# Associative Property of Addition

**Associative property of addition**:

`huge color(purple)(a+(b+c)=(a+b)+c)`

Intuitively, we understand, that it is correct.

Indeed, suppose your friend Ann has 3 apples, Bob has 5 apples and Cliff has 4 apples.

Bob and Cliff give you their apples, then Ann gives you her apples: `3+(5+4)=3+9=12` (`a+(b+c)`).

But, what if Ann and Bob gave you their apples, and then Cliff gave you his apples?

You will get the same number of apples: `(3+5)+4=8+4=12` (`(a+b)+c`).

So, regardless of order, you will get all 12 apples of your friends.

**Warning**. This doesn't work with subtraction.

However, associative property of addition works for negative numbers (in fact, for real numbers) as well.

**Example 1**. `5+(3+(-4))=(5+3)+(-4)=4`.

**Example 2**. `(-5.89)+(2.51+(-3.4))=((-5.89)+2.51)+(-3.4)=-6.78`.

**Example 3**. `(5/8+3)+sqrt(2)=5/8+(3+sqrt(2))`.