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The number $s$ is rational. Which statement about $s - 2$ is true? $\newline$ Choices: $\newline$ (A) $s - 2$ is rational. $\newline$ (B) $s - 2$ is irrational. $\newline$ (C) $s - 2$ 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

s - 2

is true?

\newline

Choices:

\newline

(A)

s - 2

is rational.

\newline

(B)

s - 2

is irrational.

\newline

(C)

s - 2

can be rational or irrational, depending on the value of

s

.

Identify nature of $s$ : Identify the nature of the number $s$ . $s$ is a rational number, which means it can be expressed as a fraction of two integers, where the denominator is not zero.
Determine nature of $2$ : Determine the nature of the number $2$ . The number $2$ is an integer, which is also a rational number because it can be expressed as $\frac{2}{1}$ .
Analyze $s - 2$ : Analyze the operation $s - 2$ . $\newline$ Subtracting a rational number from another rational number will always result in a rational number. This is because the subtraction of two fractions (or integers) is another fraction (or integer).
Conclude nature of $s - 2$ : Conclude the nature of $s - 2$ . Since both $s$ and $2$ are rational, their difference $s - 2$ is also rational.

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