The number q is rational. Which statement about 2 + q is true? Choices: (A)2 + q is rational. (B)2 + q is irrational. (C)2 + q can be rational or irrational, depending on the value of q.

Identify Number 2: Identify the nature of the number 2. 2 is a whole number, which is also a rational number because it can be expressed as the fraction 2/1.Understand Sum Property: 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 fractions a/b and c/d, their sum (ad + bc) / bd is also a fraction, hence rational.Apply Property to Numbers: Apply the property to the given numbers. Since q is given to be rational and 2 is also rational, their sum 2 + q must also be rational according to the property of rational numbers.

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The number $q$ is rational. Which statement about $2 + q$ is true? $\newline$ Choices: $\newline$ (A) $2 + q$ is rational. $\newline$ (B) $2 + q$ is irrational. $\newline$ (C) $2 + q$ can be rational or irrational, depending on the value of $q$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

q

is rational. Which statement about

2 + q

is true?

\newline

Choices:

\newline

(A)

2 + q

is rational.

\newline

(B)

2 + q

is irrational.

\newline

(C)

2 + q

can be rational or irrational, depending on the value of

q

Identify Number $2$ : Identify the nature of the number $2$ . $2$ is a whole number, which is also a rational number because it can be expressed as the fraction $\frac{2}{1}$ .
Understand Sum Property: Understand the property of the sum of two rational numbers. $\newline$ The sum of two rational numbers is always rational. This is because if you have two fractions $\frac{a}{b}$ and $\frac{c}{d}$ , their sum $\frac{ad + bc}{bd}$ is also a fraction, hence rational.
Apply Property to Numbers: Apply the property to the given numbers. $\newline$ Since $q$ is given to be rational and $2$ is also rational, their sum $2 + q$ must also be rational according to the property of rational numbers.