Question

81

24)
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The sum of x and y is a rational number. Which statement is correct?
The number represented by y must be rational.
В)
The number represented by X must be rational.
The number represented by x may be rational or irrational.
The number represented by x must be rational and the number
represented by y must be rational.

Answer 1

Option B is the correct answer.

Explanation:

A rational number is the one that can be made by dividing two numbers with no fractional part, for example, .75 or 1/2.

An irrational number is a real number that can't be made by dividing two numbers that don't have fractional part.

In this case, the answer is the number represented by x may be rational or irrational because one part of the sum doesn't have to be defined as irrational.

Answer 2

The number represented by x may be rational or irrational

Explanation:

Rational and irrational numbers

For this answer, we must remind that a rational number is such that it can be expressed as a fraction. Irrational numbers cannot. Examples of rational numbers are

`-2,(3)/(4),0,3.21,1.3333...`

Examples of irrational numbers are

`√(2),\pi, 1+√(3), e^5,sin1`

To help us to better explain this answer, let's suppose

`x=1+√(2)\ ,\ y=1-√(2)`

They both are irrational and their sum is rational as shown:

`x+y=1+√(2)+1-√(2)=2`

The first option: "The number represented by y must be rational" is false because y is not rational

The second option: "The number represented by X must be rational." and the last option: "The number represented by x must be rational and the number

represented by y must be rational" are equally false.

The only true option is: "The number represented by x may be rational or irrational".

We can clearly see one member of a sum doesn't necessarily define it as irrational