# how to pronounce the equation



## Wishfull

Hello.
I would like to know how to pronounce this equation;
*X^2 -X -6 = (X-3)(X+2)*

My try is;
Eks squared, minus eks minus six, equal, eks minus three, parenthesized, multiplied by eks plus two, parenthesized.

I was taught by a native English speaker, but I couldn't remember it well.
I want to make sure if this is correct.

equal →equals ?
equal→　"is" is more natural?

Thanks in advance.


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## Nunty

The way I was taught is to say the parentheses as "the quantity of": 
Eks squared minus eks minus six equal*s* *the quantity *eks minus three *times *(or "multiplied by") *the quantity *eks plus two.


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## envie de voyager

This is how I was taught to say this (North America):

*X^2 -X -6 = (X-3)(X+2)*
Eks squared minus eks minus six equals eks minus three in brackets times eks plus two in brackets.

We were taught that in mathematics, these ( ) are brackets and these [ ] or these { } are parentheses.


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## boozer

Just a small clarification. While both Nunty and envie de voyageur have given excellent options, is it also possible to use "into"  instead of "multiplied by" and "times"? And is it also possible to just say "eks square" instead of "eks squared"? Because I think I've seen both of these...
E.g.
Eks *square* minus eks minus six equals eks minus three in brackets *into* eks plus two in brackets.


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## Nunty

Hmmm... not sure about that, boozer.

"Into" is a marker of division, so I would read:

(x-3)/(y+4) 

as

the quantity x-3 divided by the quantity y+4

or 

the quantity y+4 into the quantity x-3.


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## natkretep

envie de voyager said:


> We were taught that in mathematics, these ( ) are brackets and these [ ] or these { } are parentheses.



In British style ( ) are (round) brackets, [ ] are square brackets and { } are curly brackets. I would continue to use them like that in maths.

It's also possible to name the open and close bracket, particularly if there are more things within those brackets. So I might say:

*X^2 -X -6 = (X-3)(X+2)*

as 

_Ex squared minus ex minus six equals open bracket ex minus three close bracket, open bracket ex plus two close bracket_.

If there is visual contact, I'd probably omit the _open bracket_ and _close bracket_ but draw out brackets with my forefingers in the air.

As you can see, I would also omit 'times' or 'multiplied by'.


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## mathman

Wishfull said:


> Hello.
> I would like to know how to pronounce this equation;
> *X^2 -X -6 = (X-3)(X+2)*
> 
> My try is;
> Eks squared, minus eks minus six, equal, eks minus three, parenthesized, multiplied by eks plus two, parenthesized.
> 
> I was taught by a native English speaker, but I couldn't remember it well.
> I want to make sure if this is correct.
> 
> equal →equals ?
> equal→　"is" is more natural?
> 
> Thanks in advance.



In AE math classes, you would say:

eks squared minus eks minus six equals eks minus three times eks plus two. 

There are more complicated ways of saying the same thing, but the way I have written it is the most common.

I certainly would not talk about x - 3 as being "parenthesized" (though I would also certainly understand what was meant): that sounds very odd.


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## boozer

Nunty said:


> Hmmm... not sure about that, boozer.
> 
> "Into" is a marker of division, so I would read:
> 
> (x-3)/(y+4)
> 
> as
> 
> the quantity x-3 divided by the quantity y+4
> 
> or
> 
> the quantity y+4 into the quantity x-3.


Then the person who said "into" a number of times while giving me the dimensions of a window pane must have been drunk or drugged 
On the other hand, I'd never heard "into" used with this meaning, so it stuck.

Anyway, thanks for enlightening me, Nunty.


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## Rover_KE

I'm with Natkretep on this one.  That's what I'd say.

Rover


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## Wishfull

Thank you all.


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## AEC7

*X^2 would be prnounced  "x (ex) squared" or "x to the power of 2" and it means you miltiply the number by itself.*

*To pronounce the whole equation you would say: *
*"x squared,*
* take away x *
*take away six *
*equals*
*x take away three *
*miltiplied by *
*x add two"*


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## envie de voyager

In North America, "take away" is what we teach young children to say before we introduce them to the words "minus" or "subtract."


