The expression: $-5^2$
$begingroup$
A few people I met were debating over if $-5^2 = 25$ or $-25$.
From my experience, we assume operator precedence and get $-25.$
People are telling me however, calculators are flawed, the real answer is $25.$
Clarifying note, the expression is merely:
$-5^2$
nothing else.
What would you say?
Edit:
I've also tried saying $f(x)=-x^2$ is a parabola that opens downwards, but this was apparently a problem with graphing calculators as well.
arithmetic exponentiation
edited Nov 29 '18 at 22:43
N. F. Taussig
43.9k93355
asked Nov 29 '18 at 21:42
SzmatoPotatoSzmatoPotato
353
$endgroup$
|
show 4 more comments
$begingroup$
A few people I met were debating over if $-5^2 = 25$ or $-25$.
From my experience, we assume operator precedence and get $-25.$
People are telling me however, calculators are flawed, the real answer is $25.$
Clarifying note, the expression is merely:
$-5^2$
nothing else.
What would you say?
Edit:
I've also tried saying $f(x)=-x^2$ is a parabola that opens downwards, but this was apparently a problem with graphing calculators as well.
arithmetic exponentiation
edited Nov 29 '18 at 22:43
N. F. Taussig
43.9k93355
asked Nov 29 '18 at 21:42
SzmatoPotatoSzmatoPotato
353
$endgroup$
3
$begingroup$
It is important to distinguish between $-5^2 = -25$, and $(-5)^2 = 25$.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:43
$begingroup$
hence why I said, the expression includes no parentheses.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:49
$begingroup$
For those who downvote: please specify a reason.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:51
$begingroup$
My comment still applies.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:51
$begingroup$
What does this have to do with "calculators" ?
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:16
|
show 4 more comments
$begingroup$
A few people I met were debating over if $-5^2 = 25$ or $-25$.
From my experience, we assume operator precedence and get $-25.$
People are telling me however, calculators are flawed, the real answer is $25.$
Clarifying note, the expression is merely:
$-5^2$
nothing else.
What would you say?
Edit:
I've also tried saying $f(x)=-x^2$ is a parabola that opens downwards, but this was apparently a problem with graphing calculators as well.
arithmetic exponentiation
edited Nov 29 '18 at 22:43
N. F. Taussig
43.9k93355
asked Nov 29 '18 at 21:42
SzmatoPotatoSzmatoPotato
353
$endgroup$
A few people I met were debating over if $-5^2 = 25$ or $-25$.
From my experience, we assume operator precedence and get $-25.$
People are telling me however, calculators are flawed, the real answer is $25.$
Clarifying note, the expression is merely:
$-5^2$
nothing else.
What would you say?
Edit:
I've also tried saying $f(x)=-x^2$ is a parabola that opens downwards, but this was apparently a problem with graphing calculators as well.
arithmetic exponentiation
arithmetic exponentiation
edited Nov 29 '18 at 22:43
N. F. Taussig
43.9k93355
asked Nov 29 '18 at 21:42
SzmatoPotatoSzmatoPotato
353
edited Nov 29 '18 at 22:43
N. F. Taussig
43.9k93355
asked Nov 29 '18 at 21:42
SzmatoPotatoSzmatoPotato
353
edited Nov 29 '18 at 22:43
N. F. Taussig
43.9k93355
edited Nov 29 '18 at 22:43
N. F. Taussig
43.9k93355
edited Nov 29 '18 at 22:43
N. F. Taussig
43.9k93355
43.9k93355
asked Nov 29 '18 at 21:42
SzmatoPotatoSzmatoPotato
353
asked Nov 29 '18 at 21:42
SzmatoPotatoSzmatoPotato
353
asked Nov 29 '18 at 21:42
SzmatoPotatoSzmatoPotato
353
353
3
$begingroup$
It is important to distinguish between $-5^2 = -25$, and $(-5)^2 = 25$.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:43
$begingroup$
hence why I said, the expression includes no parentheses.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:49
$begingroup$
For those who downvote: please specify a reason.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:51
$begingroup$
My comment still applies.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:51
$begingroup$
What does this have to do with "calculators" ?
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:16
|
show 4 more comments
3
$begingroup$
It is important to distinguish between $-5^2 = -25$, and $(-5)^2 = 25$.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:43
$begingroup$
hence why I said, the expression includes no parentheses.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:49
$begingroup$
For those who downvote: please specify a reason.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:51
$begingroup$
My comment still applies.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:51
$begingroup$
What does this have to do with "calculators" ?
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:16
3
3
$begingroup$
It is important to distinguish between $-5^2 = -25$, and $(-5)^2 = 25$.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:43
$begingroup$
It is important to distinguish between $-5^2 = -25$, and $(-5)^2 = 25$.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:43
$begingroup$
hence why I said, the expression includes no parentheses.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:49
$begingroup$
hence why I said, the expression includes no parentheses.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:49
$begingroup$
For those who downvote: please specify a reason.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:51
$begingroup$
For those who downvote: please specify a reason.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:51
$begingroup$
My comment still applies.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:51
$begingroup$
My comment still applies.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:51
$begingroup$
What does this have to do with "calculators" ?
