The number q is rational. Which statement about q - 6 is true? Choices: (A)q - 6 is rational. (B)q - 6 is irrational. (C)q - 6 can be rational or irrational, depending on the value of q.

Understand Rational Numbers: Understand the nature of the number q. q is given as a rational number. Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero.Understand Integer 6: Understand the nature of the number 6. The number 6 is an integer, and all integers are rational numbers because they can be expressed as the quotient of themselves and 1 (for example, 6 can be written as 6/1).Determine Expression q - 6: Determine the nature of the expression q - 6. Since both q and 6 are rational numbers, their difference is also a rational number. This is because the set of rational numbers is closed under the operation of subtraction, which means that subtracting any two rational numbers will always result in another rational number.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The number $q$ is rational. Which statement about $q - 6$ is true? $\newline$ Choices: $\newline$ (A) $q - 6$ is rational. $\newline$ (B) $q - 6$ is irrational. $\newline$ (C) $q - 6$ can be rational or irrational, depending on the value of $q$ .

View step-by-step help

Home

Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

q

is rational. Which statement about

q - 6

is true?

\newline

Choices:

\newline

(A)

q - 6

is rational.

\newline

(B)

q - 6

is irrational.

\newline

(C)

q - 6

can be rational or irrational, depending on the value of

q

Understand Rational Numbers: Understand the nature of the number $q$ . $q$ is given as a rational number. Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero.
Understand Integer $6$ : Understand the nature of the number $6$ . The number $6$ is an integer, and all integers are rational numbers because they can be expressed as the quotient of themselves and $1$ (for example, $6$ can be written as $\frac{6}{1}$ ).
Determine Expression $q - 6$ : Determine the nature of the expression $q - 6$ . Since both $q$ and $6$ are rational numbers, their difference is also a rational number. This is because the set of rational numbers is closed under the operation of subtraction, which means that subtracting any two rational numbers will always result in another rational number.