Rational VS. Irrational Numbers
The product of a nonzero rational number and an irrational number is irrational.
Always
The product of a rational number and a rational number is always rational.
Always
The sum of a rational number and a rational number is rational.
Always
The sum of a rational number and an irrational number is irrational.
Always
The sum of two rational numbers is rational.
Always
Can NOT be expressed as the quotient of two integers such that the denominator is not zero.
Irrational Numbers
The product of an irrational and irrational number is 0.
Never
The product of two rational numbers is irrational.
Never
The sum of two irrational numbers is rational.
Never
List the ways to figure out if a number is irrational.
Pie, Non-Repeating Decimal (...), and Root of a Non-Perfect Square
Can be expressed as the quotient of two integers with a denominator that is NOT zero.
Rational Numbers
The product of a rational and irrational number is 0.
Sometimes
The product of a rational number and irrational number is irrational.
Sometimes
The product of an irrational number and an irrational number is irrational.
Sometimes
The sum of an irrational number and an irrational number is irrational.
Sometimes
The sum of two irrational numbers is rational.
Sometimes