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This property shows that when adding three or more real numbers, the grouping of numbers does not affect the sum. Example: $(a + b) + c = a + (b + c)$.

The property that for every real number, there exists an additive inverse that, when added to the original number, results in zero. Example: $a + (-a) = 0$.

This property states that changing the order of addends does not change the sum. Example: $a + b = b + a$.

The property stating that the sum of any number and zero is the number itself. Example: $a + 0 = a$.

This property combines addition and multiplication, stating that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products. Example: $a(b + c) = ab + ac$.

The property that the way in which factors are grouped does not change the product. Example: $(ab)c = a(bc)$.

If a real number $a$ is equal to $b$, and $b$ is equal to $c$, then $a$ is equal to $c$. Example: If $a = b$ and $b = c$, then $a = c$.

This property indicates that the order of factors does not affect the product. Example: $ab = ba$.

This property states that the product of any number and one is the number itself. Example: $a imes 1 = a$.