Positive and negative numbers
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.
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.
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?
7) -9++4 =
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=