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

Identify Number Nature: Identify the nature of the number 5. 5 is a whole number, which is also a rational number because it can be expressed as the fraction 5/1.Sum Property of Rationals: Understand the property of the sum of two rational numbers. The sum of two rational numbers is always rational. This is because if you have two rational numbers, a/b and c/d, their sum (ad + bc) / (bd) is also a rational number since both the numerator and the denominator are integers and the denominator is not zero.Apply Property to Numbers: Apply the property to the given numbers. Since 5 is rational and v is given to be rational, their sum 5 + v must also be rational according to the property of rational numbers.

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

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

v

is rational. Which statement about

5 + v

is true?

\newline

Choices:

\newline

(A)

5 + v

is rational.

\newline

(B)

5 + v

is irrational.

\newline

(C)

5 + v

can be rational or irrational, depending on the value of

v

Identify Number Nature: Identify the nature of the number $5$ . $5$ is a whole number, which is also a rational number because it can be expressed as the fraction $\frac{5}{1}$ .
Sum Property of Rationals: Understand the property of the sum of two rational numbers. The sum of two rational numbers is always rational. 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 both the numerator and the denominator are integers and the denominator is not zero.
Apply Property to Numbers: Apply the property to the given numbers. $\newline$ Since $5$ is rational and $v$ is given to be rational, their sum $5 + v$ must also be rational according to the property of rational numbers.