The number a is irrational. Which statement about a - 5 is true? Choices: (A)a - 5 is rational. (B)a - 5 is irrational. (C)a - 5 can be rational or irrational, depending on the value of a.

Identify Number Nature: Identify the nature of the number 5. 5 is a rational number because it can be expressed as a fraction (5/1).Subtraction Rule: Understand the subtraction of a rational number from an irrational number. When you subtract a rational number from an irrational number, the result is always irrational. This is because the rational part cannot be expressed as a fraction with the same denominator as the irrational part, and thus the irrationality is preserved.Apply Understanding: Apply the understanding to the given problem. Since a is irrational and 5 is rational, a - 5 will also be irrational.

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The number $a$ is irrational. Which statement about $a - 5$ is true? $\newline$ Choices: $\newline$ (A) $a - 5$ is rational. $\newline$ (B) $a - 5$ is irrational. $\newline$ (C) $a - 5$ can be rational or irrational, depending on the value of $a$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

a

is irrational. Which statement about

a - 5

is true?

\newline

Choices:

\newline

(A)

a - 5

is rational.

\newline

(B)

a - 5

is irrational.

\newline

(C)

a - 5

can be rational or irrational, depending on the value of

a

Identify Number Nature: Identify the nature of the number $5$ . $5$ is a rational number because it can be expressed as a fraction $\frac{5}{1}$ .
Subtraction Rule: Understand the subtraction of a rational number from an irrational number. $\newline$ When you subtract a rational number from an irrational number, the result is always irrational. This is because the rational part cannot be expressed as a fraction with the same denominator as the irrational part, and thus the irrationality is preserved.
Apply Understanding: Apply the understanding to the given problem. $\newline$ Since $a$ is irrational and $5$ is rational, $a - 5$ will also be irrational.