# 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 · 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 368-369, 2, 4, 5, 7-9, 11, 13, 15, 16

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