Classify each of the following as True or False, and explain why.

Question

(a) The sum of any pair of rational numbers is always a rational number;

(b) The difference of any pair of irrational numbers is always an irrational number;

(c) The product of any rational number and any irrational number is always an irrational number.

Answer 1

Just remember that a rational number means that it can be written as a fraction, while and irrational number cannot.

1) True: if you take 2 rational numbers and add them, you can start by finding common denominators and then adding straight across. Thus, you still have a fraction at the end -> rational number.

2) False, if the irrational numbers are the same, their difference will be 0 (which is rational, NOT irrational).

3) False, zero is a rational number, and if you multiply 0 by an irrational number you get 0 (which is again RATIONAL).

I hope that helps!

Best,

Sam