In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. Dividing 1 by a real number yields its multiplicative inverse. For example, the reciprocal of 5 is one fifth (1/5 or 0.2) (…) Multiplying by a number is the same as dividing by its reciprocal and vice versa.
Here’s another source if you’re allergic to Wikipedia.
Again, the mnemonics are for people who don’t understand, which would be people like you! 😂
Again, the mnemonics, when taught without appropriate context, cause confusion in people like you, who think that the order of operations is set to: Multiplication → Division → Addition → Subtraction, instead of being (M or D, start from the left) → (A or S, start from the left).
Again, the mnemonics, when taught without appropriate context, cause people to think that 9-3+2 is 4, when the actual result is 8, because they think that they have to calculate the addition first.
What’s the result of 2+2? What’s the result of 1+3? Are 2+2 and 1+3 the same? No! 😂 2 apples + 2 oranges = 4 pieces of fruit. 3 apples and 1 orange = 4 pieces of fruit. Is 2 apples and 2 oranges the same as 3 apples and 1 orange? 😂 Anything else you want to embarrass yourself about not understanding?
WTF are you talking about? Where did you get the 1 and 3 from? Also… Do you not know what fractions are…?
You’re the one who brought it into the conversation - you tell me!
You’re so very, very confused by all of this…
You’ll find most people find that less readable. Welcome to why textbooks never use them
I can see why you are finding them less readable - you have absolutely fundamental lacks in understanding of maths. And, sorry to burst your bubble, but maths textbooks all over the world use brackets all the time.
Just making it less readable
Not if you understand what they mean. Which is why they’re confusing for you, I guess.
which haven’t changed at all in all that time 😂 2-3 has never and still does not require brackets, same as when Arithmetic was first written.
Now that I know that you have a fundamental lack of understanding how maths works, I apologise for using the brackets earlier. Let’s try this: you can write 2 - 2 as -2 + 2, or - a slightly less legible version - as 2 + -2. You’ll get the same result, and this inversion is a perfectly “legal” mathematical operation. Which shows you how addition and subtraction are equal.
and everyone was taught that the order of DM/MD does not matter. If it did then one of them would not exist
One more time, let me welcome you to the Internet, I’m sure you’ll have a great time here!
Already posted a screenshot of one. You really need to work on your comprehension
We were not talking about monomials.
Set all the pronumerals to 1, and guess what you have - the exact same thing 😂 I see you don’t understand how pronumerals work either
If you set the pronumerals in addition/subtraction problems to 1, you would have something entirely different. And if you want to do 2x - 2x where x = 1, then your own posted fragment explains that you only need to calculate the arithmetic difference between the total postive/negative coefficients.
The arithmetic difference between -2 + 2 and 2 - 2 is the same, proving - again - that subtraction is equal to addition of a negative.
Which is my point. Which you are proving.
BTW you still have not cited any textbook whatsoever that agrees with anything that you have said
I didn’t have to, you did it for me.
Yep, 1a-2a+3a-4a=a((1+3)-(2+4)). Now set a=1 and guess what you have? 😂
Now do -(2+4) + (1+3) and guess what you have?
You know the textbook just literally told you it is, right?? 😂
I already suggested this: read it again, but slower.
says person who has no evidence whatsoever to show that they are correct, so as I said, no matter how many times you repeat it, you are still wrong 😂
You never asked for citations.
And the questions I did ask you didn’t answer anyway, because you know in both cases it proves you wrong. Notice how I didn’t need you to ask me for evidence to produce it? That’s what people who are backed up by facts can do 😂
you did it for me with your screenshot
Which proved you were wrong 😂
But here you go
Well, here you go proving you have a severe comprehension problem anyway… 😂
Multiplying by a number is the same as dividing by its reciprocal and vice versa
Yep, gives the same result, but does not say that the number and it’s inverse are the same thing 😂
Here’s another source if you’re allergic to Wikipedia
Which also wasn’t a Maths textbook 😂 So far you’re only proving my point that you can’t cite any Maths textbooks that agree with you
Again, the mnemonics, when taught without appropriate context
Which they never are
cause people to think that 9-3+2 is 4
Nope, no-one thinks that. Addition first for 9-3+2 is +(9+2)-3=+11-3=8 same correct answer as left to right, which is why the textbook teaches you to do it that way 😂
If you understand what is multiplication and what is addition
Which you’re demonstrated repeatedly that you don’t, and here we are
who think that the order of operations is set to: Multiplication → Division → Addition → Subtraction
Which is a totally valid thing to do, as is taught by the textbook 🙄
instead of being (M or D, start from the left) → (A or S, start from the left)
Which is also a valid thing to do. That’s the whole point, it does not matter which order you do addition and subtraction 😂
when the actual result is 8, because they think that they have to calculate the addition first
And when they do calculate the addition first, they get an answer of 8, as I just proved a few comments back 😂 Add all the positive numbers, then subtract the total of all the negative numbers. This is so not complicated, and yet you seem to have trouble understanding it
Where did you get the 1 and 3 from?
