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

Identify Number 2: Identify the nature of the number 2. 2 is a rational number because it can be expressed as a fraction (2/1).Consider Number u: Consider the nature of the number u. Since u is given as a rational number, it can be expressed as a fraction a/b, where a and b are integers and b is not zero.Analyze Operation: Analyze the operation 2 - u. Subtracting a rational number u from another rational number 2 will result in a rational number, because the set of rational numbers is closed under subtraction.Conclude Result: Conclude the nature of 2 - u. Since both 2 and u are rational, their difference 2 - u is also rational.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

u

is rational. Which statement about

2 - u

is true?

\newline

Choices:

\newline

(A)

2 - u

is rational.

\newline

(B)

2 - u

is irrational.

\newline

(C)

2 - u

can be rational or irrational, depending on the value of

u

Identify Number $2$ : Identify the nature of the number $2$ . $2$ is a rational number because it can be expressed as a fraction ( $2/1$ ).
Consider Number $u$ : Consider the nature of the number $u$ . Since $u$ is given as a rational number, it can be expressed as a fraction $\frac{a}{b}$ , where $a$ and $b$ are integers and $b$ is not zero.
Analyze Operation: Analyze the operation $2 - u$ . Subtracting a rational number $u$ from another rational number $2$ will result in a rational number, because the set of rational numbers is closed under subtraction.
Conclude Result: Conclude the nature of $2 - u$ . Since both $2$ and $u$ are rational, their difference $2 - u$ is also rational.