Question

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

Answer 1

Answer:

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;

   $\frac{1}{3}$  + $\frac{1}{3}$ = $\frac{2}{3}$ , because the evaluation of the denominator always results to a non-zero integer.

The product of  $\frac{1}{3}$ x $\frac{1}{3}$ = $\frac{1}{9}$, 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,

           $\frac{1}{3}$ 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.

       $\frac{1}{3}$ + 7 =  7$\frac{1}{3}$ , which is a whole number and fractional number combined.