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

Identify Number Nature: Identify the nature of the number 2. 2 is a rational number because it can be expressed as the ratio of two integers (2/1).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 integers are closed under addition and multiplication.Apply Property to Problem: Apply the property to the given problem. Since s is a rational number and 2 is a rational number, their sum (2 + s) must also be a rational number.

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

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

s

is rational. Which statement about

2 + s

is true?

\newline

Choices:

\newline

(A)

2 + s

is rational.

\newline

(B)

2 + s

is irrational.

\newline

(C)

2 + s

can be rational or irrational, depending on the value of

s

Identify Number Nature: Identify the nature of the number $2$ . $2$ is a rational number because it can be expressed as the ratio of two integers ( $\frac{2}{1}$ ).
Sum Property of Rationals: 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 rational numbers, $\frac{a}{b}$ and $\frac{c}{d}$ , their sum $\frac{ad + bc}{bd}$ is also a rational number since integers are closed under addition and multiplication.
Apply Property to Problem: Apply the property to the given problem. $\newline$ Since $s$ is a rational number and $2$ is a rational number, their sum $(2 + s)$ must also be a rational number.