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