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

Identify Number Nature: Identify the nature of the number 10. 10 is a rational number because it can be expressed as the ratio of two integers (10/1).Consider Number s: Consider the nature of the number s. Since s is given as a rational number, it can also be expressed as the ratio of two integers (p/q, where p and q are integers and q is not zero).Analyze Sum of Rational Numbers: Analyze the sum of two rational numbers. The sum of two rational numbers is always rational. This is because adding two fractions (or integers) results in another fraction (or integer) which can be simplified if necessary.Apply Property to 10 + s: Apply the property to 10 + s. Since both 10 and s are rational, their sum 10 + s must also be rational.Choose Correct Statement: Choose the correct statement from the given choices. Based on the previous steps, the correct statement about 10 + s is that it is rational.

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The number $s$ is rational. Which statement about $10 + s$ is true? $\newline$ Choices: $\newline$ (A) $10 + s$ is rational. $\newline$ (B) $10 + s$ is irrational. $\newline$ (C) $10 + s$ 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

10 + s

is true?

\newline

Choices:

\newline

(A)

10 + s

is rational.

\newline

(B)

10 + s

is irrational.

\newline

(C)

10 + s

can be rational or irrational, depending on the value of

s

Identify Number Nature: Identify the nature of the number $10$ . $10$ is a rational number because it can be expressed as the ratio of two integers ( $\frac{10}{1}$ ).
Consider Number $s$ : Consider the nature of the number $s$ . Since $s$ is given as a rational number, it can also be expressed as the ratio of two integers ( $\frac{p}{q}$ , where $p$ and $q$ are integers and $q$ is not zero).
Analyze Sum of Rational Numbers: Analyze the sum of two rational numbers. The sum of two rational numbers is always rational. This is because adding two fractions (or integers) results in another fraction (or integer) which can be simplified if necessary.
Apply Property to $10 + s$ : Apply the property to $10 + s$ . $\newline$ Since both $10$ and $s$ are rational, their sum $10 + s$ must also be rational.
Choose Correct Statement: Choose the correct statement from the given choices. $\newline$ Based on the previous steps, the correct statement about $10 + s$ is that it is rational.