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

Identify Number Nature: Identify the nature of the number 6. 6 is a rational number because it can be expressed as a fraction of two integers (6/1).Subtract Rational from Irrational: Consider the subtraction of a rational number from an irrational number. Subtracting a rational number from an irrational number results in an irrational number. This is because the difference between a rational and an irrational number cannot be expressed as a fraction of two integers.Apply Concept to Problem: Apply the concept to the given problem. Since y is irrational and 6 is rational, y - 6 will also be irrational.Check for Exceptions: Check for any exceptions that could lead to a different result. There are no values of y that would make y - 6 rational because the subtraction of a rational number from an irrational number is always irrational.

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

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Math Problems

Algebra 1

Properties of operations on rational and irrational numbers

Full solution

Q. The number

y

is irrational. Which statement about

y - 6

is true?

\newline

Choices:

\newline

(A)

y - 6

is rational.

\newline

(B)

y - 6

is irrational.

\newline

(C)

y - 6

can be rational or irrational, depending on the value of

y

Identify Number Nature: Identify the nature of the number $6$ . $6$ is a rational number because it can be expressed as a fraction of two integers ( $\frac{6}{1}$ ).
Subtract Rational from Irrational: Consider the subtraction of a rational number from an irrational number. Subtracting a rational number from an irrational number results in an irrational number. This is because the difference between a rational and an irrational number cannot be expressed as a fraction of two integers.
Apply Concept to Problem: Apply the concept to the given problem. $\newline$ Since $y$ is irrational and $6$ is rational, $y - 6$ will also be irrational.
Check for Exceptions: Check for any exceptions that could lead to a different result. $\newline$ There are no values of $y$ that would make $y - 6$ rational because the subtraction of a rational number from an irrational number is always irrational.