True or false the product of a rational number and an integer is not an integer

Question

True or false the product of a rational number and an integer is not an integer

Answer 1

This is TRUE sometimes and FALSE sometimes.  It depends on the choice of numbers.  Consider two examples:

 

(1)

 

3/2 is rational

2 is an integer

3/2 x 2 = 3 is an integer

 

(2)

 

2/3 is rational

5 is an teger

2/3 x 5 = 10/3 is NOT an integer

 

Answer 2

An integer is a rational number. Therefore an integer times and integer is an integer and the statement is false.

A rational number cold be a fraction. In that case a fraction times and integer is not an integer and the statement is true.

Because of this duality, the statement is false.