Results 1 to 9 of 9
Like Tree7Thanks
  • 1 Post By dissolvedgirl
  • 2 Post By romsek
  • 1 Post By Debsta
  • 1 Post By studiot
  • 1 Post By studiot
  • 1 Post By Plato

Thread: "Difference between" - understanding the wording of a math problem

  1. #1
    Newbie
    Joined
    Feb 2019
    From
    South Africa
    Posts
    2
    Thanks
    1

    "Difference between" - understanding the wording of a math problem

    As far as my understanding goes, if one is asked "what is the difference between x and y?" you interpret it as x - y?

    So, for example if you have "what is the difference between -2 and 1?" one can solve it as -2 - (+1)?

    Which would provide the answer as -3. However, the book's answer is 3, which looks to me like they were looking for absolute value instead of actually solving the difference between -2 and 1.

    I got that answer incorrect as I was doing it like an equation and stated it as -3, but I completely understand why it is incorrect if you take into consideration absolute value.

    Am I mistaken in my assumption here?
    Thanks from studiot
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    6,572
    Thanks
    2903

    Re: "Difference between" - understanding the wording of a math problem

    I would answer the question

    "what is the difference between x and y?"
    as "The absolute value of of x minus y"

    a "difference" is non-negative
    Thanks from dissolvedgirl and topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,237
    Thanks
    456

    Re: "Difference between" - understanding the wording of a math problem

    I'd say the difference between 3 and 5 is the same as the difference between 5 and 3, that is 2. So yes, absolute value.
    Thanks from dissolvedgirl
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Apr 2015
    From
    Somerset, England
    Posts
    263
    Thanks
    55

    Re: "Difference between" - understanding the wording of a math problem

    Welcome dissolvedgirl. +1 for a good question that brings to light a definition issue.

    I'm not at all convinced by the answers.

    My mathematics dictionary has

    "The number or quantity to be added to yield the other"

    So what would you add to (-1) to get (+3) ?

    (-1) + (+4) = (+3) so the difference is +4

    But

    (+3) + (+4) = (+7) Oh dear.

    You must add

    (+3) + (-4) = (-1)

    Consider an electric circuit with two wires one at a potential of -1 volts and the other at +3 volts.

    Which way round would you have to connect a 4 volt battery to one wire to have the free terminal at the potential of the other?
    Thanks from dissolvedgirl
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2019
    From
    South Africa
    Posts
    2
    Thanks
    1

    Re: "Difference between" - understanding the wording of a math problem

    Thanks, everyone, this makes sense.

    I looked through my study guide/textbook and nowhere does it explain this, it only states "ways with words" and under the subtraction operation is difference mentioned so it kind of misleads one into thinking that difference means subtract a from b and provide the answer.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Apr 2015
    From
    Somerset, England
    Posts
    263
    Thanks
    55

    Re: "Difference between" - understanding the wording of a math problem

    Quote Originally Posted by dissolvedgirl View Post
    Thanks, everyone, this makes sense.

    I looked through my study guide/textbook and nowhere does it explain this, it only states "ways with words" and under the subtraction operation is difference mentioned so it kind of misleads one into thinking that difference means subtract a from b and provide the answer.
    I think you should clarify this with your instructors because subtraction and difference are not necessarily the same thing.

    Further it make a big difference in more advanced maths.

    For instance the arithmetical operations of addition and multiplication are such that a + b = b + a and a*b = b*a

    But this is not generally true of subtraction or division.

    And difference is not defined as the result of subtraction.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    22,401
    Thanks
    3292
    Awards
    1

    Re: "Difference between" - understanding the wording of a math problem

    Quote Originally Posted by dissolvedgirl View Post
    I looked through my study guide/textbook and nowhere does it explain this, it only states "ways with words" and under the subtraction operation is difference mentioned so it kind of misleads one into thinking that difference means subtract a from b and provide the answer.
    I suspect in the study guide there also a statement about absolute value.
    If p & q are two points on a number line the the distance between them is $|p-q|$
    Now some may wonder 'how do we know which to subtract from which?'
    Well it does not matter, the distance from p to q is the same as the distance from q to p!
    So we have $|p-q|=|q-p|$ Moreover, because $|x|=|x-0|$ that means the absolute value of $x$ is its distance from zero.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    Apr 2015
    From
    Somerset, England
    Posts
    263
    Thanks
    55

    Re: "Difference between" - understanding the wording of a math problem

    Quote Originally Posted by Plato View Post
    I suspect in the study guide there also a statement about absolute value.
    If p & q are two points on a number line the the distance between them is $|p-q|$
    Now some may wonder 'how do we know which to subtract from which?'
    Well it does not matter, the distance from p to q is the same as the distance from q to p!
    So we have $|p-q|=|q-p|$ Moreover, because $|x|=|x-0|$ that means the absolute value of $x$ is its distance from zero.

    What Platos says is both true and helpful.

    But

    Note that difference and distance are not the same thing.


    I said that these things make a difference in more advanced maths.
    Distance, as Plato defines it, is called a metric.
    Metrics are specially choses so that it doesn't matter "which you subtract from which".

    But there is a whole section of mathematics called finite differences, in which it matters very much indeed.

    In your opening post you asked
    What is the difference between -2 and 1.
    So you have introduced what are called signed numbers and the result of this difference must be a signed number.
    Finite differences are such a case in point.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    May 2019
    From
    USA
    Posts
    7
    Thanks
    1

    Re: "Difference between" - understanding the wording of a math problem

    Very interesting discussion - I'm glad I came across this one!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Jun 11th 2015, 07:16 AM
  2. Replies: 5
    Last Post: Jan 29th 2013, 11:53 AM
  3. Replies: 2
    Last Post: Aug 6th 2011, 03:00 PM
  4. Difference between "contained" and "element of"
    Posted in the Discrete Math Forum
    Replies: 15
    Last Post: Jan 6th 2010, 09:03 AM
  5. Why is my "basic ratio" & "Z-score difference" different?!
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: Mar 7th 2008, 04:29 AM

/mathhelpforum @mathhelpforum