numbers you want for B and E (the box on the left and the box on the right). You can now find the rest of the numbers by using the equations.
Doubt they’re trying to indicate 40 = 25, so will assume there are 6 unknowns and 4 equations. Many possible solutions. You could try picking two of the numbers and then figuring out the rest. No need to slap this into a matrix.
All the possible solutions will look like this:
Put an arbitrary number x in the leftmost square, and put an arbitrary number y in the rightmost square. The other squares are then forced to a single value
I guess it is:
a+b=25
a-c = 40
d-e = 25
d-f = 40
So there is six unknowns for four equations. Which means that there is going to be multiple solutions. Preposterous task for a nine year old.
I would think it’s from top to bottom
40
L=40-20+5
R=40-10-5
25
It doesn’t say there’s only 1 correct answer so who really knows 🤷🏻♀️
But I’m also not sure if those are subtraction or division 🤷🏻♀️ as its for a 9yo I’m assuming subtraction.
This says 40=25
Unless they're working in modular arithmetic or something (which should be indicated) this is a contradiction. That's a fancy math word for bullshit.
If they’re that young, they probably can put whatever numbers they like… but negative numbers would have to be used. That seems quite young for negative numbers
There are something like 87 wonderful submissions to r/ConfidentlyIncorrect here, followed by people agreeing with them. There are probably infinite solutions to this. All real numbers can go in the outer most boxes.
Let the leftmost box be a, the left-top b, the left-bottom c, the right-top d, the right-bottom f, the rightmost g.
From what I can tell, the boxes create the following set of equations:
a - b = 40
a + c = 25
40 = d - g
25 = f - g
Therefore,
b + c = -15
d - f = 15
Therefore, choose any complex number a. b is therefore a - 40, and c is therefore 25 - a. Choose any complex number g. d is therefore 40 + g, and f is therefore 25 + g.
Here’s the thing, there are a fuckton of ways to interpret this question so it’s a pretty shite one for an adult, but the judgement of a 9 year old isn’t as clouded by all these established math rules, so it’ll actually be more easy for them. I think.
40=x-y+z
25=z+y-x
x=y+7.5
y=Any number you want
z=32.5
Second side:
40=a-b-c
25=c-b-a
a=c+7.5
b=-32.5
c=Any number you want
I used substitution. there was so much work and it was all over the place so i decided not to copy and paste it. If you’d like me to I can.
At least he will know how to solve confusing and redundantly presented math equations which he can use for future investments, like buying a car or home
Hi u/Otherwise-Special521, Please read the following message. **You are required to explain your post and show your efforts. _(Rule 1)_** If you haven't already done so, please add a comment below explaining your attempt(s) to solve this and what you need help with **specifically**. See the sidebar for advice on 'how to ask a good question'. Don't just say you "need help" with your problem. **This is a reminder for all users.** Failure to follow the rules will result in the post being removed. Thank you for understanding. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/askmath) if you have any questions or concerns.*
I don't even know in which order to read that
wtf is this nonsense?
What im trying to figure out 😭
My guess is something like this is what their looking for (not a unique solution, there are infinitely many options, but I like this one.) Right side 40=100-60 and 60-35=25 Left side: 40=50-10 and 10+15=25
Its a question for a 9 year old. I guess just find numbers that fit it. I think its from left up and down and from right up and down. Who knows it's a kids exercise i guess Edit: didnt look at the pic well so changed pretty much all the comment
Please share whenever you get the right answer
I think I've been overthinking it. On the right side, have the middle value be 40 40-0 = 40 40-15= 25 On the left use: -15 - (-55) = 40 -15 + 40 = 25 Double check if this makes sense though. Started doing this: X + Y = 25 X - Z = 40 2X + Y - Z = 65 M - N = 40 M - L = 25 2M - N - L = 65 This gets me no where
I think you’re right. My stoned ass was confused like *what number that can be subtracted from to equal 25 also works for subtraction to 40*. Clever. Goddamn it Jim Foxworthy, you got me.
