Question

True or false? If false give counterexample The product of a rational number and an integer is not an integer ​

Answer 1

Answer:

False

Step-by-step explanation:

Required

State if the product of rational numbers and integer is an integer

The statement is false and the proof is as follows

Literally, rational numbers are decimal numbers that can be represented as a fraction of two integers;

Take for instance: 0.2, 0.5, 2.25, etc.

When any of these numbers is multiplied by an integer, the resulting number can take any of two forms;

1. It can result to an integer:

For instance;

$0.2 * 5 = 1$

$0.5 * 4 = 2$

$2.25 * 8 = 18$

2. It can result in a decimal number

For instance;

$0.2 * 3 = 0.6$

$0.5 * 5 = 2.5$

$2.25 * 7 = 15.75$

From (1) above, we understand that the product can result in an integer.

Hence, the statement is false