# Associative Property of Multiplication

Associative property of multiplication:

$\color{purple}{a\times\left(b\times c\right)=\left(a\times b\right)\times c}$

As with commutative property order is not important.

Indeed, you can make sure on a couple of examples, that it is correct.

Example.

From one side, we have that ${3}\cdot{\left({4}\cdot{5}\right)}={3}\cdot{20}={60}$.

From another side, we have that ${\left({3}\cdot{4}\right)}\cdot{5}={12}\cdot{5}={60}$.

Warning. This doesn't work with division.

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

Example 2. ${5}\times{\left({3}\times{\left(-{4}\right)}\right)}={\left({5}\times{3}\right)}\times{\left(-{4}\right)}=-{60}$.

Example 3. ${\left(-{5.89}\right)}\times{\left({2.51}\times{\left(-{3.4}\right)}\right)}={\left({\left(-{5.89}\right)}\times{2.51}\right)}\times{\left(-{3.4}\right)}={50.26526}$.

Example 4. ${\left(\frac{{5}}{{8}}\times{3}\right)}\times\frac{{1}}{{2}}=\frac{{5}}{{8}}\times{\left({3}\times\frac{{1}}{{2}}\right)}=\frac{{15}}{{16}}$.