Properties of the Real Numbers
Addition Properties |
Multiplication Properties |
|
Associative Property |
$$a+(b+c)=(a+b)+c$$ | $$a \cdot (b \cdot c)=(a \cdot b) \cdot c$$ |
Commutative Property |
$$a+b=b+a$$ | $$a \cdot b = b \cdot a$$ |
Identity Property |
$$a+0=a$$ | $$a \cdot 1=a$$ |
Inverse Property |
$$a+(-a)=0$$ | $$a \cdot \frac{1}{a}=1$$ |
Distributive Property
$$a \cdot (b + c) = a \cdot b + a \cdot c$$Significance of Associativity and Commutivity
The associative and commutative properties of both addition and multiplication show that the order in which addition and multiplication operations are performed does not matter. When you have mathematical expressions combining addition and multiplication operations that is a different matter, of course.
Significance of the Identity Properties
The identity properties establish the importance of the numbers one and zero, and they are very useful for all kinds of arithmetic and algebra applications.
Significance of the Inverse Properties
The inverse properties for addition and multiplication serve to define the operations of subtraction and division respectively.
Significance of the Distributive Property
The distributive property is the basis for many elementary arithmetic number manipulation techniques and is very important in algebra as well.