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:16
$begingroup$
What does this have to do with "calculators" ?
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:16
|
show 4 more comments
6 Answers
6
active
oldest
votes
$begingroup$
By definition of the order of operations, exponentiation takes precedence over negation. Therefore,
$$
-5^2 = (-1) times 5 times 5 = -25
$$
but the alternative would be
$$
(-5)^2 = left[(-1) times 5right] times left[(-1) times 5 right] = 25.
$$
answered Nov 29 '18 at 21:45
gt6989bgt6989b
33.6k22453
$endgroup$
$begingroup$
As I said, the expression contains no parentheses. Would the 2nd part of your answer still apply?
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:48
$begingroup$
Since it contains no parentheses, @SzmatoPotato, technically, no, the second part does not apply. The assumption that it does apply is the common mistake that produces the entire controversy/debate.
$endgroup$
– Eevee Trainer
Nov 29 '18 at 21:58
$begingroup$
They are now saying "-5 isn't a negation operation it's an interger"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:05
$begingroup$
I quote: "a negative is a sign, not an operator"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:24
$begingroup$
@SzmatoPotato If you want to treat $-5$ as an integer, the convention is to specifically write $(-5)^2=25$ for the second line and $-5^2$ to mean the first line. There are multiple ways to skin the cat, but we need to end up with the same stew afterwards whichever way you choose.
$endgroup$
– gt6989b
Nov 30 '18 at 4:51
add a comment |
$begingroup$
You’re right. $-5^2$ means $-1cdot 5^2$.
$$-5^2 = -1cdot 5^2 = -25$$
They’re confusing it with $(-5)^2$, which means $(-5)cdot (-5)$.
$$(-5)^2 = (-5)cdot (-5) = +25$$
answered Nov 29 '18 at 21:53
KM101KM101
5,9661523
$endgroup$
$begingroup$
Great explanation, think this makes sense. I will hold off on marking the best answer though.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:54
add a comment |
$begingroup$
When -5^2 is written on paper, it's assumed that it's actually (-5)^2, as in the negative was already applied to the 5 before squaring. Often times this is where the confusion comes from when typing -5^2 into a calculator is equal to -25.
The calculator is not necessarily wrong. When you type -5^2, the calculator is really calculating -(5)^2. It squares the 5 first, then it applies the negative(multiplies the equation by negative 1.) This is really what the negative sign means, multiplying the number by -1. When we teach and learn -'s though, we automatically multiply it out, since -5 and -(5) equals the same thing, which is -5. Just know that when you put a negative sign in your calculator, you're really putting "-1x...", "negative one times..."
answered Nov 29 '18 at 22:01
Thomas FallicaThomas Fallica
311
$endgroup$
$begingroup$
What you are saying is false. $-5^2 = -1 cdot 5^2$, while $(-5)^2 = (-5)(-5)$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:49
add a comment |
$begingroup$
Without a parentheses the negative is taken as a -1, so it would read as ${-1*5^2}$, which would equal -25. With a parentheses, it would be read as $({-5)^2}$ which equals 25.
answered Nov 29 '18 at 21:51
Xavier StantonXavier Stanton
311211
$endgroup$
$begingroup$
Hi, thanks for the answer. Can you clarify what you mean by "With a parentheses, it would be read as −52 which equals 25."
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:52
$begingroup$
Put the -5 inside the parentheses. it will look like (-5)^2
$endgroup$
– Xavier Stanton
Nov 29 '18 at 21:53
$begingroup$
The way you wrote the second sentence is needlessly confusing. You should distinguish between $-5^2$ and $(-5)^2$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:46
$begingroup$
Do you get what I'm saying though?
$endgroup$
– Xavier Stanton
Nov 30 '18 at 1:06
add a comment |
$begingroup$
To properly answer you question, I need a graphing calculator. I don't have one, but I do have a scientific calculator, a CVS knock-off of a Sharp 2-line model.
I pressed the negation key "+/-", the display shows "-0". So far so good. Then I press 5 and the display changes to "-5". But then I press the $x^2$ key and then "(-5)²" goes up on the top line of the display. So this calculator has clearly understood my button pushing to mean "$(-5)^2$", not "$-(5^2)$".
Hmm... I wonder about reverse Polish... $(-5)^2$ would be $5 - 5 - times$, while $-(5^2)$ would be $0 , 5 , 5 times -$ (press Enter when you need to follow a number with another number).
