Question

which of the statements using operations on rational or irrational numbers always results in a rational number?

a) irrarional + irrational
b) irrational ÷ irrational
c) rational + irrational
d) rational ÷ rational​

Answer 1

Hm a irrational number is a number like this:

$1.999999\inf$

So adding a rational number, like 2, it would be irrational still:

$2+1.999999\inf=3.999999\inf$

That being said, answer C is wrong

Now, what is 2/2? Or 4/1? Whole numbers are one of the 3 types of rational numbers.

$2\ /\ 2=1\\\\4\ / 1=\ 4$

Thus the answer appears to be D

Now lets use the process of elimination to double check the answer:

The wording of your question is what will help us out here:

Which of the statements using operations on rational or irrational numbers always results in a rational number?

Because of that, any of the choices that involve a irrational number can result with another irrational number like so:

$a)\ 1.999\inf+ 1.999\inf=3.888\inf\\\\b)\ 2.999\inf / 1.999\inf= 1.50025\inf$

And there you go, the only answer that hasn't been proven wrong is answer D.

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