I like your take and I was thinking of doing a similar one too what with the negatives, as I knew the right side would be easy with one direction, but honestly the whole thing is ridiculous. 40 - 0 is easy to make 40 with but the opposite of 0 - 40 just get us -40. We’re given no sense of direction so we can only assume the math goes this certain way and then the math will only work that certain way. I don’t know what the point is when it comes down to giving this to a 9 year old, but it perhaps it just promotes creative thinking. Like how will they solve this? Sure they got a variety of answers or just nothing. Personally I’m awful at math so I’m always giving a ..creative answer
They have learned negative numbers, rjght? Because then you can just fill in two random numbers on either side, and fill the rest in accordingly. Without negative numbers, this is not solvable.
It's not solvable either with that, it's a circular equation of four terms of which two of those are already distinct. This question makes no sense whatsoever. Someone tried to be clever and made a mess of a question.
We have agreed on the "intended interpretation" of this notation, see my other comment. Questions like these often do not follow standard notation. The only problem is that that has not been made clear either in the question, or in the post. But luckily, the diamond shape is quite suggestive.
We have agreed on the "intended interpretation" of this notation, see my other comment. Questions like these often do not follow standard notation. The only problem is that that has not been made clear either in the question, or in the post. But luckily, the diamond shape is quite suggestive.
Agreed. Maybe I am reading it wrong, but the only answer I can come up with is "false". Am I wrong to view this as: 25 = x + y - z = 40 = a - b - c = 25
In that case you end up with infinitely many solutions, so you can pick whatever number you want in respect to another number. 40=x-y+z, 25=z+y-x, x=y+7.5, y=Any number you want, z=32.5, 40=a-b-c, 25=c-b-a, a=c+7.5, b=-32.5, c=Any number you want,
Yes but I cant seem to find the numbers that satisfy it
Maybe I'm missing the rules of this diamond, but the idea is to find numbers (in clockwise direction, starting at 11 o'clock) a f b e c d such that b-a=40, b+c=25, e-d=25 and e-f=40, right? Or are there more requirements?
No more other requirements, I did the same thing as you and used algebra
So just pick two random numbers for b and e, and then you can compute the rest by standard arithmetic.
That's how I interpreted the question, except b-a=40, b+c=25
Thanks, I edited it. I made an error with typing it over.
Right side: 40=100-60 and 60-35=25 Left side: 40=50-10 and 10+15=25 No negative numbers needed
The interpretation of the diamond I used was different that this. I have another comment in this chain that explains that I for instance read this first subtraction in the opposite order. So in that case, you do need negative numbers. But then again, if the question doesn't explain its notation, who knows at this point what it means.
Exactly, if there aren't enough instructions to remove an interpretation, then that interpretation is correct. Along with all others possible.
I suppose as long as the order of the numbers means nothing
Wdym? The order is top to bottom and each expression lies on a straight line
Ah yes, top to bottom like everything is normally read.
If the instructions don't specify, then there is no incorrect interpretation.
a-b = 40 40 = c-d a+x = 25 25 = y-d We have 4 equations and 6 unknowns. We need more information for there to be a unique solution.
Doesnt ask for a unique solution. These equations are enough to come up with some solution. Tho a bit of a hassle without knowing some linear algebra lol.
I recommend refusing to answer this nonsense and writing a note that your household refuses to recognize the validity of poorly structured questions such as this one. It's not like the grades of a 9-year-old really matter, so as long as they actually understand addition and subtraction rules, there's really no harm in taking the opportunity to make a statement.
Idk, you can make a stand here, but it’s likely that the teacher doesn’t know that this is a bad question in the first place. Elementary teachers are frequently bad a math, and so they probably just stick to their worksheets and do their best. Next week will probably have another poorly structured exercise. Rather than teaching your child to ignore their work, work on explaining what is strange here, talk to the teacher, admit that you will just try your best, and then move on.
On the other hand, teach your child to stand up for themself to authority figures and not to accept unrealistic or ill-founded expectations of them.
Or you can teach them that your teacher is fallible, makes mistakes, and it can become a conversation between you, the teacher, and your child. You don't want to teach your children that every disagreement has to be where you plant your flag and pick a fight. There's no one to "stand up to" in this situation. The teacher is just clueless here. You don't need to be a bully.
I agree. As an artist who sucks at math and always have this and word questions should never BE!
