negative and positive

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mikerod111:

on negatives and positives, is there a general rule for them. I.E. negative plus negative = positive is this true for all mathematics (adding, subtracting, multiplying and dividing)?

Hey mikerod111!

I consider it easiest to visualize them on a number line, or perhaps considering a staircase.

If we go down, and then down some more, we're obviously going down.
So minus + minus = minus.

If we go down, and then up, we won't immediately know if we're lower or higher than the starting point.
So minus + plus = uncertain.

If we go a (positive) number of times down, we're effectively going down.
So plus x minus = minus.

If we go the other direction, that is a negative number of times down, we're retracing our steps, so we're effectively going up.
So minus x minus = plus.
This may be a bit much to consider every time you run into it, so it's a good idea to memorize this one: minus x minus = plus.

If we're going down, and take a (positive) fraction of that, we're still going down.
So minus / plus = minus.

And so on...


Here's a couple of general rules that are useful to remember:
1. minus x minus = plus
2. The rules for multiplication are the same as the rules for division.
3. In case of doubt, consider a stair case, the number line, a thermometer, going up to heaven or down to h**l, or whatever works for you.

mikerod111:

on negatives and positives, is there a general rule for them. I.E. negative plus negative = positive is this true for all mathematics (adding, subtracting, multiplying and dividing)?

Hi mikerod111

You've already got 2 good answers and I am about to give you a 3rd.

For multiply and divide it is very simple. If the signs are the same then the answer is positive. If the signs are different the answer is negative. See, simple.

For addition and subtraction it is a bit trickier.
Like I like Serena, I am a big user of number lines. Until you get used to it you should actually draw your number lines. I am assuming that you know how to do that.
Zero in the middle, positive numbers going off to the right, negative numbers going off to the left.

Say it is 1+6. You start at 1 then go 6 places in the positive direction and you get 7 (yea, I know, you already knew that)
Now -3+8 Start at -3 and go 8 in the positive direction and what do you get?
Now 4 - 9 start at 4 and go 9 in the negative direction and what do you get?
Now -2- 8 start at -2 and go 8 in the negative direction and what do you get?

When you get good at it you can stop drawing the number line but you should still imagine it. If you use a note book, imagine 0 in the crease of the book, the positive numbers will be on the right and the negative numbers on the left.

Now, what about those pesky + - things
for starters, If you see something like 7+(-8) it is exactly the same as 7+ - 8 (You can put the bracket in or take it away - it doesn't matter.)
That goes for 3 - - 6 = 3- (-6) as well.

Now think of a thermometer. 0 degrees is in the middle. The positive numbers are hot numbers. The negative or minus numbers are cold numbers.
Let's think about 4+ + 5 you are adding heat so it must get hotter. So it is 4+5
What about 6+-7 This time you are adding cold. So it has to get colder. It must be 6-7
And 8 - + 3. This time you are taking away heat so it has got to get colder. It must be 8-3
and lastly -1 - - 4. This time you are taking away coldness so it has to get warmer. It must be -1+4

With pluses and minuses you can also think of it like this.
If two signs are so close together that you can put a circle around them without anything getting in the way then,
if the signs are the same you replace them with a positive.
if the signs are different you replace them with a negative.

I am going to give you some questions to answer now.

1) Now -3+8 Start at -3 and go 8 in the positive direction and what do you get?
2) Now 4 - 9 start at 4 and go 9 in the negative direction and what do you get?
3) Now -2- 8 start at -2 and go 8 in the negative direction and what do you get?
4) 0-8=
5) -2-+6=
6) 1-4+(-7)=
7) -9++4 =
8) 13+(-5)=
9) -4 x 6 =
10) 3 x -6 =
11) -5 x -3=
12) 20 / -4=
13) -8 / 2=
14) -15 / -5=
15) +4 x +7=