If Jerry Springer got involved in this debate, I think he would cap it off saying that "Ultimately, communication among humans is subject to the vagaries of shared experiences, and in those gaps, ambiguities creep in." Or something along those lines.
answered Dec 6 '18 at 5:22
Robert SoupeRobert Soupe
11k21950
$endgroup$
add a comment |
$begingroup$
By the rules of precedence, in mathematical notation $-5^2=-(5^2)$, not $(-5)^2$.
For the same reason, $-5-5$ is not $(-5)(-5)$. No discussion.
If this concerns calculator input, the answer is not unique.
answered Nov 29 '18 at 22:07
Yves DaoustYves Daoust
125k671222
$endgroup$
$begingroup$
What would you say to "if you're assuming it's an operation you're bringing into question how you can ever write negative numbers"? I'm unsure of how to answer this one.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:13
$begingroup$
@SzmatoPotato: sorry, I can't decipher your question.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:15
$begingroup$
I think they mean -5 implies (-5) the integer, and I'm unsure of how to dispute this.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:16
$begingroup$
@SzmatoPotato: there are rules of precedence.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:17
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3019259%2fthe-expression-52%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
6 Answers
6
active
oldest
votes
6 Answers
6
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
By definition of the order of operations, exponentiation takes precedence over negation. Therefore,
$$
-5^2 = (-1) times 5 times 5 = -25
$$
but the alternative would be
$$
(-5)^2 = left[(-1) times 5right] times left[(-1) times 5 right] = 25.
$$
answered Nov 29 '18 at 21:45
gt6989bgt6989b
33.6k22453
$endgroup$
$begingroup$
As I said, the expression contains no parentheses. Would the 2nd part of your answer still apply?
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:48
$begingroup$
Since it contains no parentheses, @SzmatoPotato, technically, no, the second part does not apply. The assumption that it does apply is the common mistake that produces the entire controversy/debate.
$endgroup$
– Eevee Trainer
Nov 29 '18 at 21:58
$begingroup$
They are now saying "-5 isn't a negation operation it's an interger"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:05
$begingroup$
I quote: "a negative is a sign, not an operator"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:24
$begingroup$
@SzmatoPotato If you want to treat $-5$ as an integer, the convention is to specifically write $(-5)^2=25$ for the second line and $-5^2$ to mean the first line. There are multiple ways to skin the cat, but we need to end up with the same stew afterwards whichever way you choose.
$endgroup$
– gt6989b
Nov 30 '18 at 4:51
add a comment |
$begingroup$
By definition of the order of operations, exponentiation takes precedence over negation. Therefore,
$$
-5^2 = (-1) times 5 times 5 = -25
$$
but the alternative would be
$$
(-5)^2 = left[(-1) times 5right] times left[(-1) times 5 right] = 25.
$$
answered Nov 29 '18 at 21:45
gt6989bgt6989b
33.6k22453
$endgroup$
$begingroup$
As I said, the expression contains no parentheses. Would the 2nd part of your answer still apply?
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:48
$begingroup$
Since it contains no parentheses, @SzmatoPotato, technically, no, the second part does not apply. The assumption that it does apply is the common mistake that produces the entire controversy/debate.
$endgroup$
– Eevee Trainer
Nov 29 '18 at 21:58
$begingroup$
They are now saying "-5 isn't a negation operation it's an interger"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:05
$begingroup$
I quote: "a negative is a sign, not an operator"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:24
$begingroup$
@SzmatoPotato If you want to treat $-5$ as an integer, the convention is to specifically write $(-5)^2=25$ for the second line and $-5^2$ to mean the first line. There are multiple ways to skin the cat, but we need to end up with the same stew afterwards whichever way you choose.
$endgroup$
– gt6989b
Nov 30 '18 at 4:51
add a comment |
$begingroup$
By definition of the order of operations, exponentiation takes precedence over negation. Therefore,
$$
-5^2 = (-1) times 5 times 5 = -25
$$
but the alternative would be
$$
(-5)^2 = left[(-1) times 5right] times left[(-1) times 5 right] = 25.
$$
answered Nov 29 '18 at 21:45
gt6989bgt6989b
33.6k22453
$endgroup$
By definition of the order of operations, exponentiation takes precedence over negation. Therefore,
$$
-5^2 = (-1) times 5 times 5 = -25
$$
but the alternative would be
$$
(-5)^2 = left[(-1) times 5right] times left[(-1) times 5 right] = 25.
$$
answered Nov 29 '18 at 21:45
gt6989bgt6989b
33.6k22453
answered Nov 29 '18 at 21:45
gt6989bgt6989b
33.6k22453
answered Nov 29 '18 at 21:45
gt6989bgt6989b
33.6k22453
answered Nov 29 '18 at 21:45
gt6989bgt6989b
33.6k22453
33.6k22453
$begingroup$
As I said, the expression contains no parentheses. Would the 2nd part of your answer still apply?
