The numbers used to measure real-world quantities such as length, area, volume, speed, electrical charges, probability of rain, room temperature, gross national products, growth rates, and so forth, are called real numbers. They include such number as , , , , , , , and . The basic algebraic properties of the real numbers can be expressed in terms of the two fundamental operations of addition and multiplication.
Basic Algebraic Properties:
Let and denotes real numbers.
(1) The Commutative Properties
The commutative properties says that the order in which we either add or multiplication real number doesn’t matter.
(2) The Associative Properties
The associative properties tells us that the way real numbers are grouped when they are either added or multiplied doesn’t matter. Because of the associative properties, expressions such as and makes sense without parentheses.
(3) The Distributive Properties
The distributive properties can be used to expand a product into a sum, such as or the other way around, to rewrite a sum as product:
(4) The Identity Properties
We call the additive identity and the multiplicative identity for the real numbers.
(5) The Inverse Properties
(a) For each real number , there is real number , called the additive inverse of , such that (b) For each real number , there is a real number , called the multiplicative inverse of , such that Although the additive inverse of , namely , is usually called the negative of , you must be careful because isn’t necessarily a negative number. For instance, if...