Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 $q$ .

View step-by-step help

View step-by-step help

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.

More problems from Properties of operations on rational and irrational numbers

Question

t

is irrational. Which statement about

t - \sqrt{47}

\newline

\newline

t - \sqrt{47}

\newline

t - \sqrt{47}

\newline

t - \sqrt{47}

can be rational or irrational, depending on the value of

t

Posted 3 months ago

Question

(\frac{3}{14})\cdot(\frac{7}{71})

rational or irrational?

\newline

1

\newline

\newline

\newline

(C) It can be either rational or irrational

Posted 3 months ago

Question

Is the following number rational or irrational?

\newline

\frac{\pi}{5}

\newline

1

\newline

\newline

Posted 2 months ago

Question

Is the following number rational or irrational?

\newline

-3+\pi

\newline

1

\newline

\newline

Posted 3 months ago

Question

Is the following number rational or irrational?

\newline

-0.\overline{32}

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

\sqrt{121}

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

0.5555

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

7.11

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

\frac{0.3}{0.9}

\newline

1

\newline

\newline

Posted 4 months ago

Question

Is the following number rational or irrational?

\newline

-11\pi

\newline

1

\newline

\newline

Posted 2 months ago