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

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

c

is rational. Which statement about

c + 10

is true?

\newline

Choices:

\newline

(A)

c + 10

is rational.

\newline

(B)

c + 10

is irrational.

\newline

(C)

c + 10

can be rational or irrational, depending on the value of

c

.

Identify Number Type: Identify whether $10$ is a rational or irrational number. $\newline$ $10$ is an integer, and all integers are rational numbers because they can be expressed as a fraction where the denominator is $1$ ( $\frac{10}{1}$ ).
Rational Number Explanation: We know: $\newline$ $c$ is a rational number. $\newline$ $10$ is a rational number. $\newline$ Adding two rational numbers always results in a rational number.
Sum of Rational Numbers: Therefore, $c + 10$ is also a rational number. $\newline$ This is because the sum of two rational numbers is always rational.

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