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

#### dissolvedgirl

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?

• 1 person

#### romsek

MHF Helper

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

a "difference" is non-negative

• 2 people

#### Debsta

MHF Helper
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.

• 1 person

#### studiot

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.

(+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?

• 1 person

#### dissolvedgirl

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.

#### studiot

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.

• 1 person

#### Plato

MHF Helper
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.

• 1 person

#### studiot

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.