# Commutative Property of Multiplication

**Commutative property of multiplication**:

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

What does it mean?

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

Indeed, as can be seen from illustration, we can count there are 3 circles in a row, and there are 2 rows, so total number of squares is $$${3}\times{2}={6}$$$.

From another side, we can rotate picture and count circles in another way: 3 rows, and in each row 2 circles: $$${2}\times{3}={6}$$$.

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

For example, $$$\frac{{3}}{{2}}\ne\frac{{2}}{{3}}$$$.

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

**Example 1.** $$${3}\times{\left(-{4}\right)}={\left(-{4}\right)}\times{3}=-{12}$$$.

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

**Example 3.** $$$-\frac{{5}}{{8}}\times\frac{{2}}{{3}}={\left(-\frac{{5}}{{8}}\right)}\times\frac{{2}}{{3}}=-\frac{{5}}{{12}}$$$.

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