Try our Free Online Math Solver!

RATIONAL NUMBERS
• Rational numbers : are of the form
where a and b are both integers and b
≠ 0.
NOTE: Every integer, whole number, and fraction is a rational number.
• Let be any rational number and n be
a nonzero integer. Then
• Let be any rational number. Then
• is a positive rational number when either
a and b are both positive or when a and b are
both negative .
• is a negative rational number when a
and b have different signs (one negative and one pos
itive).
Properties of Rational Number Addition
• Closure Property: Rational number + Rational number = Rational number.
• Commutative Property:
• Associative Property: .
• Identity Property:
• Additive Inverse Property: For every rational number
, there exists a unique rational
number  such that
 is called the additive inverse .
Properties of Rational Number Multiplication
• Closure Property: Rational number ยท Rational number = Rational number.
• Commutative Property:
• Associative Property:
• Identity Property:
• Multiplicative Inverse Property: For every nonzero rational number
, there exists a
unique rational number such that
is called the multiplicative
inverse or reciprocal .
• Distributive Property :
Cross Multiplication of Rational Number Inequality :
Let and
be rational numbers with
b > 0 and d > 0. Then
if and only if ad < bc:
NOTE: BE CAREFUL!!! Both denominators must be positive in order to use this. DO
NOT use
if one of the denominators is negative unless you first the rational number
using
EXAMPLES: Put the appropriate sign (<, =, >) between each pair of rational
numbers to make
a true statement.
HOMEWORK: pp 368369, 2, 4, 5, 79, 11, 13, 15, 16
Prev  Next 