Question

Consider that x = −5 and y = −4. Which statement is true about x + y? A) The sum of x and y is a rational number. B) The sum of x and y is an imaginary number. C) The sum of x and y is an irrational number. D) The sum of x and y is neither rational nor irrational.

Answer 1

Your answer is A. The sum of x and y is a rational number .

Answer 2

A) The sum of x and y is a rational number.

Explanation:

We will first prove that the given values of x and y are rational and then we will prove the fact that the sum of two rational numbers is a rational number.

A rational number is a number which is in the form
`(p)/(q)`, where p and q are integers and q ≠ 0.

We can write - 5 as
`(-5)/(1)` and clearly 1 ≠ 0.

So, x = -5 is a rational number.

Similarly, y = -4 is also a rational number.

For the second part of the proof, consider any two rational numbers
`(p)/(q)` and
`(r)/(s)`.

Now,

`(p)/(q) +(r)/(s) =(ps+rq)/(qs)`

Since p, q, r and s are integers, ps + rq is also an integer.

Moreover, since q ≠ 0 and s ≠ 0, qs ≠ 0.

Therefore,
`(ps+rq)/(qs)` is also a rational number.

Hence, sum of two rational numbers is also a rational number.

Since x = -5 and y = -4 are rational numbers, x + y = (-5) + (-4) = -9 is also a rational number.