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## mathman

AEC7 said:


> *X^2 would be prnounced  "x (ex) squared" or "x to the power of 2" and it means you miltiply the number by itself.*
> 
> *To pronounce the whole equation you would say: *
> *"x squared,*
> * take away x *
> *take away six *
> *equals*
> *x take away three *
> *miltiplied by *
> *x add two"*



While the latter is technically ok, and I would certainly understand what the speaker meant, it would sound very strange in a (AE) math class.


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## Rover_KE

AEC7 said:


> *
> 
> To pronounce the whole equation you would say:
> "x squared,
> take away x
> take away six
> equals
> x take away three
> miltiplied by
> x add two"*


*


But this reading takes no account of the brackets and would lead to a different solution.

Rover*


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## Esca

Rover, 
Just as Mathman suggested, you can use timing in spoken language to indicate the parentheses. In this case, I'd say "_ex-minus-three_ ... *times* ... _ex-plus-two_."
Of course, saying "the quantity ex minus three" would be clearer.


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## kalamazoo

I would say
X-squared minus 6 minus 3 equals

and then either as Mathman suggests:
ex minus three times ex plus two
or to avoid any misunderstaindgs
the quantity ex minus three times the quantity ex plus two.


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## Rover_KE

natkretep said:


> _Ex squared minus ex minus six equals open bracket ex minus three close bracket, open bracket ex plus two close bracket_.
> 
> 
> I still say this is the correct answer to the question.
> 
> Rover


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## Cagey

Rover_KE said:


> natkretep said:
> 
> 
> 
> _Ex squared minus ex minus six equals open bracket ex minus three close bracket, open bracket ex plus two close bracket_.
> 
> 
> 
> I still say this is the correct answer to the question.
> 
> Rover
Click to expand...

I don't deny that it is correct in BrE.  It sounds odd to a speaker of AmE.


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## Cypherpunk

Rover_KE said:


> natkretep said:
> 
> 
> 
> _Ex squared minus ex minus six equals open bracket ex minus three close bracket, open bracket ex plus two close bracket_.
> 
> 
> I still say this is the correct answer to the question.
> 
> Rover
> 
> 
> 
> 
> 
> 
> Cagey said:
> 
> 
> 
> I don't deny that it is correct in BrE.  It sounds odd to a speaker of AmE.
> 
> Click to expand...
> 
> 
> This is actually fairly common in _computer science_ classes, when you are discussing equations or programming expressions, so it sounds fine to me. As Cagey says, though, it is _far_ less common to hear this in a math class.
Click to expand...


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## kalamazoo

I do a lot of programming and would refer to "(" and ")" as parentheses, not brackets though.  Of course I may be behind the times.


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## Cypherpunk

'Parentheses' is the name for these, when you are in a language class, while 'brackets' is the recommended usage in math and science courses. However, it is so common to call them 'parentheses' that many teachers don't bother or remember, because that's what they grew up saying and hear from other teachers all the time.


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## Judica

mathman said:


> In AE math classes, you would say:
> 
> eks squared minus eks minus six equals eks minus three times eks plus two.
> 
> There are more complicated ways of saying the same thing, but the way I have written it is the most common.
> 
> I certainly would not talk about x - 3 as being "parenthesized" (though I would also certainly understand what was meant): that sounds very odd.



This would be my answer as well. Also, in agreement, there would be no mention of parentheses/ brackets/etc.


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## mathman

Cypherpunk said:


> 'Parentheses' is the name for these, when you are in a language class, while 'brackets' is the recommended usage in math and science courses. However, it is so common to call them 'parentheses' that many teachers don't bother or remember, because that's what they grew up saying and hear from other teachers all the time.



I don't agree. Parentheses are parentheses. I have never heard anyone in  math or science call )( "brackets." Brackets are [ and ].


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## Cagey

I distinguish between _parentheses _and _brackets _the same way.

However, as I understand it, BrE speakers often call our _parentheses _"brackets".  From the Cambridge Advanced Learner's Dictionary: *parentheses *MAINLY US   
 plural noun (UK USUALLY (round) *brackets*)
the ( ) punctuation marks that are put around a word, phrase or sentence in a piece of writing to show that what is inside them should be considered as separate from the main part.​


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## PlainandTall

Nunty's "the quantity of" is the one  I learned in school.


