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

Respuesta :

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;

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

The product of  [tex]\frac{1}{3}[/tex] x [tex]\frac{1}{3}[/tex] = [tex]\frac{1}{9}[/tex], 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,

           [tex]\frac{1}{3}[/tex] 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.

       [tex]\frac{1}{3}[/tex] + 7 =  7[tex]\frac{1}{3}[/tex] , which is a whole number and fractional number combined.

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