From an example of how 2+2 and 1+3 aren’t the same thing, even though they equal the same value, which you are now trying to avoid addressing because you know it proves you are wrong 😂
Do you not know what fractions are…?
I’m starting to wonder if you do, given you think 2/2 is the same thing as 2x½ - one has a fraction, the other doesn’t, but you think they are the same thing 🙄
You’re so very, very confused by all of this
says person not remembering that they brought it up to begin with… 😂
you have absolutely fundamental lacks in understanding of maths
says person who thinks doing addition first for 9-3+2 is 4 😂
maths textbooks all over the world use brackets all the time
Not for 2-2 they don’t. Go ahead and cite one. I’ll wait
you can write 2 - 2 as -2 + 2, or - a slightly less legible version - as 2 + -2. You’ll get the same result, and this inversion is a perfectly “legal” mathematical operation. Which shows you how addition and subtraction are equal
Which proves my point that you can do addition and subtraction in any order, given you just admitted that 2-2 and -2+2 give the same result 😂
One more time, let me
deflect from the point, yet again
We were not talking about monomials
No, we were talking about textbooks teaching to do addition first, and you then deflected into talking about monomials, because you knew it proved you were wrong 😂
If you set the pronumerals in addition/subtraction problems to 1, you would have
The exact same thing as an expression written without pronumerals 😂 I see you’re still not understanding how pronumerals work then
difference between -2 + 2 and 2 - 2 is the same, proving - again - that subtraction is equal to addition of a negative
and thus proving again that they can be done in any order 😂 It’s so hilarious watching you prove yourself wrong
Which is my point. Which you are proving
No, you’re actually proving my point 🤣
I didn’t have to, you did it for me.
I only posted things that prove you wrong, but apparently I don’t need to because you are proving yourself wrong 🤣
Now do -(2+4) + (1+3) and guess what you have?
The exact same answer, -2, again proving you can do them in any order 🤣
I already suggested this: read it again, but slower.
It still says add all positive numbers first, then subtract the total of the negative numbers. I’m not sure what you think is going to happen - are you expecting the words to magically change if you read it slowly? 🤣
Yes, because I finished third grade in primary school. Do you also expect evidence of gravity?
And the questions I did ask you didn’t answer anyway
Go back and read the comments again. I know they’re getting lengthy, but I’m sure if you put your mind to it, you can find the answers.
Which proved you were wrong
Yeah, if you ignore what the text says and just assume it does what you want, then sure, it proves me wrong. However, if you actually read the letters on the screenshot, you’ll find that it does not, in fact, prove me wrong, it does the opposite.
Well, here you go proving you have a severe comprehension problem anyway… 😂
Oh wow, so you’re also incapable of scrolling down to the sources part of the article…?
Yep, gives the same result, but does not say that the number and it’s inverse are the same thing 😂
Yeah, speaking of reading comprehension - I never said anything like that. I said that, in terms of the order of operations, addition/subtraction and multiplication/division are equal, because they can be inverted (subtraction into addition of negative numbers, division into multiplication of fractions) to achieve, as you observed, the exact same result. Which means that - if you ensure that children learn and understand that concept, you can skip subtraction and division from the mnemonics, because children will understand that - again, in terms of order of operations - division = multiplication, and subtraction = addition.
Which also wasn’t a Maths textbook
OK, how about this: let’s do what grown up mathematicians do: prove that what I linked to is wrong.
Which they never are (…) Nope, no-one thinks that
One more time: welcome to the Internet, I’m sure you’ll find many surprises here, but overall it’s a pretty great place.
Addition first for 9-3+2 is +(9+2)-3=+11-3=8 same correct answer as left to right, which is why the textbook teaches you to do it that way
I like how you’re doing exactly what I’m talking about while still saying I’m incorrect.
Which you’re demonstrated repeatedly that you don’t, and here we are
OK, sure, quote one example equation I did here that proves I’m not understanding these concepts. :)
Which is a totally valid thing to do, as is taught by the textbook
But is not reinforced by the mnemonic itself. Reading comprehension, remember?
