The Rational Numbers
Properties of Rational Number Multiplication
Let and be any rational numbers .
• Closure: is a rational number.
• Identity: where 1 can be represented as m/m, for m ≠ 0
o Over Addition :
o Over Subtraction :
Let and be any rational numbers. Then
Let and be any rational numbers where is nonzero. Then the following are
Ordering Rational Numbers
There are four equivalent methods to order rational numbers.
• Number- line Approach :
if and only if a/b occurs to the left of c/b on the
• Cross-Multiplication Approach: Let b > 0 and d > 0 .
if and only if
ad < bc .
Properties of Ordering Rational Numbers
• Transitive: If and , then
• Addition: If then
o By a positive number then
o By a negative number then
• Density Property: If
then there exists a rational number