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## natkretep

Cagey said:


> However, as I understand it, BrE speakers often call our _parentheses _"brackets".



In Britspeak:

( )  brackets, or round brackets if there's likely to be ambiguity
[ ]  square brackets
{ } curly brackets
< > angle brackets



PlainandTall said:


> Nunty's "the quantity of" is the one  I learned in school.



'The quantity of' must be an American or North American convention for reading out items within brackets (parentheses). I haven't heard of this before.


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## se16teddy

Rover_KE said:


> But this reading takes no account of the brackets and would lead to a different solution.


Point of information: wishfull's equation doesn't really have a 'solution' in that it is true for all values of x!


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## netrapture

While mathman's pronunciation is the one that would be used by a mathematically educated AmE speaker, it is infrequent in my experience to pronounce out loud an equation that has parentheses. Rather it would be written down and shown  - either on the board on on paper. Also it would be possible to make a hand gesture showing parentheses while saying each parenthesized expression.


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## mathman

netrapture said:


> While mathman's pronunciation is the one that would be used by a mathematically educated AmE speaker, it is infrequent in my experience to pronounce out loud an equation that has parentheses. Rather it would be written down and shown  - either on the board on on paper. Also it would be possible to make a hand gesture showing parentheses while saying each parenthesized expression.



Usually, when writing at the board, or on paper, one is also pronouncing the statement (assuming that one is not alone), so I think this mathematical statement is in fact often pronounced. When it is, the parentheses are usually not pronounced, though they of course could be (or, as others have suggested, one could use "the quantity" to indicate where the parentheses go). 

I would not argue that parentheses are generally not pronounced in mathematical statements: they are pronounced when you want to be very clear about who is doing what to whom. But in the original question, the mathematical statement given is the factoring of a monic trinomial into binomial factors, and anyone encountering such a statement would (in that context) understand where the parentheses go without their being explicitly stated. 

The original question, anyway, was how the statement was pronounced.


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## Au101

There are a huge number of acceptable forms of pronunciation for mathematical equations and it can often cause confusion. In my maths class, we would probably say:

_eks squared, minus eks, minus six equals eks minus three_ (said very quickly) [a short pause] _eks plus two_ (said very quickly). 

You may hear this often as saying "brackets", or "parentheses" is tiresome and in my class, and this may not be common, but we often mark brackets by changes in speed, or tone of voice.


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## JamesM

Nunty said:


> The way I was taught is to say the parentheses as "the quantity of":
> Eks squared minus eks minus six equal*s* *the quantity *eks minus three *times *(or "multiplied by") *the quantity *eks plus two.


 
I'm seconding Nunty's way of reading it after speaking with my friend Perry, who is a high school math teacher here in the U.S.


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## Rover_KE

I have to say I find some of these replies absolutely astonishing.

We are talking about a science here, where terminological exactitude ought to be a given, and incapable of misinterpretation. Mathematicians throughout the world should surely be able to understand each other unequivocally.

Are we to believe that the verbalisation of potentially life-changing equations has to rely on vague hand gestures, random pauses or arbitrarily stressed syllables?

Rover


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## Loob

So, Rover, do you have a transcription that makes everything clear???

Personally, I'd rely on intonation to make it clear that (X-3) and (X+2) are within brackets.  I'd say "x-3" [special intonation] "times" "x+2" [special intonation].  I might also use "scare quotes".


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## mathman

Rover_KE said:


> I have to say I find some of these replies absolutely astonishing.
> 
> We are talking about a science here, where terminological exactitude ought to be a given, and incapable of misinterpretation. Mathematicians throughout the world should surely be able to understand each other unequivocally.
> 
> Are we to believe that the verbalisation of potentially life-changing equations has to rely on vague hand gestures, random pauses or arbitrarily stressed syllables?
> 
> Rover



Generally, mathematical language is extremely precise. The issue with the given equation is not really a matter of precision of expression. If you speak the given equation, persons with a certain level of mathematical sophistication (and not, for this equation, of a very high level: it's elementary algebra) will understand that you are factoring a polynomial, which is why the "eks minus three times eks plus two" is sufficient (I wouldn't generally leave out the "times," though). You can add information ("the quantity," "left parenthesis/bracket, right parenthesis/bracket," pauses, "air parentheses/brackets," etc.), but that isn't really necessary. People (with that level of sophistication) would understand perfectly well what you mean without such additional information.