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:48
$begingroup$
Since it contains no parentheses, @SzmatoPotato, technically, no, the second part does not apply. The assumption that it does apply is the common mistake that produces the entire controversy/debate.
$endgroup$
– Eevee Trainer
Nov 29 '18 at 21:58
$begingroup$
They are now saying "-5 isn't a negation operation it's an interger"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:05
$begingroup$
I quote: "a negative is a sign, not an operator"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:24
$begingroup$
@SzmatoPotato If you want to treat $-5$ as an integer, the convention is to specifically write $(-5)^2=25$ for the second line and $-5^2$ to mean the first line. There are multiple ways to skin the cat, but we need to end up with the same stew afterwards whichever way you choose.
$endgroup$
– gt6989b
Nov 30 '18 at 4:51
add a comment |
$begingroup$
As I said, the expression contains no parentheses. Would the 2nd part of your answer still apply?
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:48
$begingroup$
Since it contains no parentheses, @SzmatoPotato, technically, no, the second part does not apply. The assumption that it does apply is the common mistake that produces the entire controversy/debate.
$endgroup$
– Eevee Trainer
Nov 29 '18 at 21:58
$begingroup$
They are now saying "-5 isn't a negation operation it's an interger"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:05
$begingroup$
I quote: "a negative is a sign, not an operator"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:24
$begingroup$
@SzmatoPotato If you want to treat $-5$ as an integer, the convention is to specifically write $(-5)^2=25$ for the second line and $-5^2$ to mean the first line. There are multiple ways to skin the cat, but we need to end up with the same stew afterwards whichever way you choose.
$endgroup$
– gt6989b
Nov 30 '18 at 4:51
$begingroup$
As I said, the expression contains no parentheses. Would the 2nd part of your answer still apply?
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:48
$begingroup$
As I said, the expression contains no parentheses. Would the 2nd part of your answer still apply?
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:48
$begingroup$
Since it contains no parentheses, @SzmatoPotato, technically, no, the second part does not apply. The assumption that it does apply is the common mistake that produces the entire controversy/debate.
$endgroup$
– Eevee Trainer
Nov 29 '18 at 21:58
$begingroup$
Since it contains no parentheses, @SzmatoPotato, technically, no, the second part does not apply. The assumption that it does apply is the common mistake that produces the entire controversy/debate.
$endgroup$
– Eevee Trainer
Nov 29 '18 at 21:58
$begingroup$
They are now saying "-5 isn't a negation operation it's an interger"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:05
$begingroup$
They are now saying "-5 isn't a negation operation it's an interger"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:05
$begingroup$
I quote: "a negative is a sign, not an operator"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:24
$begingroup$
I quote: "a negative is a sign, not an operator"
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:24
$begingroup$
@SzmatoPotato If you want to treat $-5$ as an integer, the convention is to specifically write $(-5)^2=25$ for the second line and $-5^2$ to mean the first line. There are multiple ways to skin the cat, but we need to end up with the same stew afterwards whichever way you choose.
$endgroup$
– gt6989b
Nov 30 '18 at 4:51
$begingroup$
@SzmatoPotato If you want to treat $-5$ as an integer, the convention is to specifically write $(-5)^2=25$ for the second line and $-5^2$ to mean the first line. There are multiple ways to skin the cat, but we need to end up with the same stew afterwards whichever way you choose.
$endgroup$
– gt6989b
Nov 30 '18 at 4:51
add a comment |
$begingroup$
You’re right. $-5^2$ means $-1cdot 5^2$.
$$-5^2 = -1cdot 5^2 = -25$$
They’re confusing it with $(-5)^2$, which means $(-5)cdot (-5)$.
$$(-5)^2 = (-5)cdot (-5) = +25$$
answered Nov 29 '18 at 21:53
KM101KM101
5,9661523
$endgroup$
$begingroup$
Great explanation, think this makes sense. I will hold off on marking the best answer though.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:54
add a comment |
$begingroup$
You’re right. $-5^2$ means $-1cdot 5^2$.
$$-5^2 = -1cdot 5^2 = -25$$
They’re confusing it with $(-5)^2$, which means $(-5)cdot (-5)$.
$$(-5)^2 = (-5)cdot (-5) = +25$$
answered Nov 29 '18 at 21:53
KM101KM101
5,9661523
$endgroup$
$begingroup$
Great explanation, think this makes sense. I will hold off on marking the best answer though.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:54
add a comment |
$begingroup$
You’re right. $-5^2$ means $-1cdot 5^2$.
$$-5^2 = -1cdot 5^2 = -25$$
They’re confusing it with $(-5)^2$, which means $(-5)cdot (-5)$.
$$(-5)^2 = (-5)cdot (-5) = +25$$
answered Nov 29 '18 at 21:53
KM101KM101
5,9661523
$endgroup$
You’re right. $-5^2$ means $-1cdot 5^2$.
