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

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Properties of operations on rational and irrational numbers

Full solution

Q. The number

v

is rational. Which statement about

10 + v

is true?

\newline

Choices:

\newline

(A)

10 + v

is rational.

\newline

(B)

10 + v

is irrational.

\newline

(C)

10 + v

can be rational or irrational, depending on the value of

v

.

Identify Number $10$ : Identify the nature of the number $10$ . $10$ is an integer, which is also a rational number because it can be expressed as the ratio of two integers $(\frac{10}{1})$ .
Properties of Rational Numbers: Understand the properties of rational numbers. $\newline$ The sum of two rational numbers is always a rational number. This is because if you have two rational numbers, $\frac{a}{b}$ and $\frac{c}{d}$ , their sum $\frac{ad + bc}{bd}$ is also a rational number since it can be expressed as the ratio of two integers.
Apply Property to Numbers: Apply the property to the given numbers. $\newline$ Since $v$ is a rational number and $10$ is a rational number, their sum $(10 + v)$ must also be a rational number according to the property of rational numbers.
Conclude Correct Statement: Conclude the correct statement from the given choices. $\newline$ Based on the property that the sum of two rational numbers is rational, the statement about $10 + v$ being rational is true.

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