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## Rover_KE

Thank you, mathman.

Your point is well-made.

Rover


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## entangledbank

To chip in on a thread that's several days out of date, because it's interesting. Like several others, I'd say: 'ex minus \/three, times 'ex plus \two (where the ' and \/ and \ mark intonation). In such a simple equation you don't need to mention the brackets, because the other interpretation "three times ex" isn't available: you'd say "three ex" for that.

If you really had to read out the exact equation (say over the phone and it was more complex and non-obvious than this), I'd read "open bracket" and "close bracket" where present, and at a lower pitch than the rest.

Intonation isn't some optional add-on like hand gestures: it's an integral part of the structure of a sentence, and conveys the grammar better than punctuation does in writing.


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## panjandrum

There is no ambiguity in "eks minus three times eks minus two".
It can only be (x-3)(x-2)

The implied alternative, x-3x-2, would be spoken quite differently (apart from being unlikely): eks minus three eks minus 2.

And as others have said, intonation and timing also make clear what is intended.

I would speak the brackets only in a complex formula - someone said that earlier but I've forgotten who 

I have never come across "the quantity of" - yet another learning moment.

I find it difficult to believe that AE-speaking mathematicians can cope with saying "open parenthesis", or some such, in a complex situation.  It sounds like a magical command, something of the power of "open sesame".  "Open bracket" is a lot shorter and more prosaic - or perhaps simply more familiar to me.

Isn't it curious how much fun everyone has with this topic.


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## mathman

panjandrum said:


> There is no ambiguity in "eks minus three times eks minus two".
> It can only be (x-3)(x-2)
> 
> The implied alternative, x-3x-2, would be spoken quite differently (apart from being unlikely): eks minus three eks minus 2.
> 
> And as others have said, intonation and timing also make clear what is intended.
> 
> I would speak the brackets only in a complex formula - someone said that earlier but I've forgotten who
> 
> I have never come across "the quantity of" - yet another learning moment.
> 
> I find it difficult to believe that AE-speaking mathematicians can cope with saying "open parenthesis", or some such, in a complex situation.  It sounds like a magical command, something of the power of "open sesame".  "Open bracket" is a lot shorter and more prosaic - or perhaps simply more familiar to me.
> 
> Isn't it curious how much fun everyone has with this topic.



AE-speaking mathematicians would probably not say "open parenthesis," at least I've never heard any say that. We might say "left paren(thesis), x - 3, right paren(thesis)." But the most common way would be to say "the quantity x - 3 times the quantity x + 2," if we wanted to explicitly emphasize who is doing what to whom. Ordinarily, "the quantity" would be left out. And I have never heard anyone say "the quantity of x - 3": there's no "of."


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## Rover_KE

panjandrum said:


> There is no ambiguity in "eks minus three times eks minus two".
> It can only be (x-3)(x-2)




I don't agree. It can also be heard as 'x minus 3 times x minus 2'.

Let x = 5, and the first case simplifies to 6, and the second to 8.

Rover


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## Loob

You've lost me there, Rover....

Did you mean _x-3(x-2) _or _x-3x-2?_ I can't get either of them to reduce to 8 with _x_ = 5.

I'd say the first, but not the second, as 'x minus 3 times x minus 2'. However, it would have a quite different intonation pattern from (_x-3)(x-2)._

We seem to have moved seamlessly, by the way, from (x-3)(x+2) to (x-3)(x-2)


panjandrum said:


> Isn't it curious how much fun everyone has with this topic.


