The sum or product of a non-zero rational number and an irrational number is always
Rational.
Irrational.
A repeating decimal.
A fraction.

Solution:

By definition we know that an irrational number in the form of a decimal goes on without repeating (non terminating, non repeating decimal). 

By definition we know that a rational number in the form of decimal repeats or terminates.

So multiplying or adding a non terminating non repeating number to a terminating repeating number the result will be a non terminating non repeating number.

For example - Consider a rational number 5

Irrational number √2

By adding we get 5 + √2 

By multiplying 5 x √2 = 5√2 

Therefore, the sum or product of a non-zero rational number and an irrational number is always an irrational number. 

The sum or product of a non-zero rational number and an irrational number is always

Summary:

The sum or product of a non-zero rational number and an irrational number is always an irrational number.