I disagree, in the early years is where you want to atleast get the fundamentals down. Like "here is how you set up and addition problem". Then you see this mess? I guess in the end I am not a teacher so I wouldn't know, but my gut tells me this is bad for learning. Hell i'd even consider a shape problem (Like if you have 10 apples and eat 1 how many apples do you have left?) like we used to do better, cause then at least it connects the kid with what you are writing. 9th grade is 4th. If i remember this is the age you should be doing fractions and negative integers. If you get lost early in math its pretty much impossible to do the harder topics.
Are you sure you meant to say "disagree"? Kind of sounds more like agreement to me.
Oh well i guess only for the part where it is like "its not like the grades of a 9-year old really matter". I think they do, in that education of fundamentals is pretty important, but its also important to know what the grade is tied to. If its tied to a meaningless skill/question then it is definitely meaningless and you should complain to give it meaning.
My point was that so long as they have the necessary knowledge, the grade itself doesn't matter as there are no ramifications from it. Hell, they can even get an F and nothing happens unless the parent(s) consent to holding them back or having them take a remedial course. Unlike in high school, their GPA doesn't actually affect anything - it's purely the knowledge itself that matters. The only reasons for even having grades at that level are to communicate the status of students with their parents and to begin teaching students to associate the quality of their work with grades, which if the assignments are good (unlike this one), will help ease the transition into high school later.
Ah that makes a good point, i understand now
40 ≠ 25 so I don't know how to interpret this nonsense.
I think the intention is that you don't actually consider the series of operations, just 1 operation at a time. So, the circle represents the set of equations (if read in a clockwise direction): 40 = A - B; B - C = 25; 25 = D + E; E - F = 40 Though, since they're using explicit subtraction symbols, it's not at all clear which direction the operations are meant to be read. I've assumed clockwise here, but it could be some other ordering that was intended.
I'm pretty sure the answer is 8.
I’m pretty sure your avatar is 8 & mine 9.
Why was 6 afraid of 7?
Because 6 saw 9 beat up 8.
No cause 7,8,9.
This looks like a poorly concepted way of teaching basic operations. It's only adding an extra layer of complexity for no reason
This is a problem for a 9 year old…which put this kid in the third or fourth grade. The formatting is poor and very problematic for kids that learning about operational properties. My questions to the teacher would be… Since when is subtraction commutative?
I agree. Maybe some arrows that show the order of operations would be nice. But if they have to come up with this "creative" stuff, why not make it like a cross word puzzle but with numbers. That avoid a lot of ambiguity.
>Since when is subtraction commutative? That is the point it isn't. That is why the result is 40 on one side and 25 on the other.
Do the numbers have to be the same or something?
Im guessing yes
Zero is a number. Subtract that from both sides.
It’s gotta be at least 8 fr fr
This is unsolvable. For a system of 2 equations and 3 unknowns, there is an infinite number of solutions
In equations with IMS, you can pick whatever numbers you want and it will be equally correct.
This is either very easy or very hard. SMH
On the left center, pick a number less than 25, and on the right pick a number greater than 40, then the rest is self explanatory, just remember that the number on the top left will be negative. See? Easy! Even a 9 year old could do it.
This is so wrong... if you wrote it all out in a single line they're saying 25=40.... sorry my math is too ancient!!
Only if you don’t treat each diagonal like it’s own expression. I can see how it’s confusing when kids don’t understand and then take it home to parents who aren’t familiar. It’s kind of ironic though because I feel like the lateral thinking skills these exercises are intended to teach are the exact same skills parents lack that make them bad at understanding math framed differently then they expect. Definitely a catch 22 type situation
I can see how this might help kids think differently about math problems, but in a practical sense no one does calculations this way to solve actual problems. It seems counterproductive to avoid maintaining consistent notation when teaching introductory maths, since they'll have to relearn everything later.
For sure. I think with math being broadly exposed to a bunch of types of learning ultimately works best. I’ve definitely seen the reverse thing happen where students are good at solving math problems presented on paper in a math class but fail to recognize how math is useful or see it’s application in day to day life Plus who knows if questions such as this are helpful anyway. Particularly if it’s just frustrating parents and students it might be counterproductive. I do think math needs to try harder to show that it’s basically an art form and the real math is recognizing and framing problems, showing that your answer is correct. And not memorizing that 9x7=63; or worse, the “order of operations”. So I understand the motivation to teach differently
I'm curious why you bring up order of operations, I tend to agree that memorizing tables of multiplication or division is not really teaching people to think, but how you perform operations is pretty important in any late high school or college math. I also see a lot of students struggle with basic algebra because of this.
