# 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`