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: $-8ntimes-3=24n$