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The number $b$ is rational. Which statement about $b - 6$ is true? $\newline$ Choices: $\newline$ (A) $b - 6$ is rational. $\newline$ (B) $b - 6$ is irrational. $\newline$ (C) $b - 6$ can be rational or irrational, depending on the value of $b$ .

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

b

is rational. Which statement about

b - 6

is true?

\newline

Choices:

\newline

(A)

b - 6

is rational.

\newline

(B)

b - 6

is irrational.

\newline

(C)

b - 6

can be rational or irrational, depending on the value of

b

.

Understand nature of $b$ : Understand the nature of the number $b$ . Since $b$ is given as a rational number, it can be expressed as the quotient of two integers, where the denominator is not zero.
Analyze $b - 6$ : Analyze the operation $b - 6$ . $\newline$ Subtracting a rational number $b$ by an integer $6$ (which is also a rational number since it can be expressed as $\frac{6}{1}$ ) will result in another rational number because the difference of two rational numbers is always rational.
Conclude nature of $b - 6$ : Conclude the nature of $b - 6$ . Since both $b$ and $6$ are rational, their difference $b - 6$ is also rational. This is true regardless of the specific value of $b$ , as long as $b$ is rational.

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t - \sqrt{47}

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t - \sqrt{47}

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can be rational or irrational, depending on the value of

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