$$-5^2 = -1cdot 5^2 = -25$$
They’re confusing it with $(-5)^2$, which means $(-5)cdot (-5)$.
$$(-5)^2 = (-5)cdot (-5) = +25$$
answered Nov 29 '18 at 21:53
KM101KM101
5,9661523
edited Nov 29 '18 at 21:58
answered Nov 29 '18 at 21:53
KM101KM101
5,9661523
answered Nov 29 '18 at 21:53
KM101KM101
5,9661523
answered Nov 29 '18 at 21:53
KM101KM101
5,9661523
5,9661523
$begingroup$
Great explanation, think this makes sense. I will hold off on marking the best answer though.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:54
add a comment |
$begingroup$
Great explanation, think this makes sense. I will hold off on marking the best answer though.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:54
$begingroup$
Great explanation, think this makes sense. I will hold off on marking the best answer though.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:54
$begingroup$
Great explanation, think this makes sense. I will hold off on marking the best answer though.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:54
add a comment |
$begingroup$
When -5^2 is written on paper, it's assumed that it's actually (-5)^2, as in the negative was already applied to the 5 before squaring. Often times this is where the confusion comes from when typing -5^2 into a calculator is equal to -25.
The calculator is not necessarily wrong. When you type -5^2, the calculator is really calculating -(5)^2. It squares the 5 first, then it applies the negative(multiplies the equation by negative 1.) This is really what the negative sign means, multiplying the number by -1. When we teach and learn -'s though, we automatically multiply it out, since -5 and -(5) equals the same thing, which is -5. Just know that when you put a negative sign in your calculator, you're really putting "-1x...", "negative one times..."
answered Nov 29 '18 at 22:01
Thomas FallicaThomas Fallica
311
$endgroup$
$begingroup$
What you are saying is false. $-5^2 = -1 cdot 5^2$, while $(-5)^2 = (-5)(-5)$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:49
add a comment |
$begingroup$
When -5^2 is written on paper, it's assumed that it's actually (-5)^2, as in the negative was already applied to the 5 before squaring. Often times this is where the confusion comes from when typing -5^2 into a calculator is equal to -25.
The calculator is not necessarily wrong. When you type -5^2, the calculator is really calculating -(5)^2. It squares the 5 first, then it applies the negative(multiplies the equation by negative 1.) This is really what the negative sign means, multiplying the number by -1. When we teach and learn -'s though, we automatically multiply it out, since -5 and -(5) equals the same thing, which is -5. Just know that when you put a negative sign in your calculator, you're really putting "-1x...", "negative one times..."
answered Nov 29 '18 at 22:01
Thomas FallicaThomas Fallica
311
$endgroup$
$begingroup$
What you are saying is false. $-5^2 = -1 cdot 5^2$, while $(-5)^2 = (-5)(-5)$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:49
add a comment |
$begingroup$
When -5^2 is written on paper, it's assumed that it's actually (-5)^2, as in the negative was already applied to the 5 before squaring. Often times this is where the confusion comes from when typing -5^2 into a calculator is equal to -25.
The calculator is not necessarily wrong. When you type -5^2, the calculator is really calculating -(5)^2. It squares the 5 first, then it applies the negative(multiplies the equation by negative 1.) This is really what the negative sign means, multiplying the number by -1. When we teach and learn -'s though, we automatically multiply it out, since -5 and -(5) equals the same thing, which is -5. Just know that when you put a negative sign in your calculator, you're really putting "-1x...", "negative one times..."
answered Nov 29 '18 at 22:01
Thomas FallicaThomas Fallica
311
$endgroup$
When -5^2 is written on paper, it's assumed that it's actually (-5)^2, as in the negative was already applied to the 5 before squaring. Often times this is where the confusion comes from when typing -5^2 into a calculator is equal to -25.
The calculator is not necessarily wrong. When you type -5^2, the calculator is really calculating -(5)^2. It squares the 5 first, then it applies the negative(multiplies the equation by negative 1.) This is really what the negative sign means, multiplying the number by -1. When we teach and learn -'s though, we automatically multiply it out, since -5 and -(5) equals the same thing, which is -5. Just know that when you put a negative sign in your calculator, you're really putting "-1x...", "negative one times..."
answered Nov 29 '18 at 22:01
Thomas FallicaThomas Fallica
311
answered Nov 29 '18 at 22:01
Thomas FallicaThomas Fallica
311
answered Nov 29 '18 at 22:01
Thomas FallicaThomas Fallica
311
answered Nov 29 '18 at 22:01
Thomas FallicaThomas Fallica
311
311
$begingroup$
What you are saying is false. $-5^2 = -1 cdot 5^2$, while $(-5)^2 = (-5)(-5)$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:49
add a comment |
$begingroup$
What you are saying is false. $-5^2 = -1 cdot 5^2$, while $(-5)^2 = (-5)(-5)$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:49
$begingroup$
What you are saying is false. $-5^2 = -1 cdot 5^2$, while $(-5)^2 = (-5)(-5)$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:49
$begingroup$
What you are saying is false. $-5^2 = -1 cdot 5^2$, while $(-5)^2 = (-5)(-5)$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:49
add a comment |
$begingroup$
Without a parentheses the negative is taken as a -1, so it would read as ${-1*5^2}$, which would equal -25. With a parentheses, it would be read as $({-5)^2}$ which equals 25.