Which is also a valid thing to do. That’s the whole point, it does not matter which order you do addition and subtraction 😂
I’m glad I was able to explain this to you. You go ahead and pretend like you’re explaining it to me, I’m just happy you finally managed to understand that.
And when they do calculate the addition first, they get an answer of 8, as I just proved a few comments back 😂 Add all the positive numbers, then subtract the total of all the negative numbers. This is so not complicated, and yet you seem to have trouble understanding it
See above.
From an example of how 2+2 and 1+3 aren’t the same thing, even though they equal the same value, which you are now trying to avoid addressing because you know it proves you are wrong 😂
Why are you bringing 1 + 3 into the mix when the examples were 2 + 2 and 2 * 2? What are you trying to say here?
I’m starting to wonder if you do, given you think 2/2 is the same thing as 2x½ - one has a fraction, the other doesn’t, but you think they are the same thing 🙄
I’m going to ask you a couple of questions so you can research that and then pretend to explain them to me, like you did above:
What is the result of 2 / 2?
What is the result of 2 * ½?
What is the reciprocal of 2?
says person not remembering that they brought it up to begin with… 😂
There’s no confusion from my side. I understand how brackets work and that was a perfectly valid use - for readability’s sake.
says person who thinks doing addition first for 9-3+2 is 4
Now you’re just inventing things I never said. That’s not nice.
Not for 2-2 they don’t. Go ahead and cite one. I’ll wait
It wasn’t 2 - 2, tho. Or did you fail to read that correctly too?
Which proves my point that you can do addition and subtraction in any order, given you just admitted that 2-2 and -2+2 give the same result 😂
Again, I’m glad you’re slowly getting to the point I was making. It’s weird how you’re still phrasing it like I was somehow wrong, but I’m just happy you learned something.
The exact same thing as an expression written without pronumerals 😂 I see you’re still not understanding how pronumerals work then
Considering that’s exactly what I did, how do you see that as me not understanding pronumerals? I’m asking out of sheer curiosity at this point.
and thus proving again that they can be done in any order 😂 It’s so hilarious watching you prove yourself wrong (…) [and the rest of the comment]
You’re so cute when you’re trying to turn this whole argument on its head after realising how silly your initial points were! <3
That’s the thing - I’m not wrong.
Yet again? You never asked for citations. I also didn’t have to, as you did it for me with your screenshot.
But here you go:
Here’s another source if you’re allergic to Wikipedia.
Again, the mnemonics, when taught without appropriate context, cause confusion in people like you, who think that the order of operations is set to: Multiplication → Division → Addition → Subtraction, instead of being (M or D, start from the left) → (A or S, start from the left).
Again, the mnemonics, when taught without appropriate context, cause people to think that
9-3+2is4, when the actual result is8, because they think that they have to calculate the addition first.WTF are you talking about? Where did you get the 1 and 3 from? Also… Do you not know what fractions are…?
You’re so very, very confused by all of this…
I can see why you are finding them less readable - you have absolutely fundamental lacks in understanding of maths. And, sorry to burst your bubble, but maths textbooks all over the world use brackets all the time.
Not if you understand what they mean. Which is why they’re confusing for you, I guess.
Now that I know that you have a fundamental lack of understanding how maths works, I apologise for using the brackets earlier. Let’s try this: you can write
2 - 2as-2 + 2, or - a slightly less legible version - as2 + -2. You’ll get the same result, and this inversion is a perfectly “legal” mathematical operation. Which shows you how addition and subtraction are equal.One more time, let me welcome you to the Internet, I’m sure you’ll have a great time here!
We were not talking about monomials.
If you set the pronumerals in addition/subtraction problems to 1, you would have something entirely different. And if you want to do
2x - 2xwherex = 1, then your own posted fragment explains that you only need to calculate the arithmetic difference between the total postive/negative coefficients.The arithmetic difference between
-2 + 2and2 - 2is the same, proving - again - that subtraction is equal to addition of a negative.Which is my point. Which you are proving.
I didn’t have to, you did it for me.
