Question

The product of two rational numbers is __ rational. A) always B)sometimes C)never

Answer 1

Always if you multiply a rational number by another you will get a rational number

Answer 2

The product of two rational numbers will be rational. Why? A rational number is described as a number that can represented as a/b where b does not equal 0.

An irrational cannot be represented as a/b where b does not equal 0.

Thus, if you multiply two numbers in their a/b equivalent, you will get an a/b where b is not equal to 0 form.

Example: 

Multiply 10 by 4.

We can represent 10 with the fraction equivalent 10/1. Same goes with 4. 4/1.


Now multiply.

10/1 * 4/1 = 40/1 = 40

As we can see, the number is still an irrational number.