answered Nov 29 '18 at 21:51
Xavier StantonXavier Stanton
311211
$endgroup$
$begingroup$
Hi, thanks for the answer. Can you clarify what you mean by "With a parentheses, it would be read as −52 which equals 25."
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:52
$begingroup$
Put the -5 inside the parentheses. it will look like (-5)^2
$endgroup$
– Xavier Stanton
Nov 29 '18 at 21:53
$begingroup$
The way you wrote the second sentence is needlessly confusing. You should distinguish between $-5^2$ and $(-5)^2$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:46
$begingroup$
Do you get what I'm saying though?
$endgroup$
– Xavier Stanton
Nov 30 '18 at 1:06
add a comment |
$begingroup$
Without a parentheses the negative is taken as a -1, so it would read as ${-1*5^2}$, which would equal -25. With a parentheses, it would be read as $({-5)^2}$ which equals 25.
answered Nov 29 '18 at 21:51
Xavier StantonXavier Stanton
311211
$endgroup$
$begingroup$
Hi, thanks for the answer. Can you clarify what you mean by "With a parentheses, it would be read as −52 which equals 25."
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:52
$begingroup$
Put the -5 inside the parentheses. it will look like (-5)^2
$endgroup$
– Xavier Stanton
Nov 29 '18 at 21:53
$begingroup$
The way you wrote the second sentence is needlessly confusing. You should distinguish between $-5^2$ and $(-5)^2$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:46
$begingroup$
Do you get what I'm saying though?
$endgroup$
– Xavier Stanton
Nov 30 '18 at 1:06
add a comment |
$begingroup$
Without a parentheses the negative is taken as a -1, so it would read as ${-1*5^2}$, which would equal -25. With a parentheses, it would be read as $({-5)^2}$ which equals 25.
answered Nov 29 '18 at 21:51
Xavier StantonXavier Stanton
311211
$endgroup$
Without a parentheses the negative is taken as a -1, so it would read as ${-1*5^2}$, which would equal -25. With a parentheses, it would be read as $({-5)^2}$ which equals 25.
answered Nov 29 '18 at 21:51
Xavier StantonXavier Stanton
311211
edited Nov 30 '18 at 1:08
answered Nov 29 '18 at 21:51
Xavier StantonXavier Stanton
311211
answered Nov 29 '18 at 21:51
Xavier StantonXavier Stanton
311211
answered Nov 29 '18 at 21:51
Xavier StantonXavier Stanton
311211
311211
$begingroup$
Hi, thanks for the answer. Can you clarify what you mean by "With a parentheses, it would be read as −52 which equals 25."
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:52
$begingroup$
Put the -5 inside the parentheses. it will look like (-5)^2
$endgroup$
– Xavier Stanton
Nov 29 '18 at 21:53
$begingroup$
The way you wrote the second sentence is needlessly confusing. You should distinguish between $-5^2$ and $(-5)^2$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:46
$begingroup$
Do you get what I'm saying though?
$endgroup$
– Xavier Stanton
Nov 30 '18 at 1:06
add a comment |
$begingroup$
Hi, thanks for the answer. Can you clarify what you mean by "With a parentheses, it would be read as −52 which equals 25."
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:52
$begingroup$
Put the -5 inside the parentheses. it will look like (-5)^2
$endgroup$
– Xavier Stanton
Nov 29 '18 at 21:53
$begingroup$
The way you wrote the second sentence is needlessly confusing. You should distinguish between $-5^2$ and $(-5)^2$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:46
$begingroup$
Do you get what I'm saying though?
$endgroup$
– Xavier Stanton
Nov 30 '18 at 1:06
$begingroup$
Hi, thanks for the answer. Can you clarify what you mean by "With a parentheses, it would be read as −52 which equals 25."
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:52
$begingroup$
Hi, thanks for the answer. Can you clarify what you mean by "With a parentheses, it would be read as −52 which equals 25."
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:52
$begingroup$
Put the -5 inside the parentheses. it will look like (-5)^2
$endgroup$
– Xavier Stanton
Nov 29 '18 at 21:53
$begingroup$
Put the -5 inside the parentheses. it will look like (-5)^2
$endgroup$
– Xavier Stanton
Nov 29 '18 at 21:53
$begingroup$
The way you wrote the second sentence is needlessly confusing. You should distinguish between $-5^2$ and $(-5)^2$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:46
$begingroup$
The way you wrote the second sentence is needlessly confusing. You should distinguish between $-5^2$ and $(-5)^2$.