Now do
-(2+4) + (1+3)and guess what you have?I already suggested this: read it again, but slower.
says person who has no evidence whatsoever to show that they are correct, so as I said, no matter how many times you repeat it, you are still wrong 😂
And the questions I did ask you didn’t answer anyway, because you know in both cases it proves you wrong. Notice how I didn’t need you to ask me for evidence to produce it? That’s what people who are backed up by facts can do 😂
Which proved you were wrong 😂
Well, here you go proving you have a severe comprehension problem anyway… 😂
Yep, gives the same result, but does not say that the number and it’s inverse are the same thing 😂
Which also wasn’t a Maths textbook 😂 So far you’re only proving my point that you can’t cite any Maths textbooks that agree with you
Which they never are
Nope, no-one thinks that. Addition first for 9-3+2 is +(9+2)-3=+11-3=8 same correct answer as left to right, which is why the textbook teaches you to do it that way 😂
Which you’re demonstrated repeatedly that you don’t, and here we are
Which is a totally valid thing to do, as is taught by the textbook 🙄
Which is also a valid thing to do. That’s the whole point, it does not matter which order you do addition and subtraction 😂
And when they do calculate the addition first, they get an answer of 8, as I just proved a few comments back 😂 Add all the positive numbers, then subtract the total of all the negative numbers. This is so not complicated, and yet you seem to have trouble understanding it
From an example of how 2+2 and 1+3 aren’t the same thing, even though they equal the same value, which you are now trying to avoid addressing because you know it proves you are wrong 😂
I’m starting to wonder if you do, given you think 2/2 is the same thing as 2x½ - one has a fraction, the other doesn’t, but you think they are the same thing 🙄
says person not remembering that they brought it up to begin with… 😂
says person who thinks doing addition first for 9-3+2 is 4 😂
Not for 2-2 they don’t. Go ahead and cite one. I’ll wait
Which proves my point that you can do addition and subtraction in any order, given you just admitted that 2-2 and -2+2 give the same result 😂
deflect from the point, yet again
No, we were talking about textbooks teaching to do addition first, and you then deflected into talking about monomials, because you knew it proved you were wrong 😂
The exact same thing as an expression written without pronumerals 😂 I see you’re still not understanding how pronumerals work then
and thus proving again that they can be done in any order 😂 It’s so hilarious watching you prove yourself wrong
No, you’re actually proving my point 🤣
I only posted things that prove you wrong, but apparently I don’t need to because you are proving yourself wrong 🤣
The exact same answer, -2, again proving you can do them in any order 🤣
It still says add all positive numbers first, then subtract the total of the negative numbers. I’m not sure what you think is going to happen - are you expecting the words to magically change if you read it slowly? 🤣
Yes, because I finished third grade in primary school. Do you also expect evidence of gravity?
Go back and read the comments again. I know they’re getting lengthy, but I’m sure if you put your mind to it, you can find the answers.
Yeah, if you ignore what the text says and just assume it does what you want, then sure, it proves me wrong. However, if you actually read the letters on the screenshot, you’ll find that it does not, in fact, prove me wrong, it does the opposite.
Oh wow, so you’re also incapable of scrolling down to the sources part of the article…?
Yeah, speaking of reading comprehension - I never said anything like that. I said that, in terms of the order of operations, addition/subtraction and multiplication/division are equal, because they can be inverted (subtraction into addition of negative numbers, division into multiplication of fractions) to achieve, as you observed, the exact same result. Which means that - if you ensure that children learn and understand that concept, you can skip subtraction and division from the mnemonics, because children will understand that - again, in terms of order of operations - division = multiplication, and subtraction = addition.
OK, how about this: let’s do what grown up mathematicians do: prove that what I linked to is wrong.
One more time: welcome to the Internet, I’m sure you’ll find many surprises here, but overall it’s a pretty great place.
I like how you’re doing exactly what I’m talking about while still saying I’m incorrect.
OK, sure, quote one example equation I did here that proves I’m not understanding these concepts. :)
But is not reinforced by the mnemonic itself. Reading comprehension, remember?
I’m glad I was able to explain this to you. You go ahead and pretend like you’re explaining it to me, I’m just happy you finally managed to understand that.
See above.
Why are you bringing
1 + 3into the mix when the examples were2 + 2and2 * 2? What are you trying to say here?I’m going to ask you a couple of questions so you can research that and then pretend to explain them to me, like you did above:
2 / 2?2 * ½?There’s no confusion from my side. I understand how brackets work and that was a perfectly valid use - for readability’s sake.
Now you’re just inventing things I never said. That’s not nice.
It wasn’t
2 - 2, tho. Or did you fail to read that correctly too?Again, I’m glad you’re slowly getting to the point I was making. It’s weird how you’re still phrasing it like I was somehow wrong, but I’m just happy you learned something.
Considering that’s exactly what I did, how do you see that as me not understanding pronumerals? I’m asking out of sheer curiosity at this point.
You’re so cute when you’re trying to turn this whole argument on its head after realising how silly your initial points were! <3