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The number $t$ is rational. Which statement about $t - 10$ is true? $\newline$ Choices: $\newline$ (A) $t - 10$ is rational. $\newline$ (B) $t - 10$ is irrational. $\newline$ (C) $t - 10$ can be rational or irrational, depending on the value of $t$ .

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

t

is rational. Which statement about

t - 10

is true?

\newline

Choices:

\newline

(A)

t - 10

is rational.

\newline

(B)

t - 10

is irrational.

\newline

(C)

t - 10

can be rational or irrational, depending on the value of

t

.

Identify Number $10$ : Identify the nature of the number $10$ . $10$ is an integer, which is also a rational number since it can be expressed as a fraction $(10/1)$ .
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 $t$ is rational and $10$ is rational, their difference $(t - 10)$ must also be rational.
Conclude Expression Nature: Conclude the nature of the expression $t - 10$ . The statement about $t - 10$ being rational is true, regardless of the value of $t$ , as long as $t$ is rational.

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