Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational. You can do this by providing examples of each

Rational numbers are fractional numbers, whose numerator and denominator are integers and the denominator is ever zero.

Step-by-step explanation:

The sum of rational numbers gives a rational number;

     + = , because the evaluation of the denominator always results to a non-zero integer.

The product of   x = , which multiply both numerator and denominator to give integer numbers.

The sum and product of rational and irrational numbers are always irrational numbers, for instance,

            x 7 = 2.3 , which is a number which decimal points that can only be represented by the product irrational number and rational number , where 7 is an irrational number.

        + 7 =  7 , which is a whole number and fractional number combined.