Adding and subtracting signs directly near each other

When adding `(+)` and subtracting `(-)` signs that are directly beside each other, the same rules that apply to multiplying and dividing apply here too. i.e.

1-When the signs are different the answer is negative
2-When the signs are the same the answer is positive

Or the other way of remembering this is

My friend's friend is my friend `(++=+)`
My friend's enemy is my enemy `(+\-\=-)`
My enemy's friend is my enemy `(-+=-)`
My enemy's enemy is my friend `(-\-\=+)`

The main issue to remember is

`(-\-\=+)` that is: 2 wrongs make a right

Examples

`3+(+3)=6`   (signs are the same so positive)

`3-(+3)=0`   (signs are different so negative)

`3+(-3)=0`  (signs are different so negative)

`3-(-3)=6`   (signs are the same so positive)

NOTE:

If there were three negatives in a row

`3-(-5)-5`

Then you would complete one calculation first, beginning on the left

`3-(-5)=8`

and now relook at the equation

`8-5`

You can now complete the calculation

`8-5=3`

So `3-(-5)-5=3`

Difficult examples

Example 1

What is the answer to the following?

`9-(-4)+(-3)`

Complete one calculation first, beginning on the left

`9-(-4)=9+4=13`    (signs the same so positive)

Now the sum becomes

`13+(-3)`

Now we can complete the calculation

`13+(-3)=13-3=10`   (signs different so negative)

Answer: `9-(-4)+(-3)=10`

Example 2

What is the answer to the following?

`3z-\(-7z)`

`3z-\(-7z)=>` When the signs are the same the answer is positive

So `3z-\(-7z)=3z+7z`

and `3z+7z=10z`

Answer: `=10z`

Example 3

What is the answer to the following?

`3times(-3)times(-3)`

Complete one calculation first

`3times-3`  actually means `+3times(-3)`

When the signs are different the answer is negative

So `+3times(-3)=-9`

so the sum now becomes `-9times(-3)`

When the signs are the same the answer is positive

`-9times(-3)=+27`

Answer: `=+27`

Example 4

What is the answer to

`3-3-3`

This calculation is easy because the positives and negatives are not next to each other so you would treat it as a normal sum.

`3-3-3=0-3=-3`

Answer: `3-3-3=-3`

Example 5

What is 

`-8ntimes(-3)`

`-8ntimes(-3)=24n`

Because signs are the same so its positive

Answer: `-8ntimes-3=24n`