It’s important to know. As are times tables. But the order of operations is just an arbitrary convention to keep notation simpler in certain cases. There’s no mathematical reason behind it. It gets worse when people mix in notation that rarely ever is used like the obelus for division and then post ‘problems’ that people argue over. I think it creates a false impression that this is what math is, when in reality it’s like seeing colour and color can be spelled differently and then inferring “isn’t literature nonsense”
>But the order of operations is just an arbitrary convention to keep notation simpler in certain cases. There’s no mathematical reason behind it. As someone who uses complex mathematics daily, I wholeheartedly disagree. The order of operations exists to provide a framework, without it you can interpret an equation multiple ways. There's a nice example given here https://en.m.wikipedia.org/wiki/Order_of_operations Math has to be more exact than you make it seem, language is completely different.
The modern order of operations are just an arbitrary convention though, primarily so that polynomials can be written without parentheses. It’s very useful for notation, similar to spelling rules. Imagine say somebody programming a computer. The logical units of addition, multiplication, division, and exponentiation are all independent binary operations with no inherent presidence over each other. When it comes to telling how to parse an expression like (3x + 2). We know to arrange these operations into the stack as add( multiply( 3, x ), 2). But we could have chose the convention to be strict left to right or something else. The subjects of group, field, and category theory cover these topics, and discuss the properties of algebraic operations in depth. Again the order of operations is great. It’s useful to be able to have a shared understanding of written notation but it doesn’t ‘have’ to be that way. And in fact in practice it isn’t. Division for example is typically written with a horizontal line which inherently parenthesis the numerator and denominator. This is again partially because polynomials are often found in radicals and we prefer to write them without parens. This is why in math it’s important to understand why the set of rules you’re learning applies. What is the difference between 3(x+2) and (3x)+2. Why do we choose to recognize one as “the” 3x+2.
Top to bottom: (left) -115, -75, 100; (right) 60, 100, 75
For the left side, we want a tuple (a, b, c) such that a + b - c = 40 and c - b + a = 25. There are infinitely many solutions (in particular, there is a solution for any choice of c) so we may simply plug in c = 0 and solve for a and b. We have a + b = 40 and a - b = 25 => 2a = 65 => a = 32.5, b = 7.5 Solve the right side similarly.
You got it!
This guy cracked the code
Let’s try to avoid negatives as much as possible. I’m also going to avoid 0 just because. This means that for the left side we want to write 40 as a - b where b < 25 because b + something positive must be 25. If b = 24, a = 40 + 24 = 64, and for the left, we have this. 40 = 64 - 24 25 = 24 + 1 For the right side, we want to write 40 as a - b where b > 25 so that b - something positive = 25 If b = 26, a = 40 + 26 = 66, and for the right side, we have this. 40 = 66 - 26 25 = 26 - 1 In the end, it should look something like this 40 64 66 24 26 1 1 25
But 40≠64–24+1≠25, maybe it's about order of operations, ie x–y+z=25 and z+y–x=40?
40 40 80 80 -55 55 Something like this?..
It took me a minute to notice this, but there's no indicator that the far left and far right squares would be the start of any computation. It might be the case that the "middle value" in each chain is just part of the chain, not anything special. So, my reading of the left side would be that: 40 = a - b + c, and simultaneously, 25 = c + b - a. By combination, 65 = 2c, so the bottom-left box is 32.5. I'm a bit stuck on solving for A and B from there, and don't have a ton of time to dedicate to trying combinations at the moment (I presume subtracting the two equations would help in some way,) just wanted to pass along a different reading of the problem from what I've seen so far.
20-(-20)=40 20+5=25 30-(-10)=40 30-5=25
On the left side, from top to bottom do: -7.5, 0, 32.5
I think you're supposed to read the expressions starting from the left/right corner then going to the top/bottom corner, then solve that system of equations
So basically this is impossible, if you put it right, it would be: 40 = x-y-z = 25 Meaning 40=25? That doesn't make any sense.
