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Commutative Property of Addition

Commutative property of addition:

a+b=b+a\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≠b−a{a}-{b}\ne{b}-{a}.

For example, 4−3≠3−4{4}-{3}\ne{3}-{4}.

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

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

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

Example 3. 58−23=58+(−23)=(−23)+58\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.