 # 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

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