# Commutative Property of Addition

**Commutative property of addition**:

$$$\color{purple}{a+b=b+a}$$$

What does it mean?

It means, that order of numbers doesn't matter.

Indeed, suppose your first friend (let's call it Tom) gave you 3 apples, then your another friend (let's call it Jim) gave your 4 apples. You got total of 7 apples.

But does really matter, who gave the apples first? If Jim gave you 4 apples and then Tom gave you 3 apples, you got also 7 apples.

**Warning**: it doesn't work with subtraction, i.e. $$${a}-{b}\ne{b}-{a}$$$.

For example, $$${4}-{3}\ne{3}-{4}$$$.

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

**Example 1.** $$${3}+{\left(-{4}\right)}={\left(-{4}\right)}+{3}$$$.

**Example 2.** $$${\left(-{2.51}\right)}+{\left(-{3.4}\right)}={\left(-{3.4}\right)}+{\left(-{2.51}\right)}$$$.

**Example 3.** $$$\frac{{5}}{{8}}-\frac{{2}}{{3}}=\frac{{5}}{{8}}+{\left(-\frac{{2}}{{3}}\right)}={\left(-\frac{{2}}{{3}}\right)}+\frac{{5}}{{8}}$$$.

**Conclusion.** So, the basic rule here is following: whenever you see addition, you can interchange addends.