i believe this is pre-algebra?

[i.suck.at.math]

The distance between the corresponding points of A and its opposite number is 12 units on the number line. Find the product of A and its opposite number

ps. English isn't my first language but i tried my best translating the problem. hope everything is correct

 

[Otis]

Hello ISAM. Do you have a picture of the Real number line? Two numbers are opposites if they're the same distance away from zero. Look at the Real number line.

For example, if you're located at 4 on the Real number line, and I'm located at -4, then we are both four units away from zero. Therefore, 4 and -4 are opposites, and the distance between them is 8.

Opposite Numbers Definition (Illustrated Mathematics Dictionary)

Illustrated definition of Opposite Numbers: Numbers that are in opposite positions on the number line. Such as minus6 and 6 Or minus150 and 150...

www.mathsisfun.com

?

 

[Deleted member 4993]

The distance between the corresponding points of A and its opposite number is 12 units on the number line. Find the product of A and its opposite number

ps. English isn't my first language but i tried my best translating the problem. hope everything is correct

What does "opposite number" of A mean?

What would be the opposite number of, say, 9?

Would it be -9 ?​

​

or would it be 1/9 ?​

 

[HallsofIvy]

The distance between the corresponding points of A and its opposite number is 12 units on the number line. Find the product of A and its opposite number

ps. English isn't my first language but i tried my best translating the problem. hope everything is correctfthn

As Subhotosh Kahn told you, "opposite number" is NOT standard mathematical notation!

If the "opposite number" to A is its "additive inverse", -A, then the distance between them is A- (-A)= 2A= 12. So A= 12/2= 6 and the "opposite number" is -6. So the question is asking you to find (6)(-6).

But if the "oppposite number to A is its "multiplicative inverse", 1/A, then the distance between A and 1/A is A- 1/A= (A^2- 1)/A= 12 so A^2- 1=12A. A^2- 12A- 1= 0. Completing the square A^2- 12A+ 36= (A- 6)^2= 37 so A= 6 plus or minus sqrt{37}.
The product of those two numbers is (6+ sqrt(37))(6- sqrt(37)= 36- 37= -1.

I suspect the first of those was intended but you should check to make sure!

 

[Otis]

What would be the opposite number of, say, 9?
Would it be -9 ?or would it be 1/9 ?

I suppose (if you wanted 1 pizza) we could view me giving you 9 times as many pizzas to be the opposite of me giving you 1/9th of a pizza, but I've not heard of that viewpoint.

Or maybe because 9 is on opposite sides of the fraction bar in 1/9 and 9/1.

Is that a thing, in some places? To call reciprocals "opposite numbers", I mean.

 

[Otis]

"opposite number" is NOT standard mathematical notation!

Maybe so, but the phrase is ubiquitous in pre- and beginning-algebra.

Wikipedia says, "In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number),[1] sign change,[2] and negation.[3]"

Graphically speaking, opposite numbers lie on opposite sides of zero and zero is midway between them.

I think also, it's a precursor to describing subtraction as "adding the opposite" because that language is used once students start solving equations. Lessons are often a mixture of technical and layman's language.