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Associative Property of Multiplication

Associative property of multiplication:

a×(b×c)=(a×b)×c\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⋅(4⋅5)=3⋅20=60{3}\cdot{\left({4}\cdot{5}\right)}={3}\cdot{20}={60}.

From another side, we have that (3⋅4)⋅5=12⋅5=60{\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×(3×(−4))=(5×3)×(−4)=−60{5}\times{\left({3}\times{\left(-{4}\right)}\right)}={\left({5}\times{3}\right)}\times{\left(-{4}\right)}=-{60}.

Example 3. (−5.89)×(2.51×(−3.4))=((−5.89)×2.51)×(−3.4)=50.26526{\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. (58×3)×12=58×(3×12)=1516{\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}}.