Algebra Honors (Period 6 & 7)

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.
3 = 3/1= 6/2 = 12/4 = -15/-5
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 8/3 or 17/7?
the LCD is 21
8/3 = 56/21
17/7 = 51/21
so 8/3 > 17/7

For all integers a and b and all positive integers c and d
a/c > b/d if an only if ad > bc
a/c < b/d 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)

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 umber 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
a + (1/2)(b-a);
the number one third of the way from a to b would be
a + (1/3)(b-a) and so on