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The number $s$ is rational. Which statement about $8 + s$ is true? $\newline$ Choices: $\newline$ (A) $8 + s$ is rational. $\newline$ (B) $8 + s$ is irrational. $\newline$ (C) $8 + s$ can be rational or irrational, depending on the value of $s$ .

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

s

is rational. Which statement about

8 + s

is true?

\newline

Choices:

\newline

(A)

8 + s

is rational.

\newline

(B)

8 + s

is irrational.

\newline

(C)

8 + s

can be rational or irrational, depending on the value of

s

.

Identify Number $8$ : Identify the nature of the number $8$ . $8$ is a whole number, which is also a rational number because it can be expressed as the fraction $\frac{8}{1}$ .
Sum of Rational Numbers: Understand the property of the sum of two rational numbers. The sum of two rational numbers is always a rational number. This is because if you have two fractions $\frac{a}{b}$ and $\frac{c}{d}$ , their sum $\frac{ad + bc}{bd}$ is also a fraction, which means it is a rational number.
Apply Property to Numbers: Apply the property to the given numbers. $\newline$ Since $s$ is a rational number and $8$ is a rational number, their sum $8 + s$ must also be a rational number.

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