Algebra Honors (Periods 5 & 6)

Properties of Rational Numbers 11-1

A real number that can be expressed as the quotient of two integers is called a rational number

A rational number can be written as a quotient of integers in an unlimited number of ways.

To determine which of two rational numbers is greater, you can write them with the same positive denominator and compare the numerators

Which is greater                                                           

?

the LCD is 21   

  

  

For all  integers  a and b and all positive integers c and d

   if an only if ad > bc

 if and only if ad < bc

This method compares the product of the extremes with the product of the means

Thus 4/7 > 3/8 because (4)(8) > (3)(7)

Rational Numbers differ from Integers in several ways. For example, given an integer, there IS a next greater integer.

That is, -8 is greater than -9. 1 follows 0, 35 follows 34 and so on. There is no “Next Greater” rational number after a given rational number.

The Density Property for Rational Numbers
Between every pair of different rational numbers there is another rational number

The density property implies that it is possible to find an unlimited or endless number of rational numbers between two given rational numbers.

If a and b are rational numbers and a < b  then the number halfway from a to b is

 and the number one third of the way from a to b would be

and so on.