The number q is rational. Which statement about q + 2 is true? Choices: (A)q + 2 is rational. (B)q + 2 is irrational. (C)q + 2 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.Properties of Rational Numbers: Understand the properties of rational numbers. The sum of two rational numbers is always a rational number. This is because if you have two fractions a/b and c/d, their sum (ad + bc) / bd is also a fraction, which means it is a rational number.Apply Property to Problem: Apply the property to the given problem. Since q is a rational number and 2 is a rational number, their sum q + 2 must also be a rational number.

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The number $q$ is rational. Which statement about $q + 2$ is true? $\newline$ Choices: $\newline$ (A) $q + 2$ is rational. $\newline$ (B) $q + 2$ is irrational. $\newline$ (C) $q + 2$ 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

q + 2

is true?

\newline

Choices:

\newline

(A)

q + 2

is rational.

\newline

(B)

q + 2

is irrational.

\newline

(C)

q + 2

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 $\frac{2}{1}$ .
Properties of Rational Numbers: Understand the properties of rational numbers. The sum of two rational numbers is always a rational number. 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, which means it is a rational number.
Apply Property to Problem: Apply the property to the given problem. $\newline$ Since $q$ is a rational number and $2$ is a rational number, their sum $q + 2$ must also be a rational number.