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The number $b$ is rational. Which statement about $b - 8$ is true? $\newline$ Choices: $\newline$ (A) $b - 8$ is rational. $\newline$ (B) $b - 8$ is irrational. $\newline$ (C) $b - 8$ 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 - 8

is true?

\newline

Choices:

\newline

(A)

b - 8

is rational.

\newline

(B)

b - 8

is irrational.

\newline

(C)

b - 8

can be rational or irrational, depending on the value of

b

.

Identify Number $8$ : Identify the nature of the number $8$ . $8$ is an integer, and all integers are rational numbers because they can be expressed as a fraction where the denominator is $1$ (e.g., $\frac{8}{1}$ ).
Properties of Rational Numbers: Understand the properties of rational numbers. The difference between two rational numbers is always a rational number. This is because if you have two fractions $\frac{a}{b}$ and $\frac{c}{d}$ , their difference $\left(\frac{a}{b}\right) - \left(\frac{c}{d}\right)$ can be expressed as a single fraction which is also a rational number.
Apply Property to Problem: Apply the property to the given problem. $\newline$ Since $b$ is a rational number and $8$ is a rational number, their difference $b - 8$ will also be a rational number.

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