$endgroup$
– N. F. Taussig
Nov 29 '18 at 22:46
$begingroup$
Do you get what I'm saying though?
$endgroup$
– Xavier Stanton
Nov 30 '18 at 1:06
$begingroup$
Do you get what I'm saying though?
$endgroup$
– Xavier Stanton
Nov 30 '18 at 1:06
add a comment |
$begingroup$
To properly answer you question, I need a graphing calculator. I don't have one, but I do have a scientific calculator, a CVS knock-off of a Sharp 2-line model.
I pressed the negation key "+/-", the display shows "-0". So far so good. Then I press 5 and the display changes to "-5". But then I press the $x^2$ key and then "(-5)²" goes up on the top line of the display. So this calculator has clearly understood my button pushing to mean "$(-5)^2$", not "$-(5^2)$".
Hmm... I wonder about reverse Polish... $(-5)^2$ would be $5 - 5 - times$, while $-(5^2)$ would be $0 , 5 , 5 times -$ (press Enter when you need to follow a number with another number).
If Jerry Springer got involved in this debate, I think he would cap it off saying that "Ultimately, communication among humans is subject to the vagaries of shared experiences, and in those gaps, ambiguities creep in." Or something along those lines.
answered Dec 6 '18 at 5:22
Robert SoupeRobert Soupe
11k21950
$endgroup$
add a comment |
$begingroup$
To properly answer you question, I need a graphing calculator. I don't have one, but I do have a scientific calculator, a CVS knock-off of a Sharp 2-line model.
I pressed the negation key "+/-", the display shows "-0". So far so good. Then I press 5 and the display changes to "-5". But then I press the $x^2$ key and then "(-5)²" goes up on the top line of the display. So this calculator has clearly understood my button pushing to mean "$(-5)^2$", not "$-(5^2)$".
Hmm... I wonder about reverse Polish... $(-5)^2$ would be $5 - 5 - times$, while $-(5^2)$ would be $0 , 5 , 5 times -$ (press Enter when you need to follow a number with another number).
If Jerry Springer got involved in this debate, I think he would cap it off saying that "Ultimately, communication among humans is subject to the vagaries of shared experiences, and in those gaps, ambiguities creep in." Or something along those lines.
answered Dec 6 '18 at 5:22
Robert SoupeRobert Soupe
11k21950
$endgroup$
add a comment |
$begingroup$
To properly answer you question, I need a graphing calculator. I don't have one, but I do have a scientific calculator, a CVS knock-off of a Sharp 2-line model.
I pressed the negation key "+/-", the display shows "-0". So far so good. Then I press 5 and the display changes to "-5". But then I press the $x^2$ key and then "(-5)²" goes up on the top line of the display. So this calculator has clearly understood my button pushing to mean "$(-5)^2$", not "$-(5^2)$".
Hmm... I wonder about reverse Polish... $(-5)^2$ would be $5 - 5 - times$, while $-(5^2)$ would be $0 , 5 , 5 times -$ (press Enter when you need to follow a number with another number).
If Jerry Springer got involved in this debate, I think he would cap it off saying that "Ultimately, communication among humans is subject to the vagaries of shared experiences, and in those gaps, ambiguities creep in." Or something along those lines.
answered Dec 6 '18 at 5:22
Robert SoupeRobert Soupe
11k21950
$endgroup$
To properly answer you question, I need a graphing calculator. I don't have one, but I do have a scientific calculator, a CVS knock-off of a Sharp 2-line model.
I pressed the negation key "+/-", the display shows "-0". So far so good. Then I press 5 and the display changes to "-5". But then I press the $x^2$ key and then "(-5)²" goes up on the top line of the display. So this calculator has clearly understood my button pushing to mean "$(-5)^2$", not "$-(5^2)$".
Hmm... I wonder about reverse Polish... $(-5)^2$ would be $5 - 5 - times$, while $-(5^2)$ would be $0 , 5 , 5 times -$ (press Enter when you need to follow a number with another number).
If Jerry Springer got involved in this debate, I think he would cap it off saying that "Ultimately, communication among humans is subject to the vagaries of shared experiences, and in those gaps, ambiguities creep in." Or something along those lines.
answered Dec 6 '18 at 5:22
Robert SoupeRobert Soupe
11k21950
answered Dec 6 '18 at 5:22
Robert SoupeRobert Soupe
11k21950
answered Dec 6 '18 at 5:22
Robert SoupeRobert Soupe
11k21950
answered Dec 6 '18 at 5:22
Robert SoupeRobert Soupe
11k21950
11k21950
add a comment |
add a comment |
$begingroup$
By the rules of precedence, in mathematical notation $-5^2=-(5^2)$, not $(-5)^2$.
