Operations with Rational and Irrational Numbers

Irrational Number

• Any decimal that does not terminate or repeat

• A whole number that can be divided evenly

• A fraction that can be expressed as a ratio of two integers

• A decimal that terminates or repeats

Rational Number

• Any number that can be written as a fraction: Terminating decimals and repeating decimals

• Any number that cannot be expressed as a fraction

• Only whole numbers and integers

• Numbers that have non-repeating, non-terminating decimals

Rational + Rational

• ALWAYS RATIONAL

• ALWAYS IRRATIONAL

• CAN BE RATIONAL OR IRRATIONAL

• NEVER RATIONAL

Irrational x Rational

• ALWAYS RATIONAL

• ALWAYS IRRATIONAL (EXCEPT if Rational Number is zero then answer will be rational)

• SOMETIMES RATIONAL

• NEVER RATIONAL

Irrational + Irrational

• Always Irrational

• Sometimes Rational

• Always Rational

• Never Rational

Irrational x Irrational

• Always Irrational

• Sometimes Rational

• Always Rational

• Never Rational

Rational x Rational

• ALWAYS RATIONAL

• SOMETIMES IRRATIONAL

• NEVER RATIONAL

• ALWAYS IRRATIONAL

Rational + Irrational

• ALWAYS RATIONAL

• SOMETIMES RATIONAL

• ALWAYS IRRATIONAL

• NEVER IRRATIONAL