The number q is rational. Which statement about q - 8 is true? Choices: (A)q - 8 is rational. (B)q - 8 is irrational. (C)q - 8 can be rational or irrational, depending on the value of q.

Identify Number 8: Identify the nature of the number 8. 8 is an integer, and all integers are rational numbers because they can be expressed as a ratio of integers (for example, 8 can be written as 8/1).Properties of Rational Numbers: Understand the properties of rational numbers. Rational numbers are numbers that can be expressed as a ratio of two integers. The set of rational numbers is closed under addition and subtraction, which means that the sum or difference of any two rational numbers is also a rational number.Apply Properties to Expression: Apply the properties of rational numbers to the expression q - 8. Since q is a rational number and 8 is a rational number, their difference q - 8 must also be a rational number according to the properties of rational numbers.

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The number $q$ is rational. Which statement about $q - 8$ is true? $\newline$ Choices: $\newline$ (A) $q - 8$ is rational. $\newline$ (B) $q - 8$ is irrational. $\newline$ (C) $q - 8$ 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 - 8

is true?

\newline

Choices:

\newline

(A)

q - 8

is rational.

\newline

(B)

q - 8

is irrational.

\newline

(C)

q - 8

can be rational or irrational, depending on the value of

q

Identify Number $8$ : Identify the nature of the number $8$ . $8$ is an integer, and all integers are rational numbers because they can be expressed as a ratio of integers (for example, $8$ can be written as $\frac{8}{1}$ ).
Properties of Rational Numbers: Understand the properties of rational numbers. Rational numbers are numbers that can be expressed as a ratio of two integers. The set of rational numbers is closed under addition and subtraction, which means that the sum or difference of any two rational numbers is also a rational number.
Apply Properties to Expression: Apply the properties of rational numbers to the expression $q - 8$ . Since $q$ is a rational number and $8$ is a rational number, their difference $q - 8$ must also be a rational number according to the properties of rational numbers.