For the same reason, $-5-5$ is not $(-5)(-5)$. No discussion.
If this concerns calculator input, the answer is not unique.
answered Nov 29 '18 at 22:07
Yves DaoustYves Daoust
125k671222
$endgroup$
$begingroup$
What would you say to "if you're assuming it's an operation you're bringing into question how you can ever write negative numbers"? I'm unsure of how to answer this one.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:13
$begingroup$
@SzmatoPotato: sorry, I can't decipher your question.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:15
$begingroup$
I think they mean -5 implies (-5) the integer, and I'm unsure of how to dispute this.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:16
$begingroup$
@SzmatoPotato: there are rules of precedence.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:17
add a comment |
$begingroup$
By the rules of precedence, in mathematical notation $-5^2=-(5^2)$, not $(-5)^2$.
For the same reason, $-5-5$ is not $(-5)(-5)$. No discussion.
If this concerns calculator input, the answer is not unique.
answered Nov 29 '18 at 22:07
Yves DaoustYves Daoust
125k671222
$endgroup$
$begingroup$
What would you say to "if you're assuming it's an operation you're bringing into question how you can ever write negative numbers"? I'm unsure of how to answer this one.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:13
$begingroup$
@SzmatoPotato: sorry, I can't decipher your question.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:15
$begingroup$
I think they mean -5 implies (-5) the integer, and I'm unsure of how to dispute this.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:16
$begingroup$
@SzmatoPotato: there are rules of precedence.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:17
add a comment |
$begingroup$
By the rules of precedence, in mathematical notation $-5^2=-(5^2)$, not $(-5)^2$.
For the same reason, $-5-5$ is not $(-5)(-5)$. No discussion.
If this concerns calculator input, the answer is not unique.
answered Nov 29 '18 at 22:07
Yves DaoustYves Daoust
125k671222
$endgroup$
By the rules of precedence, in mathematical notation $-5^2=-(5^2)$, not $(-5)^2$.
For the same reason, $-5-5$ is not $(-5)(-5)$. No discussion.
If this concerns calculator input, the answer is not unique.
answered Nov 29 '18 at 22:07
Yves DaoustYves Daoust
125k671222
edited Nov 29 '18 at 22:27
answered Nov 29 '18 at 22:07
Yves DaoustYves Daoust
125k671222
answered Nov 29 '18 at 22:07
Yves DaoustYves Daoust
125k671222
answered Nov 29 '18 at 22:07
Yves DaoustYves Daoust
125k671222
125k671222
$begingroup$
What would you say to "if you're assuming it's an operation you're bringing into question how you can ever write negative numbers"? I'm unsure of how to answer this one.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:13
$begingroup$
@SzmatoPotato: sorry, I can't decipher your question.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:15
$begingroup$
I think they mean -5 implies (-5) the integer, and I'm unsure of how to dispute this.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:16
$begingroup$
@SzmatoPotato: there are rules of precedence.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:17
add a comment |
$begingroup$
What would you say to "if you're assuming it's an operation you're bringing into question how you can ever write negative numbers"? I'm unsure of how to answer this one.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:13
$begingroup$
@SzmatoPotato: sorry, I can't decipher your question.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:15
$begingroup$
I think they mean -5 implies (-5) the integer, and I'm unsure of how to dispute this.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:16
$begingroup$
@SzmatoPotato: there are rules of precedence.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:17
$begingroup$
What would you say to "if you're assuming it's an operation you're bringing into question how you can ever write negative numbers"? I'm unsure of how to answer this one.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:13
$begingroup$
What would you say to "if you're assuming it's an operation you're bringing into question how you can ever write negative numbers"? I'm unsure of how to answer this one.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:13
$begingroup$
@SzmatoPotato: sorry, I can't decipher your question.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:15
$begingroup$
@SzmatoPotato: sorry, I can't decipher your question.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:15
$begingroup$
I think they mean -5 implies (-5) the integer, and I'm unsure of how to dispute this.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:16
$begingroup$
I think they mean -5 implies (-5) the integer, and I'm unsure of how to dispute this.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 22:16
$begingroup$
@SzmatoPotato: there are rules of precedence.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:17
$begingroup$
@SzmatoPotato: there are rules of precedence.
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:17
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3019259%2fthe-expression-52%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
3
$begingroup$
It is important to distinguish between $-5^2 = -25$, and $(-5)^2 = 25$.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:43
$begingroup$
hence why I said, the expression includes no parentheses.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:49
$begingroup$
For those who downvote: please specify a reason.
$endgroup$
– SzmatoPotato
Nov 29 '18 at 21:51
$begingroup$
My comment still applies.
$endgroup$
– MisterRiemann
Nov 29 '18 at 21:51
$begingroup$
What does this have to do with "calculators" ?
$endgroup$
– Yves Daoust
Nov 29 '18 at 22:16