Left side 15 25 10 Right side 40 80 55
So wait they want an answer to 40=x-y-z=25=a+b-c? That's the dumbest question. I'm thinking it's meant to be the far left and right numbers should have some number added or subtracted to give the two knowns, but still there are infinite answers to that so I say this is a bad question.
x + y - z = 40 x - y + z = 25 Solve for positive integral values of x,y and z.
3 unknowns needs a minimum of 3 equations to solve. This question has infinite answers
Of all the infinite answers, they need only two.
I think what it's asking is for you to find some numbers A,B,C,D,E,F such that B - A = 40, B + C = 25, D - E = 40, and F - E = 25. This problem doesn't have a unique solution. To find a particular solution, choose any two numbers you want for B and E (the box on the left and the box on the right). You can now find the rest of the numbers by using the equations.
Doubt they’re trying to indicate 40 = 25, so will assume there are 6 unknowns and 4 equations. Many possible solutions. You could try picking two of the numbers and then figuring out the rest. No need to slap this into a matrix.
Many being infinite in this case
All the possible solutions will look like this: Put an arbitrary number x in the leftmost square, and put an arbitrary number y in the rightmost square. The other squares are then forced to a single value
I guess it is: a+b=25 a-c = 40 d-e = 25 d-f = 40 So there is six unknowns for four equations. Which means that there is going to be multiple solutions. Preposterous task for a nine year old.
x - y - z = 25 z - y - x = 40 a - b + c = 25 c + b - a = 40 Solve for x, y, z on one side. Solve for a, b, c on the other side. I don't see any trick.
Still unsolvable. 6 variables needs a minimum of 6 equations to solve
The design is shit: it's dead easy from top to bottom, but if you start at the left edge, as the design implies, it's insoluble.
So for left hand side (a-b)+c = 40 is one answer as (c+b)-a = 25 is the other I’m guessing here.
What is this😭
This problem alone looks like it would cause any person to develop ADHD or an anxiety disorder if it were a required part of a school curriculum. Wtf?
25=40?
There are no absolute answers. Not even sure what it teaches.
I’ve finished calc as a college student and don’t even know how to do this
It has an infinite number of solutions in N.
both hemispheres of my brain began eating itself
That why I retired from maths in grade 4
I would think it’s from top to bottom 40 L=40-20+5 R=40-10-5 25 It doesn’t say there’s only 1 correct answer so who really knows 🤷🏻♀️ But I’m also not sure if those are subtraction or division 🤷🏻♀️ as its for a 9yo I’m assuming subtraction.
This says 40=25 Unless they're working in modular arithmetic or something (which should be indicated) this is a contradiction. That's a fancy math word for bullshit.
If they’re that young, they probably can put whatever numbers they like… but negative numbers would have to be used. That seems quite young for negative numbers
There are something like 87 wonderful submissions to r/ConfidentlyIncorrect here, followed by people agreeing with them. There are probably infinite solutions to this. All real numbers can go in the outer most boxes.
Let the leftmost box be a, the left-top b, the left-bottom c, the right-top d, the right-bottom f, the rightmost g. From what I can tell, the boxes create the following set of equations: a - b = 40 a + c = 25 40 = d - g 25 = f - g Therefore, b + c = -15 d - f = 15 Therefore, choose any complex number a. b is therefore a - 40, and c is therefore 25 - a. Choose any complex number g. d is therefore 40 + g, and f is therefore 25 + g.
40=40-20+5=25 right side 40=40-7.5-7.5=25
40 - 0 = 40 = 40 - 0 40 + (-15) = 25 = 25 - 0
Here’s the thing, there are a fuckton of ways to interpret this question so it’s a pretty shite one for an adult, but the judgement of a 9 year old isn’t as clouded by all these established math rules, so it’ll actually be more easy for them. I think.
40=x-y+z 25=z+y-x x=y+7.5 y=Any number you want z=32.5 Second side: 40=a-b-c 25=c-b-a a=c+7.5 b=-32.5 c=Any number you want I used substitution. there was so much work and it was all over the place so i decided not to copy and paste it. If you’d like me to I can.
At least he will know how to solve confusing and redundantly presented math equations which he can use for future investments, like buying a car or home