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The number $c$ is rational. Which statement about $9 - c$ is true? $\newline$ Choices: $\newline$ (A) $9 - c$ is rational. $\newline$ (B) $9 - c$ is irrational. $\newline$ (C) $9 - c$ can be rational or irrational, depending on the value of $c$ .

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

c

is rational. Which statement about

9 - c

is true?

\newline

Choices:

\newline

(A)

9 - c

is rational.

\newline

(B)

9 - c

is irrational.

\newline

(C)

9 - c

can be rational or irrational, depending on the value of

c

.

Identify Number $9$ : Identify the nature of the number $9$ . $9$ is a whole number, which is also a rational number because it can be expressed as a fraction $\frac{9}{1}$ .
Properties of Rational Numbers: Understand the properties of rational numbers. Subtracting a rational number from another rational number always results in a rational number. This is because the set of rational numbers is closed under subtraction.
Apply Property to Expression: Apply the property to the given expression. $\newline$ Since $c$ is rational and $9$ is rational, their difference $(9 - c)$ will also be rational.
Conclude Expression Nature: Conclude the nature of the expression based on the previous steps. $\newline$ Therefore, the statement about $9 - c$ is that it is always rational, regardless of the value of $c$ , as long as $c$ is rational.

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