Commutative Property of Multiplication

Commutative property of multiplication:

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

commutative property of multiplicationWhat 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 3×2=6{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: 2×3=6{2}\times{3}={6}.

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

For example, 3223\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×(4)=(4)×3=12{3}\times{\left(-{4}\right)}={\left(-{4}\right)}\times{3}=-{12}.

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

Example 3. 58×23=(58)×23=512-\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.