 Yes - it's been fascinating!


entangledbank said:


> If you really had to read out the exact equation (say over the phone and it was more complex and non-obvious than this), I'd read "open bracket" and "close bracket" where present, and at a lower pitch than the rest. *Me too.*
> 
> Intonation isn't some optional add-on like hand gestures: it's an integral part of the structure of a sentence, and conveys the grammar better than punctuation does in writing. *Well said, entangledbank!*


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## Rover_KE

Hi,Loob,



Loob said:


> You've lost me there, Rover....
> 
> Did you mean _x-3(x-2) _or _x-3x-2?_ I can't get either of them to reduce to 8 with _x_ = 5.




Neither.   

x minus 3........times x.........minus 2

5 minus 3 (=2) times 5 (=10) minus 2 = 8. 

QED

Rover
x


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## Loob

Rover_KE said:


> Hi,Loob,
> 
> 
> 
> 
> Neither.
> 
> x minus 3........times x.........minus 2
> 
> 5 minus 3 (=2) times 5 (=10) minus 2 = 8.
> 
> QED
> 
> Rover
> x


Ah...

For me, that would have to be _x(x-3)-2._

_"x times ... x minus three ... minus two._


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## Wishfull

Rover_KE said:


> I don't agree. It can also be heard as 'x minus 3 times x minus 2'.
> 
> Let x = 5, and the first case simplifies to 6, and the second to 8.
> 
> Rover


 
Hi.
I think the matter becomes quite different, when we put a concrete number to "x".
For example, 

*3×(8-4)=12*

What do you pronounce?
*Three times..........eight minus four equals twelve?*

I don't think so but is this correct?
Thank you.


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## panjandrum

Now you have created an ambiguity.
The quite rigid interpretation that works (for me) with the symbolic functions does not work with concrete numbers.
What is three times eight minus four?
Now it depends entirely on how it is said, and I have to be very careful.
What is three-times-eight minus four?
Answer, 20.
What is three times ... eight-minus-four?
Answer, 12.


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## Au101

I was always taught BIDMAS/BODMAS as the order in which you do operations

Brackets
Indices/Other
Division
Multiplication
Addition
Subtraction

So, for me, if you said:

What is three times eight minus four?

I would presume you meant:

3 x 8 - 4 (which = 20)

As that is the standard order of operations, hence is, for me, implied, unless pitch, use of "open brackets/parentheses", etc. specifies otherwise.  If you meant: 

3 x (8-4) = 12 

I would indeed say:

Three times (emphasis on "times")...eight minus four (said very quickly as if one word) equals twelve.


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## natkretep

I was taught BODMAS too.  I think the 'O' stands for 'Order' - which means _indices _or _power_.


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## Loob

Me too: but it was 
_Brackets _
_Of _
_Divide _
_Multiply _
_Add _
_Subtract._

What good children we must have been to still remember it!


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## TropicalMontana

Rover_KE said:


> I have to say I find some of these replies absolutely astonishing.
> 
> We are talking about a science here, where terminological exactitude ought to be a given, and incapable of misinterpretation. Mathematicians throughout the world should surely be able to understand each other unequivocally.
> 
> Are we to believe that the verbalisation of potentially life-changing equations has to rely on vague hand gestures, random pauses or arbitrarily stressed syllables?
> 
> Rover




Indeed, and it is for this very reason that written mathematical notations were invented.  

I agree with those who prefer 'the quantity x minus three' for instances where you wanted that level of clarity, otherwise the pauses and intonations would convey the groupings (in the same way you could spell  two or more words for someone and use a pause instead of saying 'space' in between them).


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## mathman

natkretep said:


> I was taught BODMAS too.  I think the 'O' stands for 'Order' - which means _indices _or _power_.



In AE mathematics, it is PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

It's strange that BODMAS reverses the order of multiplication and division from PEMDAS.


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## Gavril

The following two expressions aren't equivalent, but they could both be (theoretically) spoken out as "a times b plus c":

1) a*b + c
2) a*(b + c)

When I was in school (in the western United States), I was taught to pronounce these expressions in the following way to avoid ambiguity:

1) "a times b plus c"
2) "a times the quantity b plus c"

Do all forms of English use the phrase "the quantity" to express meaning #2, or is there some variation from country to country?


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## natkretep

Mod note: Gavril's thread (from post 50) has been merged with an earlier thread.

Gavril, please look at the earlier posts in this thread where your question is addressed.


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