Thread: Purpose of subtracting negetive integers

I'm an old man restudying per-algebra. Ok, not real old, but it's been many years since I studied math.

What is the purpose of subtracting negetive integers?

Or should I say, when or where would I need to do that? Practical application.

Perhaps it's needed to understand algebra later on? Any other applications if the previous statement is right?

Originally Posted by MrDiedel

I'm an old man restudying per-algebra. Ok, not real old, but it's been many years since I studied math.

What is the purpose of subtracting negetive integers?

Or should I say, when or where would I need to do that? Practical application.

Perhaps it's needed to understand algebra later on? Any other applications if the previous statement is right?

You need to understand that when you start dealing with directed numbers, the act of subtraction extends to evaluating DISTANCES between numbers. So a statement like 5 - (-3) means "what is the distance between 5 and -3"? Obviously the answer is 8, the same as what you would get if you did 5 + 3.

Thanks for responding.

So after researching the term directed numbers, I've come to conclude that is another way of saying integers. Correct me if I'm wrong here.

Therefore I've created the following statement.

The purpose of subtracting integers, (directed numbers) is to find the distance between them on an integer number line.

The number line becomes a useful visual aid for me, yet it causes me trouble as well.

(+2) - (-2) = 4
With this problem, I have one mark on the -2 and one on the +2. Do I end up on the +4 on the number line? Or do I create a new section by counting the absolute value of 4?

*---|-|-|-*-|-|
-2 -1 0 1 2 3 4
The number line above is equal to the one below?
|---|-|-|-|-|-*
-2 -1 0 1 2 3 4
or do I do it like this
*----4---*
*---|-|-|-*-|-|
-2 -1 0 1 2 3 4
Or am I just thinking about this too much?

And what statement could I make about adding integers? Could I say..

The purpose of adding integers, (directed numbers) is to find the distance from zero. (or the distance they travel together.)


(+3) + (-2) = 1

*---|-|-|-|-*-|
-2 -1 0 1 2 3 4

The -2 travels +3 and the +3 travels -2, therefor they meet at +1.
|---|-*-|-|-|-|
-2 -1 0 1 2 3 4

Sigh, I feel embarrassed to have to ask such elementary questions.

No, directed numbers are numbers with a sign in front of them, denoting which direction you are going away from 0 (negative to the left or down, while positive to the right or up) on a number line. It is perfectly reasonable to have directed numbers that are fractions or irrational.

Integers are all the WHOLE numbers (positive or negative or 0).

As for your other question with the number line, like I said, subtracting is the process of finding the DISTANCE between the two numbers. So if you're doing +2 - (-2) as you have suggested, you'll mark in +2 and -2 and count how many integers you need to travel to get from one to the other. Obviously it's 4. You do NOT have to do any further markings.

As for your analogy for addition, yes you could consider it to be the combined distance from 0. So something like 5 + 3, you travel 5, and then another 3, so you get to 8. If you did something like 5 + (-3), then you would be going right by 5 and then left by 3, you get to 2, so it's the same as 5 - 3 = 2.

Clear as a bell. Thanks very much. My algebra book just arrived yesterday, so I'd better hurry up and get finished with these pre-algebra lessons. Have a good one and thanks for taking the time to educate me further.

Regards,
Mr. Diedel

one area where positive and negative quantities occur with regularity is in the math of accounting, or more generally, transactions.

the "size" of the number (always identified with a positive number) is the amount of the transaction. the SIGN of the transaction indicates "who's receiving" (this is a matter of orientation, and as such is somewhat arbitrary).

traditionally, businesses associate positive signs with credits, and negative signs with debits.

a small example:

Fred and Joe start with $5 in their pockets. they make a $5 bet on a football game. Fred loses the bet, and pays Joe his $5. Joe sees the transaction as $5+$5 = $10. Fred sees the transaction as $5-$5 = $0. whether the transaction is an "add" or a "subtract" depends on whether you are Fred or Joe.

so "directed numbers" can be used anytimes we have "opposing directions" (or flows). some common examples:

up/down
in/out
right/left
gain/loss
income/debt
forward/backward
light/dark
saturated color/pale (transparent) color
hot/cold


note these are all "unilateral" opposites, if we are just talking about forward and back, we have no numerical way to express "sideways".

Fred didn't bring his money, so he has a debt of -$5. He places another bet of $5 and loses yet again, and therefore he has a another debt of -$5, or -$5 + (-$5).
One man says he'll pay 1/2 of Fred's debt, so Fred can now subtract one. He now writes -$5 - -$5 because he's subtracting a debt. Now instead of -$10 or -$5 he has 0 debt? LOL I know my thinking must be wrong somewhere, but I like this math so far. ha ha

Oh wait, I think I figured out my mistake. He's not subtracting a debt from his debit sheet, he's adding funds from another source. But it was funnier thinking about it the other way.
I have 2 debts, -$5 and -$5.
Someone takes care of one debt, so I subtract one of my debts.
1 debt of -$5 minus 1 debt of -$5 = 0 debt! COOL! ha ha ha

Deveno, thanks for responding and telling me where I could find this type of math problem. Maybe we can work on my new formula for future banking of the people! LOL Ok, I'd better get back to reality and start working on this prealgebra so I can get into my brand new algebra book.