The number a is rational. Which statement about a - 3 is true? Choices: (A)a - 3 is rational. (B)a - 3 is irrational. (C)a - 3 can be rational or irrational, depending on the value of a.

Identify Number 3: Identify the nature of the number 3. 3 is a whole number, which is also a rational number because it can be expressed as a fraction (3/1).Properties of Rational Numbers: Understand the properties of rational numbers. Rational numbers are closed under addition and subtraction. This means that the sum or difference of two rational numbers is always a rational number.Apply Property to Expression: Apply the property of rational numbers to the expression a - 3. Since a is rational and 3 is rational, their difference a - 3 must also be rational.

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The number $a$ is rational. Which statement about $a - 3$ is true? $\newline$ Choices: $\newline$ (A) $a - 3$ is rational. $\newline$ (B) $a - 3$ is irrational. $\newline$ (C) $a - 3$ can be rational or irrational, depending on the value of $a$ .

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Math Problems

Algebra 2

Properties of operations on rational and irrational numbers

Full solution

Q. The number

a

is rational. Which statement about

a - 3

is true?

\newline

Choices:

\newline

(A)

a - 3

is rational.

\newline

(B)

a - 3

is irrational.

\newline

(C)

a - 3

can be rational or irrational, depending on the value of

a

Identify Number $3$ : Identify the nature of the number $3$ . $3$ is a whole number, which is also a rational number because it can be expressed as a fraction $(\frac{3}{1})$ .
Properties of Rational Numbers: Understand the properties of rational numbers. Rational numbers are closed under addition and subtraction. This means that the sum or difference of two rational numbers is always a rational number.
Apply Property to Expression: Apply the property of rational numbers to the expression $a - 3$ . Since $a$ is rational and $3$ is rational, their difference $a - 3$ must also be rational.